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IMA Newsletter #408

October 2010

2010-2011 Program

See http://www.ima.umn.edu/2010-2011/ for a full description of the 2010-2011 program on Simulating Our Complex World: Modeling, Computation and Analysis.

2010-2011 IMA Participating Institutions Conferences

IMA Events

Board of Governor's Meeting

October 10-11, 2010

IMA Tutorial

Computing with Uncertainty

October 16-17, 2010

Organizers: Fabio Nobile (Politecnico di Milano), R. Tyrrell Rockafellar (University of Washington), Christoph Schwab (ETH Zürich), Raul F. Tempone (King Abdullah University of Science & Technology), Roger J.B. Wets (University of California)

IMA Annual Program Year Workshop

Computing with Uncertainty: Mathematical Modeling, Numerical Approximation and Large Scale Optimization of Complex Systems with Uncertainty

October 18-22, 2010

Organizers: Fabio Nobile (Politecnico di Milano), R. Tyrrell Rockafellar (University of Washington), Christoph Schwab (ETH Zürich), Raul F. Tempone (King Abdullah University of Science & Technology), Roger J.B. Wets (University of California)

IMA Tutorial

Tutorials on Some Novel Discretization Techniques

October 30-31, 2010

Speakers: Pavel B. Bochev (Sandia National Laboratories), Bernardo Cockburn (University of Minnesota Twin Cities), Jan S. Hesthaven (Brown University), Thomas Yizhao Hou (California Institute of Technology), Jie Shen (Purdue University), Ragnar Winther (University of Oslo)
Schedule

Friday, October 1

10:45am-11:15am Coffee breakLind Hall 400

Monday, October 4

10:45am-11:15am Coffee breakLind Hall 400
2:00pm-3:00pm Clawpack tutorialRandall J. Leveque (University of Washington)Lind Hall 305

Tuesday, October 5

10:45am-11:15am Coffee breakLind Hall 400
11:15am-12:15pm Multigrid methods for Maxwell’s equationsJintao Cui (University of Minnesota)Lind Hall 305 PS
2:00pm-3:00pm Clawpack tutorialRandall J. Leveque (University of Washington)Lind Hall 305

Wednesday, October 6

10:45am-11:15am Coffee breakLind Hall 400
2:00pm-3:00pm Clawpack tutorialRandall J. Leveque (University of Washington)Lind Hall 305

Thursday, October 7

10:45am-11:15am Coffee breakLind Hall 400
11:15am-12:15pm Special course: Finite element exterior calculusDouglas N. Arnold (University of Minnesota)Lind Hall 305

Friday, October 8

10:45am-11:15am Coffee breakLind Hall 400
1:25pm-2:25pm Challenges and solutions in clinical image analysisOsama Masoud (ViTAL Images, Inc.)Vincent Hall 16 IPS

Monday, October 11

10:45am-11:15am Coffee breakLind Hall 400
2:00pm-5:00pm Tutorial: Deal. II Finite element libraryGuido Kanschat (Texas A & M University)Lind Hall 305

Tuesday, October 12

10:45am-11:15am Coffee breakLind Hall 400
11:15am-12:15pm Hierarchical approximations, coarse-graining and fast lattice Monte Carlo simulationsPetr Plechac (University of Tennessee)Lind Hall 305 PS

Wednesday, October 13

10:45am-11:15am Coffee breakLind Hall 400
2:00pm-5:00pm Tutorial: Deal. II Finite element libraryGuido Kanschat (Texas A & M University)Lind Hall 305

Thursday, October 14

10:45am-11:15am Coffee breakLind Hall 400
11:15am-12:15pm Special course: Finite element exterior calculusDouglas N. Arnold (University of Minnesota)Lind Hall 305
3:30pm-4:30pm School of Math colloquium: Nonconforming finite element methods for the Maxwell eigenproblemSusanne C. Brenner (Louisiana State University)Vincent Hall 16

Friday, October 15

10:45am-11:15am Coffee breakLind Hall 400
11:15am-12:15pm Calculating storm surge and other coastal hazards using GeoclawKyle Mandli (University of Washington)Lind Hall 401
1:25pm-2:25pm A Novel approach to tight bounds and statistical information of rounding errorsPeter Tang (D. E. Shaw Research)Vincent Hall 16 IPS

Saturday, October 16

8:30am-9:00am Registration and coffeeKeller Hall 3-176 T10.16-17.10
9:00am-9:45am Lecture 1.Problem formulation; examples of elliptic, parabolic, hyperbolic equations with stochastic data; well posedness; the case of infinite dimensional input data (random field); data representation; expansions using a countable number of random variables; truncation and convergence results Christoph Schwab (ETH Zürich)Keller Hall 3-180 T10.16-17.10
9:45am-10:00am BreakKeller Hall 3-176 T10.16-17.10
10:00am-10:45am Lecture 2. Mathematical problems parametrized by a finite number of input random variables (finite dimensional case). Perturbation techniques and second order moment analysis. Sampling methods: Monte Carlo and variants; convergence analysisRaul F. Tempone (King Abdullah University of Science & Technology)Keller Hall 3-180 T10.16-17.10
10:45am-11:00am BreakKeller Hall 3-176 T10.16-17.10
11:00am-11:45am Lecture 3. Approximation of functions using polynomial or piecewise polynomial functions either by projection or interpolation. Stochastic Galerkin method (SGM): derivation; algorithmic aspects; preconditioning of the global system. Stochastic Collocation Method (SCM): collocation on tensor grids; sparse grid approximation; construction of generalized sparse gridsRaul F. Tempone (King Abdullah University of Science & Technology)Keller Hall 3-180 T10.16-17.10
11:45am-1:30pm Lunch T10.16-17.10
1:30pm-3:00pm A brief review of variational analysisRoger J.B. Wets (University of California, Davis)Keller Hall 3-180 T10.16-17.10
3:00pm-3:15pm BreakKeller Hall 3-176 T10.16-17.10
3:15pm-4:15pm Random setsRoger J.B. Wets (University of California, Davis)Keller Hall 3-180 T10.16-17.10

Sunday, October 17

8:45am-9:00am CoffeeKeller Hall 3-176 T10.16-17.10
9:00am-10:30am Random lsc functions and expectation functionalsRoger J.B. Wets (University of California, Davis)Keller Hall 3-180 T10.16-17.10
10:30am-11:00am BreakKeller Hall 3-176 T10.16-17.10
11:00am-12:00pm Introduction to the calculus of expectation functionalsRoger J.B. Wets (University of California, Davis)Keller Hall 3-180 T10.16-17.10
12:00pm-1:30pm Lunch T10.16-17.10
1:30pm-2:15pm Lecture 4. Elliptic equations with random input parameters: regularity results; convergence analysis for Galerkin and Collocation approximations. Anisotropic approximationsRaul F. Tempone (King Abdullah University of Science & Technology)Keller Hall 3-180 T10.16-17.10
2:15pm-2:30pm BreakKeller Hall 3-176 T10.16-17.10
2:30pm-3:15pm Lecture 5. Numerical examples, numerical comparison of SGM and SCM. Adaptive approximationRaul F. Tempone (King Abdullah University of Science & Technology)Keller Hall 3-180 T10.16-17.10
3:15pm-3:30pm BreakKeller Hall 3-176 T10.16-17.10
3:30pm-4:15pm Lecture 6. The infinite dimensional caseChristoph Schwab (ETH Zürich)Keller Hall 3-180 T10.16-17.10

Monday, October 18

8:30am-9:15am Registration and coffee Keller Hall 3-176 W10.18-22.10
9:15am-9:30am Welcome to the IMAFadil Santosa (University of Minnesota)Keller Hall 3-180 W10.18-22.10
9:30am-10:30am Porous flow as a high dimensional challengeIan H. Sloan (University of New South Wales)Keller Hall 3-180 W10.18-22.10
10:30am-11:00am Coffee breakKeller Hall 3-176 W10.18-22.10
11:00am-12:00pm Monte Carlo sampling techniques for solving stochastic and large scale deterministic optimization problemsAlexander Shapiro (Georgia Institute of Technology)Keller Hall 3-180 W10.18-22.10
12:00pm-2:00pm Lunch W10.18-22.10
2:00pm-3:00pm Stochastic models with application to approximation of optimization problemsChristian Louis Hess (Université de Paris-Dauphine)Keller Hall 3-180 W10.18-22.10
3:00pm-4:00pm Generating and handling scenarios in stochastic programming Werner Römisch (Humboldt-Universität)Keller Hall 3-180 W10.18-22.10
4:00pm-4:30pm Coffee breakKeller Hall 3-176 W10.18-22.10
4:30pm-5:30pm Multi-resolution stochastic Galerkin methods for uncertain hyperbolic flowsOlivier Pierre Le Maître (Centre National de la Recherche Scientifique (CNRS))Keller Hall 3-180 W10.18-22.10

Tuesday, October 19

8:10am-8:30am CoffeeKeller Hall 3-176 W10.18-22.10
8:30am-9:30am Quantifying uncertainty in climate change science: Empirical information theory, fluctuation dissipation theorems, and physics based statisticsAndrew J. Majda (New York University)Keller Hall 3-180 W10.18-22.10
9:30am-10:30am Tools for analyzing variational modelsStephen Michael Robinson (University of Wisconsin)Keller Hall 3-180 W10.18-22.10
10:30am-11:00am Coffee breakKeller Hall 3-176 W10.18-22.10
11:00am-12:00pm Complexity and heuristics in stochastic optimizationTeemu Pennanen (Helsinki University of Technology)Keller Hall 3-180 W10.18-22.10
12:00pm-2:00pm Lunch W10.18-22.10
2:00pm-3:00pm Progressive hedging for multi-stage stochastic optimization problemsJean-Paul Watson (Sandia National Laboratories)
David L. Woodruff (University of California, Davis)
Keller Hall 3-180 W10.18-22.10
3:00pm-3:10pm Group photo(steps of Lind Hall in front of courtyard). W10.18-22.10
3:10pm-4:20pm Free time for discussionKeller Hall 3-180 W10.18-22.10
4:30pm-6:00pm Reception and Poster Session
Poster submissions welcome from all participants
Instructions
Lind Hall 400 W10.18-22.10
Parametric eigenvalue problemsRoman Andreev (ETH Zürich)
Discrete adapted hierarchical basis solver for the large scale radial basis function interpolation problem with applications to the best linear unbiased estimatorJulio Enrique Castrillon Candas (King Abdullah University of Science & Technology)
Sparse polynomial approximation for elliptic equations with random loadingAlexey Chernov (Rheinische Friedrich-Wilhelms-Universität Bonn)
Curse of dimensionality and low-rank approximations in stochastic mechanicsAlireza Doostan (University of Colorado)
Efficient uncertainty quantification using GPUsGaurav Gaurav (University of Minnesota)
Adaptive stochastic Galerkin methodsClaude Jeffrey Gittelson (ETH)
Coupled coarse grained MCMC methods for stochastic lattice systemsEvangelia Kalligiannaki (University of Tennessee)
Markos A. Katsoulakis (University of Massachusetts)
Petr Plechac (University of Tennessee)
A computable weak error expansion for the tau-leap methodJesper Karlsson (King Abdullah University of Science & Technology)
Uncertainty quantification & dynamic state estimation for power systemsGuang Lin (Pacific Northwest National Laboratory)
Implications of the constant rank constraint qualificationShu Lu (University of North Carolina)
Derivation of DBN structure from expert knowledge in the form of systems of ODEsNiall Madden (National University of Ireland, Galway)
A worst-case robust design optimization methodology based on distributional assumptionsMattia Padulo (National Aeronautics and Space Administration (NASA))
Stochastic parametrizations and simulations in porous media Malgorzata Peszynska (Oregon State University)
Multi-scale stochastic optimization with applications in energy systems planningSuvrajeet Sen (Ohio State University)
Efficient uncertainty quantification for experiment design in sparse Bayesian modelsFlorian Steinke (Siemens)
PySP: Stochastic programming in Python Jean-Paul Watson (Sandia National Laboratories)
David L. Woodruff (University of California, Davis)
Pyomo: An open-source tool for modeling and solving mathematical programsJean-Paul Watson (Sandia National Laboratories)
David L. Woodruff (University of California, Davis)
Tool path planning with dual spherical splineYayun Zhou (Siemens)
Adaptive multi level Monte Carlo simulationErik von Schwerin (King Abdullah University of Science & Technology)

Wednesday, October 20

8:10am-8:30am CoffeeKeller Hall 3-176 W10.18-22.10
8:30am-9:30am Accounting for variability and uncertainty in a complex brain metabolic model via a probabilistic frameworkDaniela Calvetti (Case Western Reserve University)Keller Hall 3-180 W10.18-22.10
9:30am-10:30am Validating models of complex physical systems and associated uncertainty modelsRobert D. Moser (University of Texas at Austin)Keller Hall 3-180 W10.18-22.10
10:30am-11:00am Coffee breakKeller Hall 3-176 W10.18-22.10
11:00am-12:00pm Panel Session: "Uncertainty in PDEs and optimizations, interations, synergies, challenges"
Moderator: Suvrajeet Sen (Ohio State University)
Timothy J. Barth (NASA Ames Research Center)
Omar Ghattas (University of Texas at Austin)
Alejandro Rene Jofre (University of Chile)
Robert P. Lipton (Louisiana State University)
Stephen Michael Robinson (University of Wisconsin)
Keller Hall 3-180 W10.18-22.10
12:00pm-4:30pm Lunch/Afternoon free W10.18-22.10
6:30pm-8:30pm Workshop dinner at Tea HouseTea House
2425 University Ave. SE, Mpls MN 55414
612-331-8866
W10.18-22.10

Thursday, October 21

8:10am-8:30am CoffeeKeller Hall 3-176 W10.18-22.10
8:30am-9:30am Weak Convergence of Numerical Methods for Dynamical Systems and Optimal Control, and a relation with Large Deviations for Stochastic EquationsMattias Sandberg (Royal Institute of Technology (KTH))Keller Hall 3-180 W10.18-22.10
9:30am-10:30am Measures of risk in stochastic optimizationR. Tyrrell Rockafellar (University of Washington)Keller Hall 3-180 W10.18-22.10
10:30am-11:00am Coffee breakKeller Hall 3-176 W10.18-22.10
11:00am-12:00pm An extended mathematical programming frameworkMichael C. Ferris (University of Wisconsin)Keller Hall 3-180 W10.18-22.10
12:00pm-2:00pm Lunch W10.18-22.10
2:00pm-3:00pm Second moment analysis of elliptic problems with stochastic input parametersHelmut Harbrecht (Universität Stuttgart)Keller Hall 3-180 W10.18-22.10
3:00pm-4:00pm Short LecturesKeller Hall 3-180 W10.18-22.10
Robust estimates for stochastic discrete-time nonlinear systems (robust Kalman filtering/smoothing)Aleksandr Yakovlevitch Aravkin (University of Washington)
Do electricity markets generate electricity inefficiently?Andy Philpott (University of Auckland)
On the need for uncertainty quantification in hyperbolic PDE applications at Sandia National LaboratoriesGuglielmo Scovazzi (Sandia National Laboratories)
A stochastic programming groundwater remediation — flow/transport through porous mediaJean-Paul Watson (Sandia National Laboratories)
4:00pm-4:30pm Coffee breakKeller Hall 3-176 W10.18-22.10
4:30pm-6:30pm DiscussionKeller Hall 3-180 W10.18-22.10

Friday, October 22

8:10am-8:30am CoffeeKeller Hall 3-176 W10.18-22.10
8:30am-9:30am Accelerated kinetic Monte Carlo methods: Hierarchical parallel algorithms and coarse-grainingMarkos A. Katsoulakis (University of Massachusetts)Keller Hall 3-180 W10.18-22.10
9:30am-10:30am Model reduction for uncertainty quantification and optimization under uncertainty of large-scale complex systemsKaren E. Willcox (Massachusetts Institute of Technology)Keller Hall 3-180 W10.18-22.10
10:30am-11:00am Coffee breakKeller Hall 3-176 W10.18-22.10
11:00am-12:00pm Multi-scale structural optimization in the presence of uncertainty for very large composite structuresRobert P. Lipton (Louisiana State University)Keller Hall 3-180 W10.18-22.10

Monday, October 25

10:45am-11:15am Coffee breakLind Hall 400

Tuesday, October 26

10:45am-11:15am Coffee breakLind Hall 400
11:15am-12:15pm Simulating nonholonomic mechanics using variational integrators through HamiltonizationOscar E. Fernandez (University of Minnesota)Lind Hall 305 PS
12:15pm-1:15pm Postdoc LunchLind Hall 409

Wednesday, October 27

10:45am-11:15am Coffee breakLind Hall 400

Thursday, October 28

10:45am-11:15am Coffee breakLind Hall 400
11:15am-12:15pm Special course: Finite element exterior calculusDouglas N. Arnold (University of Minnesota)Lind Hall 305

Friday, October 29

10:45am-11:15am Coffee breakLind Hall 400
1:25pm-2:25pm Predictive modeling of mental states from fMRI dataIrina Rish (IBM)Vincent Hall 16 IPS

Saturday, October 30

All Day Chair: Susanne C. Brenner (Louisiana State University) T10.30-31.10
12:30pm-1:30pm Registration and coffeeKeller Hall 3-176 T10.30-31.10
1:30pm-3:00pm Tutorial on HDG methodsBernardo Cockburn (University of Minnesota)Keller Hall 3-180 T10.30-31.10
3:00pm-3:30pm BreakKeller Hall 3-176 T10.30-31.10
3:30pm-5:00pm Introduction to finite element exterior calculus Ragnar Winther (University of Oslo)Keller Hall 3-180 T10.30-31.10

Sunday, October 31

All Day Morning Chair: Claudio Canuto (Politecnico di Torino)
Afternoon Chair: Susanne C. Brenner (Louisiana State University)
T10.30-31.10
8:45am-9:00am CoffeeKeller Hall 3-176 T10.30-31.10
9:00am-10:30am Recent advances in mutliscale finite element methodsThomas Yizhao Hou (California Institute of Technology)Keller Hall 3-180 T10.30-31.10
10:30am-11:00am BreakKeller Hall 3-176 T10.30-31.10
11:00am-12:30pm Fast spectral-Galerkin methods: from one dimension to high dimension Jie Shen (Purdue University)Keller Hall 3-180 T10.30-31.10
12:30pm-2:00pm Lunch T10.30-31.10
2:00pm-3:30pm Least-squares methods for PDEs: A fair and balanced perspectivePavel B. Bochev (Sandia National Laboratories)Keller Hall 3-180 T10.30-31.10
3:30pm-4:00pm BreakKeller Hall 3-176 T10.30-31.10
4:00pm-5:30pm Reduced complexity models you can believe inJan S. Hesthaven (Brown University)Keller Hall 3-180 T10.30-31.10
Abstracts
Roman Andreev (ETH Zürich) Parametric eigenvalue problems
Abstract: We design and analyze algorithms for the efficient sensitivity computation of eigenpairs of parametric elliptic self-adjoint eigenvalue problems (EVPs) on high-dimensional parameter spaces. We quantify the analytic dependence of eigenpairs on the parameters. For the efficient evaluation of parameter sensitivities of isolated eigenpairs on the entire parameter space we propose and analyze a sparse tensor spectral collocation method on an anisotropic sparse g rid Applications include elliptic EVPs with countably many parameters arising from elliptic differential operators with random coefficients.
Aleksandr Yakovlevitch Aravkin (University of Washington) Robust estimates for stochastic discrete-time nonlinear systems (robust Kalman filtering/smoothing)
Abstract: No Abstract
Timothy J. Barth (NASA Ames Research Center), Omar Ghattas (University of Texas at Austin), Alejandro Rene Jofre (University of Chile), Robert P. Lipton (Louisiana State University), Stephen Michael Robinson (University of Wisconsin) Panel Session: "Uncertainty in PDEs and optimizations, interations, synergies, challenges"
Moderator: Suvrajeet Sen (Ohio State University)
Abstract: No Abstract
Pavel B. Bochev (Sandia National Laboratories) Least-squares methods for PDEs: A fair and balanced perspective
Abstract: In this lecture I will present an unconventional perspective on least-squares finite element methods, which connects them to compatible methods and shows that least-squares methods can enjoy the same conservation properties as their mixed Galerkin cousins.

To a casual observer, compatible (or mimetic) methods and least squares principles for PDEs couldn't be further apart. Mimetic methods inherit key conservation properties of the PDE, can be related to a naturally occurring optimization problem, and require specially selected, dispersed degrees of freedom. The conventional wisdom about least squares is that they rely on artificial energy principles, are only approximately conservative, but can work with standard C0 nodal (or collocated) degrees of freedom. The latter is considered to be among the chief reasons to use least squares methods.

This lecture demonstrates that exactly the opposite is true about least-squares methods. First, I will argue that nodal elements, while admissible in least squares, do not allow them to realize their full potential, should be avoided and are, perhaps, the least important reason to use least squares! Second, I will show that for an important class of problems least squares and compatible methods are close relatives that share a common ancestor, and in some circumstances compute identical answers. The price paid for gaining favorable conservation properties is that one has to give up what is arguably the least important advantage attributed to least squares methods: one can no longer use C0 nodal elements for all variables.

If time permits I will explore two other unconventional uses of least-squares ideas which result in numerical schemes with attractive computational properties: a least-squares mesh-tying method that passes patch tests of arbitrary orders, and a locally conservative discontinuous velocity least-squares method for incompressible flows. The material in this talk is drawn from collaborative works with M. Gunzburger (FSU), M Hyman (Tulane), L. Olson (UIUC) and J. Lai (UIUC).


Sandia National Laboratories is a multi-program laboratory operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin company, for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000.
Susanne C. Brenner (Louisiana State University) School of Math colloquium: Nonconforming finite element methods for the Maxwell eigenproblem
Abstract: The space of H(curl) vector fields with zero divergence provides a natural setting for the the Maxwell eigenproblem with a perfectly conducting boundary. The variational formulation of the Maxwell eigenproblem based on this space is automatically free of spurious eigenvalues. However, a finite element subspace of the intersection of H(curl) and H(div) is necessarily a subspace of H1 vector fields, and it is also known that H1 vector fields are not dense in the intersection of these two spaces unless the domain is convex. Consequently it is impossible to have an H(curl) and H(div) conforming method for the Maxwell eigenproblem that works on non-convex domains. In this talk we will discuss nonconforming finite element methods that can overcome this difficulty.

Daniela Calvetti (Case Western Reserve University) Accounting for variability and uncertainty in a complex brain metabolic model via a probabilistic framework
Abstract:

In this talk we propose a probabilistic interpretation of the parameters in the system of differential equations describing a complex cellular brain metabolism model. Uncertainty in the parameter values, variability of the data over a population and errors in the collected data contribute to the variance of the distributions of the parameters. Markov chain Monte Carlo sampling schemes are employed to draw parameter sets which identify models in statistical agreement with the available data and with the a priori belief about the system. The ensemble of solutions of the differential equations corresponding to the different parameter sets provides a measure of how uncertainty in the parameters translates into variability of the predictive output of the model.

Julio Enrique Castrillon Candas (King Abdullah University of Science & Technology) Discrete adapted hierarchical basis solver for the large scale radial basis function interpolation problem with applications to the best linear unbiased estimator
Abstract: We develop an adapted discrete Hierarchical Basis (HB) to stabilize and efficiently solve the Radial Basis Function (RBF) interpolation problem with finite polynomial order. Applications to the the Best Linear Unbiased Estimator regression problem are shown. The HB forms an orthonormal set that is orthogonal to the space of polynomials of order m defined on the set of nodes in 3D. This leads to the decoupling of the RBF problem thus removing the polynomial ill-conditioning dependency from the joint problem. In particular, the adapted HB method works well for higher-order polynomials.
Alexey Chernov (Rheinische Friedrich-Wilhelms-Universität Bonn) Sparse polynomial approximation for elliptic equations with random loading
Abstract: Numerical approximation of functions in high dimensions is a hard task; e.g. the classical tensor approximation leads to the computational cost and storage requirements growing exponentially with the dimension d ("curse of dimensionality"). However, under the mixed regularity assumption, an efficient approximation via the Sparse Grid techniques is possible. In the context of classical SG, developed by Zenger, Griebel, et al. the polynomial degree of the FE basis functions is fixed and the convergence is achieved by the hierarchical refinement of their support, like in the h-version FEM. Extending the approach of Temlyakov for the periodic case, in [1,2] we aim at the construction and analysis of the sparse polynomial discretization in spirit of the p-version FEM, where the support of the FE basis functions is fixed and the convergence is achieved by increasing the polynomial degree subjected to a hyperbolic cross type restriction. Extending results in [1] for L2 and negative order Sobolev spaces, we obtain in [2] the optimal a priori convergence rates in positive order Sobolev spaces, possibly with homogeneous Dirichlet boundary conditions. One application of this approximation result is the sparse polynomial approximation of statistical moments of solutions of elliptic equations with a random loading term.

This poster is partially based on joint work with Christoph Schwab.

[1] A. Chernov and C. Schwab, Sparse p-version BEM for first kind boundary integral equations with random loading, Applied Numerical Mathematics 59 (2009) 2698–2712

[2] A. Chernov, Sparse polynomial approximation in positive order sobolev spaces with bounded mixed derivatives and applications to elliptic problems with random loading, Preprint 1003, Institute for Numerical Simulation, University of Bonn, 2010
Bernardo Cockburn (University of Minnesota) Tutorial on HDG methods
Abstract: In this tutorial, we will present the hybridizable discontinuous Galerkin (HDG) methods for diffusion problems. We will describe the main idea for devising them and will explain how to implement them efficiently. We will then compare the methods with mixed methods and the continuous Galerkin methods. Finally, we will discuss the convergence properties of the methods in terms of their stabilization parameters.
Jintao Cui (University of Minnesota) Multigrid methods for Maxwell’s equations
Abstract: In this work we study finite element methods for two-dimensional Maxwell’s equations and their solutions by multigrid algorithms. We first introduce two types of nonconforming finite element methods on graded meshes for a two-dimensional curl-curl and grad-div (CCGD) problem that appears in electromagnetics. The first method is based on a discretization using weakly continuous P1 vector fields. The second method uses discontinuous P1 vector fields. Optimal convergence rates in the energy norm and the L2 norm are established for both methods on graded meshes. Then we consider a class of symmetric discontinuous Galerkin methods for a model Poisson problem on graded meshes that share many techniques with the nonconforming methods for the CCGD problem. We establish the uniform convergence of W-cycle, V-cycle and F-cycle multigrid algorithms for the resulting discrete problems. Finally, we propose a new numerical approach for two-dimensional Maxwell’s equations that is based on the Hodge decomposition for divergence-free vector fields, and present multigrid results.
Alireza Doostan (University of Colorado) Curse of dimensionality and low-rank approximations in stochastic mechanics
Abstract: This is a joint work with Gianluca Iaccarino (Stanford University).

This work is concerned with the efficiency of some existing uncertainty propagation schemes for the solution of stochastic partial differential equations (SPDEs) with large number of input uncertain parameters. The uncertainty quantification schemes based on stochastic Galerkin projections, with global or local basis functions, and also sparse grid collocations, in their conventional form, suffer from the so called curse of dimensionality: the associated computational cost grows exponentially as a function of the number of random variables defining the underlying probability space of the problem.

In this work, to break the problem of curse of dimensionality, an efficient least-squares scheme is utilized to obtain a low-rank approximation of the solution of an SPDE with high-dimensional random input data. It will be shown that, in theory, the computational cost of the proposed algorithm grows linearly with respect to the dimension of the underlying probability space of the system. Different aspects of the proposed methodology are clarified through its application to a convection-diffusion problem.

Oscar E. Fernandez (University of Minnesota) Simulating nonholonomic mechanics using variational integrators through Hamiltonization
Abstract: Although it is well known that nonholonomic mechanical systems are not Hamiltonian, recent research has uncovered a variety of techniques which allow one to express the reduced, constrained dynamics of certain classes of nonholonomic systems as Hamiltonian. In this talk I will discuss the application of these methods to develop alternative geometric integrators for nonholonomic systems with perhaps more eacuteciency than the known nonholonomic integrators. After showing how variational integrators theoretically preserve conserved mechanical quantities (such as momentum and energy), I will discuss how Hamiltonization can be used to apply these variational integrators to certain classes of nonholonomic systems. Finally, I will discuss some current research utilizing time reparameterizations.
Michael C. Ferris (University of Wisconsin) An extended mathematical programming framework
Abstract: Co-authors: Steven Dirkse, Jan Jagla, Alexander Meeraus.

Traditional modeling approaches for mathematical programs have limitations. We outline a mechanism to describe an extended mathematical program by means of annotating existing relationships that make up a model. These extensions facilitate higher level structure identification within a model. The structures, which often involve constraints on the solution sets of other models, disjunctions, variational inequalities or complementarity relationships, can be exploited by modern large scale mathematical programming algorithms for efficient solution. Specific application to a variety of models will be given.
Gaurav Gaurav (University of Minnesota) Efficient uncertainty quantification using GPUs
Abstract: Joint work with Steven F. Wojtkiewicz ( Department of Civil Engineering, University of Minnesota).

Graphics processing units (GPUs) have emerged as a much economical and a highly competitive alternative to CPU-based parallel computing. Recent studies have shown that GPUs consistently outperform their best corresponding CPU-based parallel computing equivalents by up to two orders of magnitude in certain applications. Moreover, the portability of the GPUs enables even a desktop computer to provide a teraflop (1012 floating point operations per second) of computing power. This study presents the gains in computational efficiency obtained using the GPU-based implementations of five types of algorithms frequently used in uncertainty quantification problems arising in the analysis of dynamical systems with uncertain parameters and/or inputs.
Claude Jeffrey Gittelson (ETH) Adaptive stochastic Galerkin methods
Abstract: We consider stochastic Galerkin methods for elliptic PDE depending on a random field. Expanding this field into a series with independent coefficients introduces an infinite product structure on the probability space. This permits a discretization by tensor products of suitable orthonormal polynomials. The original problem can be reformulated as an infinite system of equations for the coefficients of the solution with respect to this basis.

Without any truncation of the series, restricting to a finite set of polynomial basis functions reduces this infinite system to a finite system of deterministic equations, which can be solved by standard finite element methods.

The only remaining challenge is the selection of active basis functions. We tackle this problem by iterative methods based on adaptive wavelet techniques. Our method uses adaptive local truncation of the series expansion to recursively refine the set of active indices.

These results are part of a PhD thesis under the supervision of Prof. Ch. Schwab, supported in part by the Swiss National Science Foundation under grant No. 200021-120290/1.
Helmut Harbrecht (Universität Stuttgart) Second moment analysis of elliptic problems with stochastic input parameters
Abstract:

We compute the expectation and the two-point correlation of the solution to elliptic boundary value problems with stochastic input data. Besides stochastic loadings, via perturbation theory, our approach covers also elliptic problems on stochastic domains or with stochastic coefficients. The solution's two-point correlation satisfies a deterministic boundary value problem with the two-fold tensor product operator on the two-fold tensor tensor product domain. We discuss the efficient solution of such tensor product problems by either a sparse grid approach based on multilevel frames or by the pivoted Cholesky decomposition. Both approaches involve only standard finite element techniques. Numerical results illustrate the algorithms.

Christian Louis Hess (Université de Paris-Dauphine) Stochastic models with application to approximation of optimization problems
Abstract: In this lecture it will be shown how basic concepts of Probability Theory, such as distribution, independence, (conditional) expectation, can be extended to the case of random sets and random (lower semi-continuous) functions. Then, some convergence results for sequences of random sets and random functions, already known for sequences or real-valued random variables, will be presented. It will be also shown how these results give rise to various applications to the convergence or approximation of some optimization problems.

Plan
  1. Review on convergence of sequences of sets and functions in the deterministic case.

    Painleve-Kuratowski's Convergence, epi-convergence, variational properties of epi-convergence.
    Convex Analysis : conjugate of an extended real-valued function, epi-sum (alias inf-convolution)...


  2. Convergence of sequences of sets and functions in a stochastic context

    Random sets and random functions : de nition, notion of equi-distribution and independence, set-valued integral.
    Strong laws of large numbers, Birkhoś Ergodic Theorem.
    Conditional expectation and martingales of random sets and random functions, almost sure convergence.
    Set-valued versions of Fatou's Lemma.


  3. Application to the approximation of optimization problems

    Convergence of discrete epi-sums to continuous epi-sum.
    Almost sure convergence of estimators.
    Convergence of integral functionals.
Jan S. Hesthaven (Brown University) Reduced complexity models you can believe in
Abstract: The development and application of models of reduced computational complexity is used extensively throughout science and engineering to enable the fast/real-time modeling of complex systems for control, design, or prediction purposes. These models, while often successful and of undisputed value, are, however, often heuristic in nature and the validity and accuracy of the output is often unknown. This limits the predictive value of such models.

In this tutorial we will review recent and ongoing efforts to develop reduced basis methods for which one can develop a rigorous a posteriori theory. The approach aims at formulating reduced models for parameterized linear partial differential equations. We will outline the theoretical developments of certified reduced basis methods, discuss an offline-online approach to ensure computational efficiency, and emphasize how an error estimator can be exploited to construct an efficient basis at minimal computational off-line cost. We also discuss recent improvements on the efficiency of the computation of the lower bounds for the error, using an improved Successive Constraint Method. The discussion will draw on examples based both on differential and integral equations formulations.

The performance of the certified reduced basis model will be illustrated through several examples to highlight the major advantages of the proposed approach as well as key open challenges in the current approach.

Time permitting we will extend the discussion to include problems with parameterized geometries and the introduction of reduced element methods to enable the efficient and accurate modeling of networks and geometrically complex configurations.
Thomas Yizhao Hou (California Institute of Technology) Recent advances in mutliscale finite element methods
Abstract: A broad range of scientific and engineering problems involve multiple scales. Traditional approaches have been known to be valid for limited spatial and temporal scales. Multiple scales dominate simulation efforts wherever large disparities in spatial and temporal scales are encountered. Such disparities appear in virtually all areas of modern science and engineering, for example, composite materials, porous media, turbulent transport in high Reynolds number flows, and so on. Here, we review some recent advances in multiscale finite element methods (MsFEM) and their applications. The notion ``multiscale finite element methods'' refers to a number of methods, such as multiscale finite volume, mixed multiscale finite element method, and the like. The concept that unifies these methods is the coupling of oscillatory basis functions via various variational formulations. One of the main aspects of this coupling is the subgrid capturing errors. We attempt to capture the multiscale structure of the solution via localized basis functions. These basis functions contain essential multiscale information embedded in the solution and are coupled through a global formulation to provide a faithful approximation of the solution.

The lecture will start with some basic ideas behind MsFEM and its error analysis. We will put special emphasis on how to design appropriate boundary conditions for the local bases to minimize the subgrid capturing errors. In some cases, limited global information is required to capture the long range correlation among small scales. One way to achieve this is through an iterative precodure between the global large scale solution and the localized subgrid scale solution. We will also compare MsFEM with a few related multiscale methods. Applications to high contrast interface problems, two-phase flows in strongly heterogeneous porous media, uncertainty quantification, and domain decompositions will be discussed. Finally, we will present a new data-driven stochastic multiscale method for solving stochastic PDEs, which is in part inspired by MsFEM.
Evangelia Kalligiannaki (University of Tennessee), Markos A. Katsoulakis (University of Massachusetts), Petr Plechac (University of Tennessee) Coupled coarse grained MCMC methods for stochastic lattice systems
Abstract: We propose a class of Monte Carlo methods for sampling dynamic and equilibrium properties of stochastic lattice systems with complex interactions. The key ingredient of these methods is that each MC step is composed by two properly coupled MC steps efficiently coupling coarse and microscoscopic state spaces, designed in virtue of coarse graining techniques for lattice systems. We achieve significant reduction of the computational cost of traditional Markov Chain Monte Carlo and kinetic Monte Carlo methods for systems with competing interactions, while capable of providing microscopic information.
Guido Kanschat (Texas A & M University) Tutorial: Deal. II Finite element library
Abstract: In the first part I will introduce deal.II and discuss its capabilities and limitation. I will give an overview of the development paradigms of the library and present the structure of a typical application based on it in order to address the question whether deal.II is the right tool for your purposes or not.

The second part of the tutorial focuses on the implementation of basic model problems, following the first six steps of the online tutorial. Starting with generating and refining simple meshes (step 1), we move on to solving Poisson's equation (step 3). We modify the program to study how to use different finite elements, solvers and to implement other bilinear forms. We wrap up by introducing techniques for dimension independent programming, adaptive iterations and multilevel methods.

The tutorial closes with the discussion of more advanced applications. We study the handling of systems of equations at hand of the Lame-Navier equations of elasticity, the (linear) Darcy equations for porous media flow, and the Stokes equations. Participants are welcome to suggest additional applications (possibly in advance). The tutorial is open-ended and we can continue working on projects during the next months.
Jesper Karlsson (King Abdullah University of Science & Technology) A computable weak error expansion for the tau-leap method
Abstract: This work develops novel error expansions with computable leading order terms for the global weak error in the tau-leap discretization of pure jump processes arising in kinetic Monte Carlo models. Accurate computable a posteriori error approximations are the basis for adaptive algorithms; a fundamental tool for numerical simulation of both deterministic and stochastic dynamical systems. These pure jump processes are simulated either by the tau-leap method, or by exact simulation, also referred to as dynamic Monte Carlo, the Gillespie algorithm or the Stochastic simulation algorithm. Two types of estimates are presented: an a priori estimate for the relative error that gives a comparison between the work for the two methods depending on the propensity regime, and an a posteriori estimate with computable leading order term.
Markos A. Katsoulakis (University of Massachusetts) Accelerated kinetic Monte Carlo methods: Hierarchical parallel algorithms and coarse-graining
Abstract: In this talk we present two intimately related approaches in speeding-up molecular simulations via Monte Carlo simulations. First, we discuss coarse-graining algorithms for systems with complex, and often competing particle interactions, both in the equilibrium and non-equilibrium settings, which rely on multilevel sampling and communication. Second, we address mathematical, numerical and algorithmic issues arising in the parallelization of spatially distributed Kinetic Monte Carlo simulations, by developing a new hierarchical operator splitting of the underlying high-dimensional generator, as means of decomposing efficiently and systematically the computational load and communication between multiple processors. The common theme in both methods is the desire to identify and decompose the particle system in components that communicate minimally and thus local information can be either described by suitable coarse-variables (coarse-graining), or computed locally on a individual processors within a parallel architecture.
Olivier Pierre Le Maître (Centre National de la Recherche Scientifique (CNRS)) Multi-resolution stochastic Galerkin methods for uncertain hyperbolic flows
Abstract: We present a multi-resolution scheme, based on piecewise polynomial approximations at the stochastic level, for the resolution of nonlinear hyperbolic problems subjected to parametric uncertainties. The numerical method rely on a Galerkin projection technique at the stochastic level, with a finite-volume discretization and a Roe solver (with entropy corrector) in space and time. A key issue in uncertain hyperbolic problem is the loss of smoothness of the solution with regard to the uncertain parameters, which calls for piecewise continuous approximations and multi-resolution schemes, together with adaptive strategies. However, discontinuities in the spatial and stochastic domains are well localized, requiring very different discretization efforts according to the local smoothness of the solution. As a result, classical discretization approaches based on the tensorization of stochastic and deterministic approximation spaces (bases) are inefficient and we propose a numerical procedure where the spatial discretization is fixed while the stochastic basis is locally adapted in space to fit the solution complexity. Examples of applications and efficiency / complexity assessment of the method will be shown.
Randall J. Leveque (University of Washington) Clawpack tutorial
Abstract: Clawpack (Conservation Laws Package) is an open source software package for solving hyperbolic systems of partial differential equations in one or more space dimensions, both with and without source terms. Equations of this type appear in a wide variety of wave propagation problems arising in nearly all fields of science and engineering. Applications include acoustics in the atmosphere or ocean, elastic waves such as seismic waves in the earth or ultrasound waves in biological materials, shock waves in aerodynamics or astrophysics, tsunamis and storm surge, detonation waves, traffic jams, and electromagnetic waves such as light pulses.

High resolution shock-capturing finite volume methods are implemented in Clawpack on logically rectangular grids (Cartesian or mapped grids). Adaptive mesh refinement capabilities are included. The core routines are in Fortran and the user interface and graphics capabilities have recently been converted to Python. A number of sample applications are included with the code.

This tutorial will be a hands-on demonstration of how to install the package, try out the sample applications, and set up a new problem, with some discussion of the plotting routines and use of adaptive refinement.

Documentation and a gallery of some applications can be viewed at http://www.clawpack.org/doc.
Guang Lin (Pacific Northwest National Laboratory) Uncertainty quantification & dynamic state estimation for power systems
Abstract: Experience suggests that uncertainties often play an important role in controlling the stability of power systems. Therefore, uncertainty needs to be treated as a core element in simulating and dynamic state estimation of power systems. In this talk, a probabilistic collocation method (PCM) will be employed to conduct uncertainty quantification of component level power system models, which can provide an error bar and confidence interval on component level modeling of power systems. Numerical results demonstrate that the PCM approach provides accurate error bar with much less computational cost comparing to classic Monte Carlo (MC) simulations. Additionally, a PCM based ensemble Kalman filter (EKF) will be discussed to conduct real-time fast dynamic state estimation for power systems. Comparing with MC based EKF approach, the proposed PCM based EKF implementation can solve the system of stochastic state equations much more efficient. Moreover, the PCM-EKF approach can sample the generalized polynomial chaos approximation of the stochastic solution with an arbitrarily large number of samples, at virtually no additional computational cost. Hence, the PCM-EKF approach can drastically reduce the sampling errors and achieve a high accuracy at reduced computational cost, compared to the classical MC implementation of EKF. The PCM-EKF based dynamic state estimation is tested on multi-machine system with various random disturbances. Our numerical results demonstrate the validity and performance of the PCM-EKF approach and also indicate the PCM-EFK approach can include the full dynamics of the power systems and ensure an accurate representation of the changing states in the power systems.
Robert P. Lipton (Louisiana State University) Multi-scale structural optimization in the presence of uncertainty for very large composite structures
Abstract:
Modern structures such as airplane wings and wind turbine blades exhibit a hierarchy of sub structures and typically make use of composite materials in their construction. Quantifying uncertainty in the strength and stiffness of composite structural materials is crucial for predicting the service lifetime of the structure. The high cost of experimental tests for large-scale hierarchical composite structures is driving a trend toward virtual testing. This requires the development of multi-scale numerical methods capable of handling large degrees of freedom spread across different length scales. In this talk we review model reduction strategies for multi-scale structural analysis in the presence of uncertainty as well as propose new multi-scale approaches that may be useful in predicting service lifetimes.
Shu Lu (University of North Carolina) Implications of the constant rank constraint qualification
Abstract: We consider a parametric set defined by finitely many equality and inequality constraints under the constant rank constraint qualification (CRCQ). The CRCQ generalizes both the linear independence constraint qualification (LICQ) and the polyhedral case, and is also related to the Mangasarian-Fromovitz constraint qualification (MFCQ) in a certain way. It induces some nice properties of the set when the parameter is fixed, and some nice behavior of the set-valued map when the parameter varies. Such properties are useful in analysis of Euclidean projectors onto the set and variational conditions defined over the set.
Niall Madden (National University of Ireland, Galway) Derivation of DBN structure from expert knowledge in the form of systems of ODEs
Abstract: This is joint with with Catherine G. Enright and Michael G. Madden, NUI Galway.

We present a methodology for constructing a Dynamic Bayesian Network (DBN) from a mathematical model in the form of a system of ordinary differential equations. The motivation for the approach comes from a multidisciplinary project centred on the use of DBNs in the modelling of the response of critically ill patients to certain drug therapies. The DBN can be used to account for at least two sources of uncertainty:
  • inadequacies in the model,
  • measurement errors (which includes the measurements in the quantities used as the model's inputs, and in the quantities it is trying to predict.)


In this presentation we investigate the DBN's ability to handle measurement errors by applying it to an abstract model, based on a system of DEs for which the true solution is known.
Andrew J. Majda (New York University) Quantifying uncertainty in climate change science: Empirical information theory, fluctuation dissipation theorems, and physics based statistics
Abstract: This lecture is based on the following papers: 1. A. Majda and B. Gershgorin, 2010: Quantifying Uncertainty in Climate Change Science Through Empirical Information Theory, PNAS in press 2. A. Majda, R. Abramov, B. Gershgorin, "High Skill in Low Frequency Climate Response through Fluctuation Dissipation Theorems Despite Structural Instability," PNAS, January 2010, Vol. 107, no. 2, pp 581 - 586. 3. B. Gershgorin, A. Majda, "Filtering A Nonlinear Slow-Fast System with Strong Fast Forcing," Comm. Math. Sci., March 2010, Vol. 8, Issue 1, pp. 67-92 4. A. Majda, B. Gershgorin, Y. Yuan, " Low Frequency Response and Fluctuation-Dissipation Theorems: Theory and Practice," JAS, available electronically, April 2010, Vol. 67, pp. 1186-1201. All papers except the first one can be found on Majda's faculty website.
Kyle Mandli (University of Washington) Calculating storm surge and other coastal hazards using Geoclaw
Abstract: Coastal flows often require the use of methods that can resolve many order of spatial and temporal scales and often these resolution requirements change in time and space. One way to resolve these scales is to take advantage of these dynamic processes and employ adaptive mesh refinement which uses various aspects of the flow to determine the current required mesh refinement. This allows for a significant savings in computation and can lead to the ability to refine further in regions of interest.

We have developed a code named GeoClaw which uses adaptive mesh refinement to solve depth averaged equations over complex bathymetry. It is based on the Clawpack software (Conservation Laws Package, www.clawpack.org), designed for solving general nonlinear hyperbolic systems using high-resolution shock-capturing finite volume methods on logically rectangular grids. We will present results from an idealized storm surge along with preliminary results involving multilayer depth averaged equations in order to include vertical structure of the surge to improve the accuracy of the model off the continental shelf.
Osama Masoud (ViTAL Images, Inc.) Challenges and solutions in clinical image analysis
Abstract: Medical Imaging continues to be an area of active research with a wide spectrum of interesting problems. The large increase in data size and the risks of radiation dose to patients are among some recent challenges that emerged in the CT scanner world and require solutions in the industry. This presentation will give an overview of some of the problems that come up in the development of advanced medical analysis software that deals with scanner data. The presentation will go into some detail to discuss challenges and solutions with respect to two problems: Brain perfusion calculation and speed optimization of a particular basic operation.
Robert D. Moser (University of Texas at Austin) Validating models of complex physical systems and associated uncertainty models
Abstract: Computational models of complex physical systems are fraught with uncertainties. These include uncertainties in initial or boundary conditions, uncertainties in model parameters and/or the experimental data used to calibrate them and uncertainties arising from imperfections in the models used in the simulations. Mathematical models of these uncertainties and their affects on the quantities the models are intended to be predicted (the quantities of interest or QoI's) are needed. It is also necessary to assess the ability of the models to represent both the physics of the phenomena being predicted and the associated uncertainties, and in particular the ability to predict the QoI's and their uncertainty. However, in the usual situation, the QoI's are not accessible for observation, since otherwise, no computational prediction would be necessary. We thus must use available or attainable observational data (and estimates of their uncertainty) to calibrate the models and evaluate the ability of the models to predict the unobserved QoI's. In this talk, a Bayesian framework for these calibration and validation processes is proposed and applied to several examples. However, a number of conceptual and practical challenges to applying these ideas in complex systems remain, and will be discussed along with possible approaches to address these problems.
Mattia Padulo (National Aeronautics and Space Administration (NASA)) A worst-case robust design optimization methodology based on distributional assumptions
Abstract: This poster outlines a novel Robust Design Optimization (RDO) methodology. The problem is reformulated in order to relax, when required, the assumption of normality of objectives and constraints, which often underlies RDO. In the second place, taking into account engineering considerations concerning the risk associated with constraint violation, suitable estimates of tail conditional expectations are introduced in the set of robustness metrics. The methodology is expected to be of significant practical usefulness for Computational Engineering Design, by guiding the construction of robust objective and constraint functions, and enabling the interpretation of the optimization results.
Teemu Pennanen (Helsinki University of Technology) Complexity and heuristics in stochastic optimization
Abstract:

Combining recent results on numerical integration and optimization, we derive a polynomial bound on the worst case complexity of a class of static stochastic optimization problems. We then describe a technique for reducing dynamic problems to static ones. The reduction technique is only a heuristic but it can effectively employ good guesses for good solutions. This is illustrated on an 82-period problem coming from pension insurance industry.

Malgorzata Peszynska (Oregon State University) Stochastic parametrizations and simulations in porous media
Abstract: Joint work with M. Ossiander and V. Vasylkivska, Department of Mathematics, Oregon State University.

Coefficients of flow and of related phenomena in subsurface are usually poorly known but are rarely smooth. We discuss parametrizations based on Karhunen-Loeve, Haar, and other series expansions, for flow data in a model of single-phase flow in porous media. We use these in finite element algorithms to compute moments of variables of interest such as pressures and fluxes. Of interest are discontinuous and multiscale porous media, as well as data generated by standard geostatistics algorithms.
Andy Philpott (University of Auckland) Do electricity markets generate electricity inefficiently?
Abstract: No Abstract
Petr Plechac (University of Tennessee) Hierarchical approximations, coarse-graining and fast lattice Monte Carlo simulations
Abstract: We shall discuss numerical analysis aspects of coarse-graining stochastic particle systems and the connection to acceleration of kinetic Monte Carlo simulations. Mathematical tools developed for error control in microscopic simulations using the coarse-grained stochastic processes and reconstruction of microscopic scales will be presented in connection with accelerating (kinetic) Monte Carlo simulations. On specific examples of lattice as well as off-lattice dynamics we demonstrate that computational implementation of constructed hierarchical algorithms results in significant speed up of simulations. The developed framework also leads to new parallel kinetic Monte Carlo algorithms that will be briefly described.
Irina Rish (IBM) Predictive modeling of mental states from fMRI data
Abstract: Traditional fMRI data analyses are mainly focused on discovering brain activation patterns using standard GLM technique that selects voxels based on their individual correlations with stimuli.However, such mass-univariate approach completely ignores voxel interactions that are often essential for understanding brain functions,and can be better captured by an alternative approach - multivariate predictive modeling. This talk summarizes our recent work in this area, with a particular focus on discovering predictive features ("biomarkers") characterizing non-local, distributed patterns of brain activity.

One example of our approach is discovering predictive subsets of voxels via sparse regression methods such as LASSO and Elastic Net. We discuss several applications, such as predicting mental states of a subject playing a virtual-reality videogame in a fMRI scanner, or predicting subject's pain perception in response to a thermal pain stimuli. We find that sparse regression produces highly predictive models that also provide evidence for the distributed nature of neural function. Next, we underscore the importance of distributed activity patterns when exploring predictive information contained in the topology of brain's functional networks. We consider a challenging task of building a discriminative model for schizophrenia, a complex psychiatric disorder that appears to be delocalized, i.e. difficult to attribute to a dysfunction of some particular brain areas. Our findings demonstrate significant advantages the functional network features can provide over both traditional region-of-interest (ROI) approach and local, task-specific linear activations produced by standard GLM. Our results suggest that schizophrenia is indeed associated with disruption of global brain properties related to its functioning as a network, which cannot be explained just by alteration of local activation patterns. Moreover, further exploitation of voxel interactions by sparse Markov Random Field (MRF) classifiers allows to attain a high predictive accuracy of 86% over 50% baseline, which is quite remarkable given that our discriminative model is based on a single fMRI experiment using a simple auditory task.
Stephen Michael Robinson (University of Wisconsin) Tools for analyzing variational models
Abstract:
Many problems of optimization and equilibrium result in models in the general class of variational conditions, sometimes in a generalized form. Thus, if the problem is one of optimization, we first write optimality conditions and then try to compute with those. If instead of an optimization model we have a model involving some kind of equilibrium, then we write conditions expressing the equilibrium situation and try to solve those conditions. In general, such conditions will involve nonsmoothness (discontinuities in the first derivative) in an essential way. This lecture will present a set of mathematical tools useful for analysis of many of the variational conditions that appear in the formulation and solution of practical problems. In essence, these enable us to do in the presence of nonsmoothness many of the things that one could do with calculus if the problem functions were smooth. They do so by exploiting the fact that the nonsmoothness in these conditions is of a highly structured kind. Although some fairly substantial mathematical analysis underlies the construction of these tools, our emphasis in this lecture will not be on the underlying mathematics. Rather, it will be on explaining what the tools are, how they are adapted to the forms of the variational conditions occurring in various problems, what they can do when applied to those conditions, and how to apply them in some example cases. We will describe the mathematical foundation and indicate how it supports the tools' capabilities, but will not go into much detail about it.
R. Tyrrell Rockafellar (University of Washington) Measures of risk in stochastic optimization
Abstract: A fundamental difficulty in stochastic optimization is the fact that decisions may not be able pin down the values of future "costs," but rather can only, within limits, shape their distributions as random variables. An upper bound on a ramdom "cost" is often impossible, or too expensive, to enforce with certainty, and so some compromise attitude must be taken to the violations that might occur. Similarly, there is no instant interpretation of what it might mean to minimize a random "cost", apart from trying to determine a lowest threshold which would be exceeded only to an acceptable degree.

Clearly, it is essential in this picture to have a theoretical framework which provides guidelines about preferences and elucidates their mathematical pros and cons. Measures of risk, coming from financial mathematics but finding uses also in engineering, are the key. Interestingly, they relate also to concepts in statistics and estimation. For example, standard deviation can be replaced by a generalized measure of deviation which is not symmetric between ups and downs, as makes sense in applications in which overestimation may be riskier than underestimation.
Werner Römisch (Humboldt-Universität) Generating and handling scenarios in stochastic programming
Abstract: First, three approaches to scenario generation besides Monte Carlo methods are considered: (i) Optimal quantization of probability distributions, (ii) Quasi-Monte Carlo methods and (iii) Quadrature rules based on sparse grids. The available theory is discussed and related to applying them in stochastic programming. Second, the problem of optimal scenario reduction and the generation of scenario trees for multistage models are addressed.
Mattias Sandberg (Royal Institute of Technology (KTH)) Weak Convergence of Numerical Methods for Dynamical Systems and Optimal Control, and a relation with Large Deviations for Stochastic Equations
Abstract:
I will present a method to prove weak convergence of numerical methods for dynamical systems, using dual solutions. This general method is applied to optimal control problems, and is used to prove convergence of approximate value functions. The theory of large deviations will also be mentioned. It makes it possible to represent rare event solutions to stochastic differential equations as solutions of optimal control problems. This representation will be used on a particular stochastic partial differential equation arising in the study of phase transitions. It will be shown how the resulting optimal control problem can be analyzed, again with the same kind of method to prove weak convergence.
Christoph Schwab (ETH Zürich) Lecture 1.Problem formulation; examples of elliptic, parabolic, hyperbolic equations with stochastic data; well posedness; the case of infinite dimensional input data (random field); data representation; expansions using a countable number of random variables; truncation and convergence results
Abstract: No Abstract
Christoph Schwab (ETH Zürich) Lecture 6. The infinite dimensional case
Abstract: We review representation results of the random solutions by so-called "generalized polynomial chaos" (gpc) expansions in countably many variables. We present recent mathematical results on regularity of such solutions as well as computational approaches for the adaptive numerical Galerkin and Collocation approximations of the infinite dimensional parametric, deterministic solution. A key principle are new sparsity estimates of gpc expansions of the parametric solution. We present such estimates for elliptic, parabolic and hyperbolic problems with random coefficients, as well as eigenvalue problems.

We compare the possible convergence rates with the best convergence results on Monte Carlo Finite Element Methods (MCFEM) and on MLMCFEM.
Guglielmo Scovazzi (Sandia National Laboratories) On the need for uncertainty quantification in hyperbolic PDE applications at Sandia National Laboratories
Abstract: A number of applications of interest at Sandia National Laboratories involve hyperbolic PDEs, and ultimately require uncertainty quantification methods. I will describe in general the nature of these applications and focus in particular on algorithms for shock hydrodynamics and transient dynamics problems based on tetrahedral finite elements. I will also be discussing perspectives on using this computational framework for complex-geometry fluid-structure interaction problems, in combination with mesh adaptation, optimization, and uncertainty quantification.
Suvrajeet Sen (Ohio State University) Multi-scale stochastic optimization with applications in energy systems planning
Abstract: Decision related to energy and environment are closely intertwined, and making choices based on only one of these factors has the potential to short-change the other. However integrated models of these systems lead to ultra large scale systems which must be approximated at different levels of granularity. In particular, uncertainties themselves need to be modeled using alternate representations. We describe multi-scale stochastic optimization models in which dynamic programming (or approximate DP) represent certain classes of decisions (e.g. control), where as stochastic programming is used for other classes of decisions (e.g. strategy). Multi-stage stochastic decomposition (a Monte Carlo-based SP method) will play an important role in making it possible to integrate DP and SP.
Alexander Shapiro (Georgia Institute of Technology) Monte Carlo sampling techniques for solving stochastic and large scale deterministic optimization problems
Abstract: The traditional approach to solving stochastic programming problems is based on construction scenarios representing a discretization of the underline (true) stochastic data process. Consequently, computational complexity of the obtained optimization problem is determined by the number of generated scenarios. Unfortunately the number of scenarios needed to approximate the "true" distribution of the data process grows exponentially both with increase of the number of random parameters and number of stages. A way of dealing with this explosion of the number of scenarios is to use randomization approaches based on Monte Carlo sampling techniques. In this talk we discuss theoretical and computational aspects of Monte Carlo sampling based approaches to solving two and multi-stage stochastic programming problems. Moreover, certain classes of deterministic problems can be formulated in terms of expected values and consequently randomization techniques can be applied to solve such large scale optimization problems. In particular, we discuss two competing approaches: the Sample Average Approximation (SAA) method and Stochastic Approximation (SA) type algorithms.
Jie Shen (Purdue University) Fast spectral-Galerkin methods: from one dimension to high dimension
Abstract: I shall talk about how to design fast spectral-Galerkin algorithms for some prototypical partial differential equations. We shall start with algorithms in one dimension, then using a tensor product approach for two and three dimensions, and hyperbolic cross/spectral sparse grid for higher dimensional problems.
Ian H. Sloan (University of New South Wales) Porous flow as a high dimensional challenge
Abstract: The problem of flow through a porous medium, with the permeability treated as a Gaussian random field, can be thought of as a high-dimensional problem: the dimensionality might be the number of terms in a truncated Karhunen-Loève expansion; or (as we prefer) the number of points in a discrete sampling of the porous medium. In this paper, describing recent joint work with F Kuo, I Graham, D. Nuyens and R Scheichl, we explore the use of quasi-Monte Carlo methods to study various expected values of the flow through the medium, and to compare the results with the Monte Carlo method. The problem is computationally difficult if the permeability changes markedly from point to point, but the numerical results (obtained by evaluating integrals with as many as one million dimensions) are encouraging.
Florian Steinke (Siemens) Efficient uncertainty quantification for experiment design in sparse Bayesian models
Abstract: We demonstrate how to perform experiment design for linear models with sparsity prior. Unlike maximum likelihood estimation, experiment design requires exact quantification of the estimation uncertainty and how this uncertainty would change given likely measurements. We employ a novel variant of the expectation propagation algorithm to approximate the posterior of the sparse linear model accurately and efficiently. The resulting experimental design method is motivated by and tested on the task of identifying gene regulatory networks with few experiments. The proposed method is one of the first to solve this problem in a statistically sound and efficient manner. In a realistic simulation study, it outperforms the only previous competitor significantly.
Peter Tang (D. E. Shaw Research) A Novel approach to tight bounds and statistical information of rounding errors
Abstract: Obtaining tight bounds on rounding errors has been so specialized and labor-intensive a task that it is seldom carried out during normal engineering practice in industry. It turns out that for absolute error analysis related to fixed point arithmetic, an automatic method can be devised for computation of linear transform. This method, implemented as a software tool, allows practicing engineers to obtain tight bounds as well as a vast amount of statistical information on forward rounding errors. The method consists of modeling the rounding error process in a way that allows mechanical computation on its propagation. When this model and propagation computation is implemented with objects and overloading in an object oriented manner, engineers can obtain detailed error information by means of algorithm implementation, not by actually carrying out error analysis. In this talk we will describe this method and illustrate its application on the very important Fast Fourier Transform.
Raul F. Tempone (King Abdullah University of Science & Technology) Lecture 2. Mathematical problems parametrized by a finite number of input random variables (finite dimensional case). Perturbation techniques and second order moment analysis. Sampling methods: Monte Carlo and variants; convergence analysis
Abstract: No Abstract
Raul F. Tempone (King Abdullah University of Science & Technology) Lecture 3. Approximation of functions using polynomial or piecewise polynomial functions either by projection or interpolation. Stochastic Galerkin method (SGM): derivation; algorithmic aspects; preconditioning of the global system. Stochastic Collocation Method (SCM): collocation on tensor grids; sparse grid approximation; construction of generalized sparse grids
Abstract: No Abstract
Raul F. Tempone (King Abdullah University of Science & Technology) Lecture 4. Elliptic equations with random input parameters: regularity results; convergence analysis for Galerkin and Collocation approximations. Anisotropic approximations
Abstract: No Abstract
Raul F. Tempone (King Abdullah University of Science & Technology) Lecture 5. Numerical examples, numerical comparison of SGM and SCM. Adaptive approximation
Abstract: No Abstract
Jean-Paul Watson (Sandia National Laboratories), David L. Woodruff (University of California, Davis) Progressive hedging for multi-stage stochastic optimization problems
Abstract: Although stochastic programming is a powerful tool for modeling decision-making under uncertainty, various impediments have historically prevented its widespread use. One key factor involves the ability of non-experts to easily express stochastic programming problems, ideally building on a likely existing deterministic model expressed through an algebraic modeling language. A second key factor relates to the difficulty of solving stochastic programming models, particularly the general mixed-integer, multi-stage case. Intricate and configurable (and often parallel) decomposition strategies are frequently required to achieve tractable run-times. We simultaneously address both of these factors in our PySP software package, which is part of the COIN-OR Coopr open-source Python project for optimization. To formulate a stochastic program in PySP, the user specifies both the deterministic base model and the scenario tree with associated uncertain parameters in the Pyomo open-source algebraic modeling language. Given these two models, PySP provides two general paths for solution of the corresponding stochastic program. The first alternative involves writing the extensive form and invoking a standard deterministic mixed-integer solver. For more complex stochastic programs, we provide an implementation of Rockafellar and Wets' Progressive Hedging algorithm. Our particular focus is on the use of Progressive Hedging as an effective heuristic for approximating general multi-stage, mixed-integer stochastic programs. By leveraging the combination of a high-level programming language (Python) and the embedding of the base deterministic model in that language (Pyomo), we are able to provide completely generic and highly configurable solver implementations on serial and parallel computers. PySP has been used by a number of research groups, including our own, to rapidly prototype and solve large and difficult stochastic programming problems.
Jean-Paul Watson (Sandia National Laboratories), David L. Woodruff (University of California, Davis) PySP: Stochastic programming in Python
Abstract: Real optimization problems have data that is uncertain and require the ability to update decisions as new information becomes available. Our poster describes open source modeling and solver software for multi-stage optimization with uncertain data, known as PySP (Python Stochastic Programming). We leverage a Python based software library called Coopr, developed at Sandia National Laboratories, to provide a full mixed integer modeling environment, which we have extended to allow for the description of multi-stage problems with data uncertainty. Users can write out the problem to be sent in its entirety to a variety of solvers or they can invoke the built-in Progressive Hedging solver that supports large-scale parallelism. The Progressive Hedging solver is fully customizable, such that users can leverage problem-specific information to accelerate solution times.
Jean-Paul Watson (Sandia National Laboratories), David L. Woodruff (University of California, Davis) Pyomo: An open-source tool for modeling and solving mathematical programs
Abstract: We describe the Python Optimization Modeling Objects (Pyomo) software package. Pyomo supports the definition and solution of mathematical programming optimization applications using the Python scripting language. Python is a powerful dynamic programming language that has a very clear, readable syntax and intuitive object orientation. Pyomo can be used to concisely represent mixed-integer linear and nonlinear programming (MILP) models for large-scale, real-world problems that involve thousands of constraints and variables. Further, Pyomo includes a flexible framework for applying optimizers to analyze these models. Pyomo is distributed with a flexible open-source license (and is part of IBM’s COIN-OR initiative), which facilitates its use by both academic and commercial users.
Jean-Paul Watson (Sandia National Laboratories) A stochastic programming groundwater remediation — flow/transport through porous media
Abstract: No Abstract
Roger J.B. Wets (University of California, Davis) A brief review of variational analysis
Abstract: Functions and their epigraphs, convexity and semicontinuity. Set convergence and epigraphical limits. Variational geometry, subgradients and subdifferential calculus.
Roger J.B. Wets (University of California, Davis) Random sets
Abstract: Definition and properties of random sets, selections. The distribution function (∼ Choquet capacity) of a random set and convergence in distribution. The expectation of a random set and the law of large numbers for random sets. SAA (Sample. Average Approximations) of random sets. Application to stochastic variational inequalities and related variational problems.
Roger J.B. Wets (University of California, Davis) Random lsc functions and expectation functionals
Abstract: Definition of random lsc (lower semicontinuous) functions and calculus. Stochastic processes with lsc paths. Properties of expectation functionals. Almost sure convergence and convergence in distribution (epigraphical sense). The Ergodic Theorem for random lsc functions and its applications: sampled variational problems, approximation, statistical estimation and homogenization.
Roger J.B. Wets (University of California, Davis) Introduction to the calculus of expectation functionals
Abstract: Decomposable spaces. Fatou’s lemma for random set and random lsc functions. Interchange of minimization and (conditional) expectation. Subdifferentiation of expectation functionals. Martingale integrands and application to financial valuation.
Karen E. Willcox (Massachusetts Institute of Technology) Model reduction for uncertainty quantification and optimization under uncertainty of large-scale complex systems
Abstract:
Uncertainty quantification approaches are generally computationally intractable for large-scale complex systems. The discretized forward models describing such systems typically are of very high dimension and are expensive to solve. The computational resources required for uncertainty quantification therefore quickly become prohibitive. Model reduction can address this challenge by producing low-order approximate models that retain the essential system dynamics but that are fast to solve. This talk will discuss formulations of model reduction problems for applications in uncertainty quantification. Key challenges include systems with input parameter spaces of very high dimension (infinite-dimensional parameters in some cases), and accounting for the statistical properties of interest in the system outputs. We demonstrate the use of reduced models for uncertainty propagation, solution of statistical inverse problems, and optimization under uncertainty for systems governed by partial differential equations. Our methods use state approximations through the proper orthogonal decomposition, reductions in parameter dimensionality through parameter basis approximations, and the empirical interpolation method for efficient evaluation of nonlinear terms.
Ragnar Winther (University of Oslo) Introduction to finite element exterior calculus
Abstract: The purpose of this tutorial is to give an introduction to finite element exterior calculus, targeted to an audience which is reasonably familiar with topics like elliptic partial differential equations, Sobolev spaces, and finite element methods. We will first give a brief review of some of the fundamental concepts of exterior calculus, such as interior and exterior products, pullbacks, the Hodge star operation, the exterior derivative, and Stokes' theorem. Then we will focus on some of the main building blocks of finite element exterior calculus. In particular, we will discuss piecewise polynomial spaces of differential forms, degress of freedom, and the construction of bounded cochain projections. In addition, an abstract theory of Hilbert complexes will be presented, and we will explain how this relates to to the stability theory for approximations of the Hodge Laplacian.
Yayun Zhou (Siemens) Tool path planning with dual spherical spline
Abstract: The novel tool path planning approach is proposed based on the offset theory and the kinematic ruled surface approximation. The designed blade surface is represented as a flank milling tool path with a cylindrical cutter in CNC machining. The drive surface is a ruled surface, which is denoted as a dual spherical spline. It is derived by kinematically approximating the offset surface of the original design as a ruled surface. This approach integrates the manufacture requirements into the design phase, which reduces the developing cycle time and the manufacturing cost.
Erik von Schwerin (King Abdullah University of Science & Technology) Adaptive multi level Monte Carlo simulation
Abstract: Microscopic models in physical sciences are often stochastic; for example time evolutions modelled by stochastic ordinary differential equations (SDEs). The numerical methods for approximating expected values of functions depending on the solution of Ito SDEs were significantly improved when the multilevel Forward Euler Monte Carlo method was introduced in [1]. This poster presents a generalization of the method in [1]. The work [1] proposed and analysed Multilevel Monte Carlo method based on a hierarchy of uniform time discretizations and control variates to reduce the computational effort required by a standard, single level, Forward Euler Monte Carlo method. The present work introduces and analyses an adaptive hierarchy of non uniform time discretizations, generated by adaptive algorithms introduced in [3,2]. These adaptive algorithms apply either deterministic time steps or stochastic time steps and are based on a posteriori error expansions first developed in [4]. Under sufficient regularity conditions, both our analysis and numerical results, which include one case with singular drift and one with stopped diffusion, exhibit savings in the computational cost to achieve an accuracy of O(TOL), from O(TOL-3) to O(TOL-1 log (TOL))2.

This poster presents joint work with H. Hoel, A. Szepessy, and R. Tempone.

References:

[1] Michael B. Giles. Multilevel Monte Carlo path simulation. Oper. Res., 56(3):607-617, 2008.

[2] Kyoung-Sook Moon, Anders Szepessy, Raul Tempone, and Georgios E. Zouraris. Convergence rates for adaptive weak approximation of stochastic diffential equations. Stoch. Anal. Appl., 23(3):511-558, 2005.

[3] Kyoung-Sook Moon, Erik von Schwerin, Anders Szepessy, and Raul Tempone. An adaptive algorithm for ordinary, stochastic and partial differential equations. In Recent advances in adaptive computation, volume 383 of Contemp. Math., pages 325-343. Amer. Math. Soc., Providence, RI, 2005.

[4] Anders Szepessy, Raul Tempone, and Georgios E. Zouraris. Adaptive weak approximation of stochastic differential equations. Comm. Pure Appl. Math., 54(10):1169-1214, 2001.
Visitors in Residence
Yasaman Adibi University of Minnesota 10/16/2010 - 10/17/2010
Slimane Adjerid Rensselaer Polytechnic Institute 10/31/2010 - 11/5/2010
Alexander Alekseenko California State University 9/1/2010 - 12/31/2010
Mohamed Almekkawy University of Minnesota 10/16/2010 - 10/17/2010
Roman Andreev ETH Zürich 10/17/2010 - 10/23/2010
Roman Andreev ETH Zürich 10/31/2010 - 11/6/2010
Aleksandr Yakovlevitch Aravkin University of Washington 10/17/2010 - 10/22/2010
Todd Arbogast University of Texas at Austin 10/31/2010 - 11/7/2010
Douglas N. Arnold University of Minnesota 9/1/2010 - 6/30/2011
Florian Augustin TU München 10/16/2010 - 10/23/2010
Gerard Michel Awanou Northern Illinois University 9/1/2010 - 6/10/2011
Blanca Ayuso de Dios Centre de Recerca Matemàtica 10/30/2010 - 12/18/2010
Constantin Bacuta University of Delaware 10/31/2010 - 11/7/2010
Nusret Balci University of Minnesota 9/1/2009 - 8/31/2011
Uday Banerjee Syracuse University 9/1/2010 - 12/4/2010
Andrew T. Barker Louisiana State University 10/31/2010 - 11/6/2010
Timothy J. Barth NASA Ames Research Center 10/17/2010 - 10/22/2010
Peter W. Bates Michigan State University 10/10/2010 - 10/11/2010
Yuri Bazilevs University of California, San Diego 10/31/2010 - 11/5/2010
Bradley M. Bell University of Washington 10/17/2010 - 10/22/2010
Naoufel Ben Abdallah Université de Toulouse III (Paul Sabatier) 10/31/2010 - 11/5/2010
Christine Bernardi Université de Paris VI (Pierre et Marie Curie) 10/31/2010 - 11/5/2010
Pavel B. Bochev Sandia National Laboratories 10/30/2010 - 11/7/2010
Daniele Boffi Università di Pavia 10/30/2010 - 11/7/2010
Francesca Bonizzoni Politecnico di Milano 10/15/2010 - 11/10/2010
Susanne C. Brenner Louisiana State University 9/1/2010 - 6/10/2011
Russell Brown University of Kentucky 10/11/2010 - 10/21/2010
James V. Burke University of Washington 10/17/2010 - 10/22/2010
Daniela Calvetti Case Western Reserve University 10/17/2010 - 10/20/2010
Claudio Canuto Politecnico di Torino 10/17/2010 - 11/7/2010
David Buck Carlson Wartburg College 10/30/2010 - 10/30/2010
Julio Enrique Castrillon Candas King Abdullah University of Science & Technology 10/15/2010 - 10/22/2010
Fatih Celiker Wayne State University 9/1/2010 - 12/31/2010
Aycil Cesmelioglu University of Minnesota 9/30/2010 - 8/30/2011
Chi Hin Chan University of Minnesota 9/1/2009 - 8/31/2011
Feng Chen Purdue University 10/30/2010 - 11/4/2010
Qiang Chen University of Delaware 10/31/2010 - 11/6/2010
Yanlai Chen University of Massachusetts, Dartmouth 10/31/2010 - 11/7/2010
Zhiming Chen Chinese Academy of Sciences 10/31/2010 - 11/7/2010
Yingda Cheng Brown University 10/31/2010 - 11/7/2010
Alexey Chernov Rheinische Friedrich-Wilhelms-Universität Bonn 10/15/2010 - 10/23/2010
David Chock NONE 10/9/2010 - 10/11/2010
Shue-Sum Chow Brigham Young University 10/31/2010 - 11/7/2010
Jonathan Claridge University of Washington 10/4/2010 - 10/8/2010
Bernardo Cockburn University of Minnesota 9/1/2010 - 6/30/2011
Robert Crone Seagate Technology 10/18/2010 - 10/22/2010
Jintao Cui University of Minnesota 8/31/2010 - 8/30/2011
Qing Cui University of Minnesota 1/1/2010 - 12/1/2010
Clint Dawson University of Texas at Austin 10/31/2010 - 11/4/2010
Leszek Feliks Demkowicz University of Texas at Austin 10/31/2010 - 11/7/2010
Alireza Doostan University of Colorado 10/18/2010 - 10/21/2010
Tobin A. Driscoll University of Delaware 8/26/2010 - 12/20/2010
Mohammad Ebtehaj University of Minnesota 10/16/2010 - 10/17/2010
Yalchin Efendiev Texas A & M University 10/18/2010 - 10/23/2010
Amr S. El-Bakry ExxonMobil 10/15/2010 - 10/22/2010
Hallie M Elich University of Minnesota 10/16/2010 - 10/17/2010
Randy H. Ewoldt University of Minnesota 9/1/2009 - 8/31/2011
Richard S Falk Rutgers University 9/19/2010 - 12/18/2010
Yue-yue Fan University of California, Davis 10/17/2010 - 10/22/2010
Xiaobing Henry Feng University of Tennessee 10/29/2010 - 12/15/2010
Oscar E. Fernandez University of Minnesota 8/31/2010 - 8/30/2011
Michael C. Ferris University of Wisconsin 10/17/2010 - 10/22/2010
Don Ford U.S. Department of Agriculture (USDA) 10/17/2010 - 10/23/2010
Juan Carlos Galvis Texas A & M University 10/18/2010 - 10/23/2010
Baskar Ganapathysubramanian Iowa State University 10/17/2010 - 10/22/2010
Carlos Andres Garavito-Garzon University of Minnesota 10/30/2010 - 10/31/2010
Lucia Gastaldi Università di Brescia 10/30/2010 - 11/7/2010
Nikolaos Gatsis University of Minnesota 10/16/2010 - 10/17/2010
Gaurav Gaurav University of Minnesota 10/16/2010 - 10/22/2010
Joscha Gedicke Humboldt-Universität 10/30/2010 - 12/4/2010
Luca Gerardo Giorda Emory University 10/15/2010 - 10/18/2010
Marc Iwan Gerritsma Technische Universiteit te Delft 10/30/2010 - 11/6/2010
Omar Ghattas University of Texas at Austin 10/17/2010 - 10/22/2010
Robert Ghrist University of Pennsylvania 10/9/2010 - 10/11/2010
Anna Gilbert University of Michigan 10/9/2010 - 10/11/2010
Andrew Kruse Gillette University of Texas at Austin 10/31/2010 - 11/6/2010
Claude Jeffrey Gittelson ETH 10/17/2010 - 10/23/2010
Jay Gopalakrishnan University of Florida 9/1/2010 - 6/30/2011
Genetha Anne Gray Sandia National Laboratories 10/17/2010 - 10/21/2010
Shiyuan Gu Louisiana State University 9/1/2010 - 6/30/2011
Helmut Harbrecht Universität Stuttgart 10/16/2010 - 10/23/2010
Xiaoming He Missouri University of Science and Technology 10/19/2010 - 10/22/2010
Christian Louis Hess Université de Paris-Dauphine 10/16/2010 - 10/22/2010
Jan S. Hesthaven Brown University 10/30/2010 - 11/6/2010
Robert L. Higdon Oregon State University 10/31/2010 - 11/6/2010
Ronald H.W. Hoppe University of Houston 9/6/2010 - 12/20/2010
Raya Horesh University of Minnesota 10/15/2010 - 11/6/2010
Mary Ann Horn National Science Foundation 10/9/2010 - 10/12/2010
Thomas Yizhao Hou California Institute of Technology 10/9/2010 - 10/11/2010
Thomas Yizhao Hou California Institute of Technology 10/30/2010 - 11/4/2010
Jason Howell Clarkson University 10/31/2010 - 11/7/2010
James W Howse Los Alamos National Laboratory 10/17/2010 - 10/23/2010
Yulia Hristova University of Minnesota 9/1/2010 - 8/31/2011
Lili Hu Georgia Institute of Technology 10/31/2010 - 11/5/2010
Nitin Jain University of Minnesota 10/18/2010 - 10/22/2010
Lijian Jiang Los Alamos National Laboratory 10/15/2010 - 10/23/2010
Alejandro Rene Jofre University of Chile 10/15/2010 - 10/20/2010
Sunnie Joshi Texas A & M University 10/30/2010 - 11/5/2010
Mihailo Jovanovic University of Minnesota 10/16/2010 - 10/17/2010
Lili Ju University of South Carolina 10/31/2010 - 11/4/2010
Evangelia Kalligiannaki University of Tennessee 10/15/2010 - 10/27/2010
Myungjoo Kang Seoul National University 10/31/2010 - 11/5/2010
Guido Kanschat Texas A & M University 9/6/2010 - 12/20/2010
Chiu-Yen Kao Ohio State University 9/1/2010 - 12/20/2010
Jesper Karlsson King Abdullah University of Science & Technology 10/14/2010 - 10/22/2010
Markos A. Katsoulakis University of Massachusetts 10/17/2010 - 10/28/2010
Markus Keel University of Minnesota 7/21/2008 - 6/30/2011
Vahid Keshavarzzadeh University of Southern California 10/15/2010 - 10/22/2010
Abdul Qayyum Masud Khaliq Middle Tennessee State University 10/17/2010 - 10/23/2010
Alan King IBM 10/17/2010 - 10/20/2010
Pawel Konieczny University of Minnesota 9/1/2009 - 8/31/2011
Kristina Kraakmo University of Central Florida 10/30/2010 - 11/3/2010
Angela Kunoth Universität Paderborn 10/31/2010 - 11/7/2010
Diane Lambert Google Inc. 10/9/2010 - 10/11/2010
Ilya Lashuk Lawrence Livermore National Laboratory 10/29/2010 - 11/5/2010
Olivier Pierre Le Maître Centre National de la Recherche Scientifique (CNRS) 10/17/2010 - 10/23/2010
Gilad Lerman University of Minnesota 9/1/2010 - 6/30/2011
Randall J. Leveque University of Washington 9/12/2010 - 10/16/2010
Dmitriy Leykekhman University of Connecticut 10/31/2010 - 11/7/2010
Chaodi Li 3M 10/18/2010 - 10/22/2010
Fengyan Li Rensselaer Polytechnic Institute 9/1/2010 - 12/20/2010
Hengguang Li University of Minnesota 8/16/2010 - 8/15/2011
Lizao Li University of Minnesota 10/16/2010 - 10/17/2010
Peng Li University of Minnesota 10/16/2010 - 10/17/2010
Wenbo Li University of Delaware 10/16/2010 - 10/18/2010
Yan Li University of Minnesota 10/30/2010 - 11/6/2010
Zhilin Li North Carolina State University 10/31/2010 - 11/5/2010
Hyeona Lim Mississippi State University 10/30/2010 - 11/4/2010
Fu Lin University of Minnesota 10/16/2010 - 10/17/2010
Guang Lin Pacific Northwest National Laboratory 10/15/2010 - 10/22/2010
Guang Lin Pacific Northwest National Laboratory 10/29/2010 - 11/3/2010
Zhi (George) Lin University of Minnesota 9/1/2009 - 8/31/2011
Robert P. Lipton Louisiana State University 10/17/2010 - 10/22/2010
Hailiang Liu Iowa State University 10/31/2010 - 11/5/2010
Jiangguo (James) Liu Colorado State University 10/31/2010 - 11/7/2010
Vanessa Lopez-Marrero IBM 10/17/2010 - 10/23/2010
Alexei Lozinski Université de Toulouse III (Paul Sabatier) 10/31/2010 - 11/6/2010
Shu Lu University of North Carolina 10/17/2010 - 10/22/2010
Ying Lu University of Minnesota 10/16/2010 - 10/17/2010
Laura Lurati Boeing 10/17/2010 - 10/22/2010
Mitchell Luskin University of Minnesota 9/1/2010 - 6/30/2011
Lina Ma Purdue University 10/31/2010 - 11/6/2010
Scott MacLachlan Tufts University 10/24/2010 - 12/3/2010
Niall Madden National University of Ireland, Galway 10/18/2010 - 12/10/2010
Andrew J. Majda New York University 10/17/2010 - 10/20/2010
Kara Lee Maki University of Minnesota 9/1/2009 - 8/31/2011
Kyle Mandli University of Washington 10/4/2010 - 10/16/2010
Yi Mao University of Tennessee 10/17/2010 - 10/22/2010
Yu (David) Mao University of Minnesota 8/31/2010 - 8/30/2011
Dionisios Margetis University of Maryland 10/17/2010 - 10/21/2010
Maider Judith Marin-McGee University of Puerto Rico 10/29/2010 - 11/6/2010
Osama Masoud ViTAL Images, Inc. 10/8/2010 - 10/8/2010
Jens Markus Melenk Technische Universität Wien 10/30/2010 - 11/7/2010
Giovanni Migliorati Politecnico di Milano 10/14/2010 - 10/24/2010
Laurie E. Miller University of Minnesota 10/16/2010 - 10/17/2010
Irina Mitrea University of Minnesota 8/16/2010 - 6/14/2011
Dimitrios Mitsotakis University of Minnesota 10/27/2010 - 8/31/2011
Rashad Moarref University of Minnesota 10/16/2010 - 10/17/2010
Peter Monk University of Delaware 9/8/2010 - 12/10/2010
Brian Edward Moore University of Central Florida 10/31/2010 - 11/3/2010
David Morton University of Texas at Austin 10/17/2010 - 10/22/2010
Robert D. Moser University of Texas at Austin 10/19/2010 - 10/22/2010
Eva Mossberg Karlstad University 10/17/2010 - 10/22/2010
Magnus Mossberg Karlstad University 10/17/2010 - 10/22/2010
Zhe Nan Louisiana State University 10/30/2010 - 11/7/2010
Michael Joseph Neilan Louisiana State University 10/15/2010 - 10/22/2010
Michael Joseph Neilan Louisiana State University 10/29/2010 - 11/7/2010
Ngoc-Cuong Nguyen Massachusetts Institute of Technology 10/31/2010 - 11/5/2010
Fabio Nobile Politecnico di Milano 10/17/2010 - 10/24/2010
Ricardo H. Nochetto University of Maryland 9/13/2010 - 12/17/2010
Alexandra Ortan University of Minnesota 9/16/2010 - 6/15/2011
Cecilia Ortiz-Duenas University of Minnesota 9/1/2009 - 8/31/2011
Miao-Jung Yvonne Ou Oak Ridge National Laboratory 8/30/2010 - 12/10/2010
Jeffrey Ovall University of Kentucky 10/31/2010 - 11/7/2010
Mattia Padulo National Aeronautics and Space Administration (NASA) 10/15/2010 - 10/23/2010
Eun-Hee Park Louisiana State University 10/30/2010 - 11/7/2010
Teemu Pennanen Helsinki University of Technology 10/16/2010 - 10/23/2010
Jaime Peraire Massachusetts Institute of Technology 10/31/2010 - 11/5/2010
Ilaria Perugia Università di Pavia 10/30/2010 - 11/6/2010
Malgorzata Peszynska Oregon State University 10/17/2010 - 10/22/2010
Arlie O. Petters Duke University 10/9/2010 - 10/11/2010
Per Pettersson Stanford University 10/15/2010 - 10/17/2010
Andy Philpott University of Auckland 10/17/2010 - 10/23/2010
Petr Plechac University of Tennessee 9/1/2010 - 12/10/2010
Catherine E. Powell University of Manchester 10/17/2010 - 10/23/2010
Serge Prudhomme University of Texas at Austin 10/17/2010 - 10/22/2010
Jingmei Qiu Colorado School of Mines 10/31/2010 - 11/3/2010
Weifeng (Frederick) Qiu University of Minnesota 8/31/2010 - 8/30/2011
Vincent Quenneville-Belair University of Minnesota 9/16/2010 - 6/15/2011
Rachel Quinlan National University of Ireland, Galway 10/18/2010 - 12/10/2010
Dana Randall Georgia Institute of Technology 10/10/2010 - 10/11/2010
Darsh Priya Ranjan University of California, Berkeley 10/29/2010 - 11/6/2010
Armin Reiser Louisiana State University 9/1/2010 - 12/15/2010
Fernando Reitich University of Minnesota 9/1/2010 - 6/30/2011
Donald Richards Pennsylvania State University 10/9/2010 - 10/11/2010
Joyce Cristina Rigelo University of Wyoming 10/17/2010 - 10/23/2010
Irina Rish IBM 10/28/2010 - 10/30/2010
Stephen Michael Robinson University of Wisconsin 10/17/2010 - 10/22/2010
R. Tyrrell Rockafellar University of Washington 10/13/2010 - 10/26/2010
Werner Römisch Humboldt-Universität 10/16/2010 - 10/22/2010
Gianluigi Rozza École Polytechnique Fédérale de Lausanne (EPFL) 10/30/2010 - 11/6/2010
Mattias Sandberg Royal Institute of Technology (KTH) 10/15/2010 - 10/23/2010
Giancarlo Sangalli Università di Pavia 10/31/2010 - 11/6/2010
Fadil Santosa University of Minnesota 7/1/2008 - 6/30/2011
Francisco-Javier Sayas University of Delaware 10/28/2010 - 11/7/2010
Reinhold Schneider TU Berlin 10/30/2010 - 11/6/2010
Joachim Schöberl Technische Universität Wien 10/31/2010 - 11/6/2010
Dominik M. Schoetzau University of British Columbia 10/30/2010 - 11/7/2010
Christoph Schwab ETH Zürich 10/15/2010 - 10/23/2010
Christoph Schwab ETH Zürich 10/31/2010 - 11/7/2010
Marc Alexander Schweitzer Rheinische Friedrich-Wilhelms-Universität Bonn 10/31/2010 - 11/7/2010
Guglielmo Scovazzi Sandia National Laboratories 10/15/2010 - 10/22/2010
Guglielmo Scovazzi Sandia National Laboratories 10/29/2010 - 11/5/2010
Suvrajeet Sen Ohio State University 10/17/2010 - 10/22/2010
Shuanglin Shao University of Minnesota 9/1/2009 - 8/31/2011
Alexander Shapiro Georgia Institute of Technology 10/17/2010 - 10/21/2010
David H. Sharp Los Alamos National Laboratory 10/8/2010 - 10/12/2010
Mikhail Shashkov Los Alamos National Laboratory 10/31/2010 - 11/5/2010
Jie Shen Purdue University 10/30/2010 - 11/6/2010
Luwei Shen University of Minnesota 10/20/2010 - 10/22/2010
Ke Shi University of Minnesota 10/30/2010 - 11/6/2010
Chi-Wang Shu Brown University 10/31/2010 - 11/6/2010
John Singler Missouri University of Science and Technology 10/19/2010 - 10/22/2010
Ian H. Sloan University of New South Wales 10/16/2010 - 10/23/2010
Erkki Somersalo Case Western Reserve University 10/18/2010 - 10/21/2010
Panagiotis E. Souganidis University of Chicago 10/10/2010 - 10/11/2010
Orhan Soykan Medtronic 10/16/2010 - 10/17/2010
Florian Steinke Siemens 10/16/2010 - 10/22/2010
Ari Stern University of California, San Diego 10/31/2010 - 11/6/2010
Rob Stevenson Universiteit van Amsterdam 10/30/2010 - 11/6/2010
Panagiotis Stinis University of Minnesota 9/1/2010 - 6/30/2011
Jiguang Sun Delaware State University 10/31/2010 - 11/7/2010
Tong Sun Bowling Green State University 10/30/2010 - 11/7/2010
Yi Sun Statistical and Applied Mathematical Sciences Institute (SAMSI) 10/31/2010 - 11/4/2010
Li-yeng Sung Louisiana State University 9/1/2010 - 6/15/2011
Vladimir Sverak University of Minnesota 10/10/2010 - 10/11/2010
Daniil Svyatskiy Los Alamos National Laboratory 10/15/2010 - 10/20/2010
Lorenzo Tamellini Politecnico di Milano 10/15/2010 - 10/23/2010
Peter Tang D. E. Shaw Research 10/14/2010 - 10/15/2010
Nicolae Tarfulea Purdue University, Calumet 9/1/2010 - 6/15/2011
Daniel M. Tartakovsky University of California, San Diego 10/17/2010 - 10/20/2010
Raul F. Tempone King Abdullah University of Science & Technology 10/14/2010 - 10/23/2010
Ramakrishna Tipireddy University of Southern California 10/15/2010 - 10/22/2010
Charles Tong Lawrence Livermore National Laboratory 10/17/2010 - 10/22/2010
Dimitar Trenev University of Minnesota 9/1/2009 - 8/31/2011
Catalin Turc Case Western Reserve University 10/31/2010 - 11/5/2010
Karsten Urban Universität Ulm 10/18/2010 - 10/22/2010
Brian Vachta Wartburg College 10/30/2010 - 10/31/2010
Panayot S Vassilevski Lawrence Livermore National Laboratory 10/31/2010 - 11/5/2010
Diane E. Vaughan Los Alamos National Laboratory 10/17/2010 - 10/20/2010
Chad N Vidden Iowa State University 10/31/2010 - 11/5/2010
Peter Edward Vincent Stanford University 10/31/2010 - 11/6/2010
Erik von Schwerin King Abdullah University of Science & Technology 10/14/2010 - 10/25/2010
Shawn W. Walker Louisiana State University 10/30/2010 - 11/6/2010
Xiaoliang Wan Louisiana State University 10/17/2010 - 10/23/2010
Wei Wang Florida International University 10/31/2010 - 11/7/2010
Jean-Paul Watson Sandia National Laboratories 10/17/2010 - 10/22/2010
Roger J.B. Wets University of California, Davis 10/13/2010 - 10/26/2010
Karen E. Willcox Massachusetts Institute of Technology 10/18/2010 - 10/22/2010
Ragnar Winther University of Oslo 10/17/2010 - 11/12/2010
Barbara Wohlmuth Technical University of Munich 10/30/2010 - 11/6/2010
Steven F. Wojtkiewicz University of Minnesota 10/18/2010 - 10/22/2010
David L. Woodruff University of California, Davis 10/17/2010 - 10/22/2010
Han Wu Minnesota State University 10/16/2010 - 10/17/2010
Huifu Xu University of Southampton 10/16/2010 - 10/22/2010
Liwei Xu Rensselaer Polytechnic Institute 10/31/2010 - 11/7/2010
Guangri Xue University of Texas at Austin 10/29/2010 - 11/7/2010
Lingzhou Xue University of Minnesota 10/16/2010 - 10/22/2010
Sergey Borisovich Yakovlev Rensselaer Polytechnic Institute 9/8/2010 - 12/15/2010
Jue Yan Iowa State University 10/31/2010 - 11/7/2010
Chin-Ann Yang University of Minnesota 10/16/2010 - 10/17/2010
Xingzhou Yang Mississippi State University 10/29/2010 - 11/4/2010
Shantia Yarahmadian Mississippi State University 10/15/2010 - 10/17/2010
Shantia Yarahmadian Mississippi State University 10/29/2010 - 10/31/2010
Xiu Ye University of Arkansas 10/31/2010 - 11/7/2010
Feng Yi University of Minnesota 10/16/2010 - 10/17/2010
Hongxia Yin Minnesota State University 10/16/2010 - 10/17/2010
Haijun Yu Purdue University 10/31/2010 - 11/6/2010
Hui Yu Iowa State University 10/31/2010 - 11/5/2010
Chuan Zhang University of Minnesota 10/16/2010 - 10/17/2010
H. Michael Zhang University of California, Davis 10/17/2010 - 10/22/2010
Zhimin Zhang Wayne State University 10/31/2010 - 11/7/2010
Zhongqiang Zhang Brown University 10/17/2010 - 10/23/2010
Shan Zhao University of Alabama 10/31/2010 - 11/2/2010
Yayun Zhou Siemens 10/16/2010 - 10/23/2010
Hui Zou University of Minnesota 10/18/2010 - 10/22/2010
Legend: Postdoc or Industrial Postdoc Long-term Visitor

IMA Affiliates:
Arizona State University, Boeing, Corning Incorporated, ExxonMobil, Ford, General Motors, Georgia Institute of Technology, Honeywell, IBM, Indiana University, Iowa State University, Korea Advanced Institute of Science and Technology (KAIST), Lawrence Livermore National Laboratory, Lockheed Martin, Los Alamos National Laboratory, Medtronic, Michigan State University, Michigan Technological University, Mississippi State University, Northern Illinois University, Ohio State University, Pennsylvania State University, Portland State University, Purdue University, Rice University, Rutgers University, Sandia National Laboratories, Schlumberger Cambridge Research, Schlumberger-Doll, Seoul National University, Siemens, Telcordia, Texas A & M University, University of Central Florida, University of Chicago, University of Delaware, University of Houston, University of Illinois at Urbana-Champaign, University of Iowa, University of Kentucky, University of Maryland, University of Michigan, University of Minnesota, University of Notre Dame, University of Pennsylvania, University of Pittsburgh, University of Tennessee, University of Wisconsin, University of Wyoming, US Air Force Research Laboratory, Wayne State University, Worcester Polytechnic Institute