Program
| Time (Eastern Time) |
Presenter | Title |
|---|---|---|
| 9:30 am - 10:15 am | Registration | |
| 10:15 am - 10:30 am | Introduction | |
| 10:30 am - 11:30 am | Plenary Talk Irene Fonseca (Carnegie Mellon University) |
From Phase Separation in Heterogeneous Media to Learning Training Schemes for Image Denoising |
| 11:30 am - 12:15 pm | Poster Blitz | |
| 12:15 pm - 1:30 pm | Working Lunch and Poster Session | |
| 1:30 pm - 3:30 pm | Program Officers Presentations and Panel Air Force Office of Scientific Research Warren P. Adams Fariba Fahroo Fred Leve National Science Foundation Troy Butler Yuliya Gorb Ludmil Zikatanov Office of Naval Research Reza Malek-Madani |
|
| 3:30 pm - 4:00 pm | Networking Break and Poster Session | |
| 4:00 pm - 5:00 pm | Plenary Talk Sven Leyffer (Argonne National Laboratory) |
Topological Design Problems and Integer Optimization |
| 5:00 pm - 5:15 pm | Closing Remarks | |
Plenary Speakers
Prof. Dr. Irene Fonseca
An internationally respected educator and researcher in applied mathematics; Irene Fonseca is the director of Carnegie Mellon's Center for Nonlinear Analysis (CNA).
In recognition for her contributions to the advancement of research in her area of expertise, Irene Fonseca was bestowed a knighthood in the Military Order of St. James (Grande Oficial da Ordem Militar de Santiago da Espada) by the then-President of Portugal, Jorge Sampaio, in 1997. For her teaching and research contributions to Carnegie Mellon University, Irene Fonseca was honored with the Mellon College of Science endowed chair in 2003 and named a University Professor in 2014. In 2012 she was elected President of the Society for Industrial and Applied Mathematics (SIAM), one of the largest organizations dedicated to mathematics and computational science in the world. In 2018 Irene Fonseca was installed as the first Kavčić-Moura University Professor of Mathematics.
Talk title: From Phase Separation in Heterogeneous Media to Learning Training Schemes for Image Denoising
Abstract:
From Phase Separation in Heterogeneous Media to Learning Training Schemes for Image Denoising
What do these two themes have in common? Both are treated variationally, both deal with energies of different dimensionalities, concepts of geometric measure theory prevail in both, and higher order penalizations are considered. Will learning training schemes for choosing these penalizations in imaging may be of use in phase transitions?
Phase Separation in Heterogeneous Media: Modern technologies and biological systems, such as temperature-responsive polymers and lipid rafts, take advantage of engineered inclusions, or natural heterogeneities of the medium, to obtain novel composite materials with specific physical properties. To model such situations using a variational approach based on the gradient theory of phase transitions, the potential and the wells may have to depend on the spatial position, even in a discontinuous way, and different regimes should be considered. In the critical case case where the scale of the small heterogeneities is of the same order of the scale governing the phase transition and the wells are fixed, the interaction between homogenization and the phase transitions process leads to an anisotropic interfacial energy. The supercritical case for fixed wells is also addressed, now leading to an isotropic interfacial energy. In the subcritical case with moving wells, where the heterogeneities of the material are of a larger scale than that of the diffuse interface between different phases, it is observed that there is no macroscopic phase separation and that thermal fluctuations play a role in the formation of nanodomains.
This is joint work with Riccardo Cristoferi (Radboud University, The Netherlands) and Likhit Ganedi (Aachen University, Germany), USA), based on previous results also obtained with Adrian Hagerty (USA) and Cristina Popovici (USA).
Learning Training Schemes for Image Denoising: Due to their ability to handle discontinuous images while having a well-understood behavior, regularizations with total variation (TV) and total generalized variation (TGV) are some of the best known methods in image denoising. However, like other variational models including a fidelity term, they crucially depend on the choice of their tuning parameters. A remedy is to choose these automatically through multilevel approaches, for example by optimizing performance on noisy/clean image training pairs. Such methods with space-dependent parameters which are piecewise constant on dyadic grids are considered, with the grid itself being part of the minimization. Existence of minimizers for discontinuous parameters is established, and it is shown that box constraints for the values of the parameters lead to existence of finite optimal partitions. Improved performance on some representative test images when compared with constant optimized parameters is demonstrated.
This is joint work with Elisa Davoli (TU Wien, Austria), Jose Iglesias (U. Twente, The Netherlands) and Rita Ferreira (KAUST, Saudi Arabia)
Dr. Sven Leyffer
joined the Mathematics and Computer Science Division at Argonne in 2002, where he is now a senior computational mathematician. Sven is a SIAM Fellow, and a senior fellow of the University of Chicago/Argonne Computation Institute.
He is the current SIAM President and serves on the editorial boards of Computational Optimization and Applications, and Mathematics of Computation.
In 2006, Leyffer (along with two colleagues) received the Lagrange Prize in Continuous Optimization, which is awarded only once every 3 years. In 2016, he received the Farkas Prize from the INFORMS Optimization Society.
Leyffer obtained his Ph.D. in 1994 from the University of Dundee, Scotland, and held postdoctoral research positions at Dundee, Argonne, and Northwestern University.
Talk title: Topological Design Problems and Integer Optimization
Abstract:
Topological design problems arise in many important engineering and scientific applications, such additive manufacturing and the design of cloaking devices. We formulate these problems as massive mixed-integer PDE-constrained optimization (MIPDECO) problems. We show that despite their seemingly hopeless complexity, MIPDECOs can be solved efficiently (at a cost comparable to a single continuous PDE-constrained optimization solve). We discuss two classes of methods: rounding techniques that are shown to be asymptotically optimal, and trust-region techniques that converge under mesh refinement. We illustrate these solution techniques with examples from topology optimization.
Organizing Committee
Harbir Antil (George Mason University)
Ratna Khatri (U.S. Naval Research Laboratory)