This workshop series is made up of four workshops held over 9 days:
Inverse problems in materials science and engineering include determination of material properties from scattering data or other measurements, design of new materials with optimized properties, determination of operational parameters to meet system performance goals. This workshop will focus on inverse problem methods and results that have a particular material science aspect.
There are many inverse and optimal design problems in which the desired unknown is the geometry of a structure. These types of problem can in general be cast as optimization problems where one would minimize data misfit in the case of inverse problems, or a cost functional, in the case of optimal design. A powerful approach for solving such problems is to parametrize the unknown geometry using a level set function.
This workshop will discuss both functional analytic and numerical linear algebra apsects. Some of the talks will focus on methods and their convergence theory, while others treat specific applications with an emphasis on numerical methods. The relationship between functional analytic and statistical approaches will also be covered.
Learning from examples can be regarded as an inverse and ill-posed problem. The workshop will focus on the problem of learning as an inverse problem, on regularization techniques to solve it and more fundamentally on the close relation between generalization and stability.
Russel Caflisch (UCLA, Mathematics and Materials Science)
David Colton (University of Delaware, Mathematics)
Peter Deuflhard (Freie Universitat, Berlin)
David Donoho (Stanford University, Statistics)
Heinz Engl (Johannes Kepler University, Austria, Industrial Math.)
Eric Michielssen (University of Illinois at Urbana-Champaign)
Stanley Osher (Institute for Pure and Applied Mathematics, Mathematics)
Tomaso Poggio (Massachusetts Institute of Technology, Brain and Cognitive Sciences)
Lothar Reichel (Kent State University)
Fadil Santosa (University of Minnesota, Mathematics)