# Variational methods

Thursday, September 7, 2017 - 9:35am - 10:10am

Adrian Sandu (Virginia Polytechnic Institute and State University)

Data assimilation is the process by which PDE-based models use measurements to produce an optimal representation of the state of the system. Different measurements bring different contributions to reducing uncertainty in the inference results. Quantifying the impact of observations is important for data pruning and for the configuration of sensor networks. This talk discusses several adjoint-based methodologies for formal observation impact assessment and for optimal design of sensor networks.

Tuesday, October 19, 2010 - 9:30am - 10:30am

Stephen Robinson (University of Wisconsin, Madison)

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.Wednesday, November 5, 2008 - 2:00pm - 2:45pm

Andrea Braides (Seconda Università di Roma Tor Vergata)

Asymptotic variational methods are aimed at describing the overall properties of an increasingly complicated system by computing an effective limit energy where some parameters are averaged out or greatly simplified. Such methods include Gamma-convergence and variational expansions. An extremely interesting field of application is that of discrete (lattice) systems, where the determination of the relevant parameters in the limit theory is part of the problem.

Tuesday, April 4, 2006 - 1:30pm - 2:30pm

Martin Rumpf (Rheinische Friedrich-Wilhelms-Universität Bonn)

Variational methods are presented which allow to correlate pairs of

implicit shapes in 2D and 3D images, to morph pairs of explicit

surfaces, or

to analyse motion pattern in movies.

A particular focus is on joint methods.

Indeed, fundamental tasks in image processing are highly interdependent:

Registration of image morphology significantly benefits from previous

denoising and structure segmentation.

On the other hand, combined information of different image modalities

makes shape

implicit shapes in 2D and 3D images, to morph pairs of explicit

surfaces, or

to analyse motion pattern in movies.

A particular focus is on joint methods.

Indeed, fundamental tasks in image processing are highly interdependent:

Registration of image morphology significantly benefits from previous

denoising and structure segmentation.

On the other hand, combined information of different image modalities

makes shape

Wednesday, May 21, 2014 - 9:20am - 10:00am

Rustum Choksi (McGill University)

Self-assembly, a process in which a disordered system of preexisting components forms an organized structure or pattern, is both ubiquitous in nature and important for the synthesis of many designer materials.

In this talk, we will address two variational paradigms for self-assembly from the point of view of analysis and computation.

The first variational model is a nonlocal perturbation (of Coulombic-type) to the well-known Ginzburg-Landau/Cahn-Hilliard free energy. The functional has a rich and complex energy landscape with many metastable states.

In this talk, we will address two variational paradigms for self-assembly from the point of view of analysis and computation.

The first variational model is a nonlocal perturbation (of Coulombic-type) to the well-known Ginzburg-Landau/Cahn-Hilliard free energy. The functional has a rich and complex energy landscape with many metastable states.

Tuesday, November 19, 2013 - 4:15pm - 4:40pm

Graham Cox (University of North Carolina, Chapel Hill)

We consider the estimation of carbon flux at the ocean-atmosphere interface from the perspective of variational data assimilation. The flux is treated as a time-dependent Neumann boundary condition for the carbon mixing ratio, which evolves according to a linear diffusive transport equation. The variational problem has a natural, infinite-dimensional Bayesian formulation.

Monday, July 15, 2013 - 11:00am - 11:50am

Mark Peletier (Technische Universiteit Eindhoven)

In this course we develop the methodology of “variational modeling” of energy-driven systems. This methodology applies to systems whose evolution (in time) is driven by the decrease of an energy, in a friction-dominated or strongly damped way. Recent developments have shown that a surprisingly large class of evolutionary systems is of this form, even though the energy and the friction mechanism may not be obvious.