<span class=strong>Reception and Poster Session</span><br><br/><br/><b>Poster submissions welcome from all participants</b><br><br/><br/><a<br/><br/>href=/visitor-folder/contents/workshop.html#poster><b>Instructions</b></a><br/><br/>
Tuesday, June 7, 2011 - 3:30pm - 5:30pm
- Poster - Sparsity reconstruction in electrical impedance tomography
Bangti Jin (Texas A & M University)
Electrical impedance tomography is a diffusive imaging
modality for determining the conductivity distributions of an object
from boundary measurements. We here propose a novel reconstruction
algorithm based on Tikhonov regularization with sparsity constraints.
The well-posedness of the formulation, and convergence rates results are
established. Numerical experiments for simulation and real data are
presented to illustrate the effectiveness of the approach.
- Poster- Observability for Initial Value Problems with Sparse Initial Data
Nicolae Tarfulea (The Pennsylvania State University)
In recent years many authors have developed a series of ideas and techniques on the reconstruction of a finite signal from many fewer observations than traditionally believed necessary. This work addresses the recovery of the initial state of a high-dimensional dynamic variable from a restricted set of measurements. More precisely, we consider the problem of recovering the sparse initial data for a large system of ODEs based on limited observations at a later time. Under certain conditions, we prove that the sparse initial data is uniquely determined and provide a way to reconstruct it.
- Poster- Uncertainty Quantification in Geophysical Mass Flows and Hazard Map Construction
Abani Patra (University at Buffalo (SUNY))
We outline here some procedures for uncertainty quantification in hazardous geophysical mass flows like debris avalanches using computer models and statistical surrogates. Novel methodologies used include techniques to propagate uncertainty in topographic representations and methodologies to improve concurrency in the map construction.
- Poster- Robust Design for Industrial Applications
Albert Gilg (Siemens AG)Utz Wever (Siemens AG)
Industrial product and process designs often exploit physical limits to improve performance. In this regime uncertainty originating from fluctuations during fabrication and small disturbances in system operations severely impacts product performance and quality. Design robustness becomes a key issue in optimizing industrial designs. We present examples of challenges and solution approaches implemented in our robust design tool RoDeO.
- Poster- Bayesian Inference for Data Assimilation using Least-Squares Finite Element Methods
Richard Dwight (Technische Universiteit te Delft)
It has recently been observed that Least-Squares Finite Element methods (LS-FEMs) can be used to assimilate experimental data into approximations of PDEs in a natural way. The approach was shown to be effective without regularization terms, and can handle substantial noise in the experimental data without filtering. Of great practical importance is that - it is not significantly more expensive than a single physical simulation. However the method as presented so far in the literature is not set in the context of an inverse problem framework, so that for example the meaning of the final result is unclear. In this paper it is shown that the method can be interpreted as finding a maximum a posteriori (MAP) estimator in a Bayesian approach to data assimilation, with normally distributed observational noise, and a Bayesian prior based on an appropriate norm of the governing equations. In this setting the method may be seen to have several desirable properties: most importantly discretization and modelling error in the simulation code does not affect the solution in limit of complete experimental information, so these errors do not have to be modelled statistically. Also the Bayesian interpretation better justifies the choice of the method, and some useful generalizations become apparent. The technique is applied to incompressible Navier-Stokes flow in a pipe with added velocity data, where its effectiveness, robustness to noise, and application to inverse problems is demonstrated.
- Poster- Information Gain in Model Validation for Porous Media
Quan Long (King Abdullah University of Science & Technology)
In this work, we use the relative entropy of the posterior probability density function (PPDF) to measure the information gain in the Bayesian model validation procedure. The entropies related to different groups of validation data are compared and we subsequently choose the validation data with the most information gain (Principle of Maximum Entropy) to predict a quantity of interest in the more complicated prediction case. The proposed procedure is independent of any model related assumption, therefore enabling an objective decision making on the rejection/adoption of cali- brated models. This work can be regarded as an extension to the Bayesian model validation method proposed by [Babusˇka et al.(2008)]. We illustrate the methodology on an numerical example dealing with the validation of models for porous media. Specifically the effective permeability of a 2D porous media is calibrated and validated. We use here synthetic data obtained by computer simulations of the Navier- Stokes equation
- Poster- Solution Method for ODEs with Random Forcing
We consider numerical methods for finding approximate solutions to ODEs with parameters which are distributed with some probabilty. In particular, we focus on those with forcing functions that have random frequencies. We apply a generalized Polynomial Chaos approach to solving such equations and introduce a method for determining the system of decoupled, deterministic equations for the gPC coefficients which avoids direct numerical integration by taking advantage of properties of orthogonal polynomials.
- Poster-A hybrid numerical method for the numerical solution of the
Dimitrios Mitsotakis (University of Minnesota, Twin Cities)
Because Benjamin equation has a spatial structure somewhat like that of the Korteweg–de Vries equation, explicit schemes have unacceptable stability
limitations. We instead implement a highly accurate, unconditionally
stable scheme that features a hybrid Galerkin FEM/pseudospectral
method with periodic splines to approximate the spatial structure and
a two-stage Gauss–Legendre implicit Runge-Kutta method for the
temporal discretization. We present several numerical experiments
shedding light in some properties of the solitary wave solutions for
the specific equation.
- Poster- Designing Optimal Spectral Filters for Inverse Problems
Julianne Chung (University of Maryland)
Spectral filtering suppresses the amplification of errors when computing solutions to ill-posed inverse problems; however, selecting good regularization parameters is often expensive. In many applications, data is available from calibration experiments. In this poster, we describe how to use this data to pre-compute optimal spectral filters. We formulate the problem in an empirical Bayesian risk minimization framework and use efficient methods from stochastic and numerical optimization to compute optimal filters. Our formulation of the optimal filter problem is general enough to use a variety of error metrics, not just the mean square error. Numerical examples from image deconvolution illustrate that our proposed filters perform consistently better than well-established filtering methods.
- Poster- High-Accuracy Blind Deconvolution of Solar Images
Paul Shearer (University of Michigan)
Extreme ultraviolet (EUV) solar images, taken by spaceborne
telescopes, are critical sources of information about the solar
corona. Unfortunately all EUV images are contaminated by blur caused
by mirror scattering and diffraction. We seek to accurately determine,
with uncertainty quantification, the true distribution of solar EUV
emissions from these blurry observations. This is a blind
deconvolution problem in which the point spread function (PSF) is
complex, very long-range, and very incompletely understood.
Fortunately, images of partial solar eclipses (transits) provide a
wealth of indirect information about the telescope PSF, as blur from
the Sun spills over into the dark transit object. We know that
deconvolution with the true PSF should remove all apparent emissions
of the transit object.
We propose a MAP-based multiframe blind deconvolution method which
exploits transits to determine the PSF and true EUV emission maps. Our
method innovates in the PSF model, which enforces approximate
monotonicity of the PSF; and in the algorithm solving the MAP
optimization problem, which is inspired by a recent accelerated
Arrow-Hurwicz method of Chambolle and Pock. When applied to the EUV
blind deconvolution problem, the algorithm estimates PSFs which remove
blur from the transit objects with unprecedented accuracy.
- Poster- A Finite-Element Algorithm for an Inverse Sturm-Liouville Problem using a Least Squares Formulation
Inverse problems arise in many areas of science and mathematics, including geophysics, astronomy, tomography and medical biology. Inverse Sturm-Liouville problems (SLP) is a branch of inverse problems that has applications in most of these areas, and our motivation for studying such problems comes from an application in biomechanics, particularly in estimating material parameters for soft tissues. We propose a constructive numerical algorithm based on finite element methods to recover the potential of a SLP using least squares formulation.
- Poster- Modeling and Analysis of HIV Evolution and Therapy
Nicoleta Tarfulea (Purdue University, Calumet)
We present a mathematical model to investigate theoretically and numerically the effect of immune effectors, such as the cytotoxic lymphocyte (CTL), in modeling HIV pathogenesis during primary infection. Additionally, by introducing drug therapy, we assess the effect of treatments consisting of a combination of several antiretroviral drugs. Nevertheless, even in the presence of drug therapy, ongoing viral replication can lead to the emergence of drug-resistant virus variances. Thus, by including two viral strains, wild-type and drug-resistant, we show that the inclusion of the CTL compartment produces a higher rebound for an individual’s healthy helper T-cell compartment than does drug therapy alone. We characterize successful drugs or drug combination scenarios for both strains of virus.
- Poster- A Multiscale Learning Approach for History Matching
Hector Klie (ConocoPhillips)
The present work describes a machine learning approach for performing history matching. It consists of a hybrid multiscale search methodology based on SVD and the wavelet transform to incrementally reduce the parameter space dimensionality. The parameter space is globally explored and sampled by the simultaneous perturbation stochastic approximation (SPSA) algorithm at a different resolution scales. At a sufficient degree of coarsening, the parameters are estimated with the aid of an artificial neural network. The neural network serves also as a convenient device to evaluate the sensitiveness of the objective function with respect to variations of each individual model parameter in the vicinity of a promising optimal solution. Preliminary results shed light on future research avenues for optimizing the use of additional sources of information such as seismic or timely sensor data in history matching procedures.
This work has been developed in collaboration with Adolfo Rodriguez (Subsurface Technology, ConocoPhillips) and Mary F. Wheeler (Center for Subsurface Modeling, University of Texas at Austin)
- Poster- Model Cross-Validation: An example from a shock-tube experiment
Corey Bryant (The University of Texas at Austin)Rebecca Morrison (The University of Texas at Austin)
The decision to incorporate cross-validation into one's validation scheme raises immediate questions, not the least of which is-- how should one partition the data into calibration and validation sets? We answer this question systematically; indeed, we present an algorithm to find the optimal partition of the data subject to some constraints. While doing this, we address two critical issues: 1) that the model be evaluated with respect to its predictions of the quantity of interest and its ability to reproduce the data, and 2) that the model be highly challenged by the validation set, assuming it is properly informed by the calibration set. This method also relies on the interaction between the experimentalist and/or modeler, who understand the physical system and the limitations of the model; the decision-maker, who understands and can quantify the cost of model failure; and us, the computational scientists, who strive to determine if the model satisfies both the modeler's and decision-maker's requirements. We also note that our framework is quite general, and may be applied to a wide range of problems. Here, we illustrate it through a specific example involving a data reduction model for an ICCD camera from a shock-tube experiment.
- Poster - Scalable parallel algorithms for uncertainty quantification in high dimensional inverse problems
Tan Bui-Thanh (The University of Texas at Austin)
Quantifying uncertainties in large-scale forward and inverse PDE
simulations has emerged as the central challenge facing the field of
computational science and engineering. In particular, when the forward
simulations require supercomputers, and the uncertain parameter
dimension is large, conventional uncertainty quantification methods
fail dramatically. Here we address uncertainty quantification in
large-scale inverse problems. We adopt the Bayesian inference
framework: given observational data and their uncertainty, the
governing forward problem and its uncertainty, and a prior probability
distribution describing uncertainty in the parameters, find the
posterior probability distribution over the parameters. The posterior
probability density function (pdf) is a surface in high dimensions,
and the standard approach is to sample it via a Markov-chain Monte
Carlo (MCMC) method and then compute statistics of the
samples. However, the use of conventional MCMC methods becomes
intractable for high dimensional parameter spaces and
expensive-to-solve forward PDEs.
Under the Gaussian hypothesis, the mean and covariance of the
posterior distribution can be estimated from an appropriately weighted
regularized nonlinear least squares optimization problem. The solution
of this optimization problem approximates the mean, and the inverse of
the Hessian of the least squares function (at this point) approximates
the covariance matrix. Unfortunately, straightforward computation of
the nominally dense Hessian is prohibitive, requiring as many forward
PDE-like solves as there are uncertain parameters. However, the data
are typically informative about a low dimensional subspace of the
parameter space. We exploit this fact to construct a low rank
approximation of the Hessian and its inverse using matrix-free Lanczos
iterations, which typically requires a dimension-independent number of
forward PDE solves. The UQ problem thus reduces to solving a fixed
number of forward and adjoint PDE problems that resemble the original
forward problem. The entire process is thus scalable with respect to
forward problem dimension, uncertain parameter dimension,
observational data dimension, and number of processor cores. We apply
this method to the Bayesian solution of an inverse problem in 3D
global seismic wave propagation with tens of thousands of parameters,
for which we observe two orders of magnitude speedups.
- Poster- Adaptive Error Modelling in MCMC Sampling for Large Scale Inverse Problems
Tiangang Cui (University of Auckland)
We present a new adaptive delayed-acceptance Metropolis-Hastings
(ADAMH) algorithm that adapts to the error in a reduced order model to
enable efficient sampling from the posterior distribution arising in
complex inverse problems. This use of adaptivity differs from existing
algorithms that tune random walk proposals, though ADAMH also
implements that. We build on the conditions given by Roberts and
Rosenthal (2007) to give practical constructions that are provably
convergent. The components are the delayed-acceptance MH of Christen
and Fox (2005), the enhanced error model of Kaipio and Somersalo
(2007), and adaptive MCMC (Haario et al., 2001; Roberts and Rosenthal,
We applied ADAMH to calibrate large scale numerical models of
geothermal fields. It shows good computational and statistical
efficiencies on measured data. We expect that ADAMH will allow
significant improvement in computational efficiency when implementing
sample-based inference in other large scale inverse problems.
- Poster- Detecting small low emission radiating sources
Moritz Allmaras (Texas A & M University)Yulia Hristova (University of Minnesota, Twin Cities)
In order to prevent smuggling of highly enriched nuclear material
through border controls new advanced detection schemes need to be
developed. Typical issues faced in this context are sources with very
low emission against a dominating natural background radiation. Sources
are expected to be small and shielded and hence cannot be detected from
measurements of radiation levels alone.
We propose a detection method that relies on the geometric singularity
of small sources to distinguish them from the more uniform background.
The validity of our approach can be justified using properties of
related techniques from medical imaging. Results of numerical
simulations are presented for collimated and Compton-type measurements
in 2D and 3D.
- Poster - Convergence of a greedy algorithm for high-dimensional convex
Virginie Ehrlacher (École des Ponts ParisTech)
In this work, we present a greedy algorithm based on a tensor product
decomposition, whose aim is to compute the global minimum of a strongly
convex energy functional. We prove the convergence of our method
provided that the gradient of the energy is Lipschitz on bounded sets.
This is a generalization of the result which was proved by Le Bris,
Lelievre and Maday (2009) in the case of a linear high dimensional
Poisson problem. The main interest of this method is that it can be used
for high dimensional nonlinear convex problems. We illustrate this
algorithm on a prototypical example for uncertainty propagation on the