Breaking the Mesh: Solving Partial Differential Equations with Deep Learning
SMAI 2019 Mini-Symposium
This repository hosts the presentations from the SMAI 2019 Mini-Symposium entitiled "Breaking the Mesh: Solving Partial Differential Equations with Deep Learning," which was held on May 13th, 2019 in Guidel Plages, France. The symposium was organized by J.B. Scoggins and Loïc Gouarin. The speaker bios and presentations are provided below in the order they were presented.
James B. Scoggins
Solving Partial Differential Equations with Deep Learning
James B. Scoggins is currently a postdoctoral researcher at the Center for Applied Mathematics (CMAP), Ecole Polytechnique, where he works on machine learning approaches for solving partial differential equations arrising in predictive modeling. In 2017, James obtained his Ph.D. in Energy Sciences jointly from CentraleSupélec in France and the von Karman Institute for Fluid Dynamics (VKI) in Belgium, where he maintains a status of collaborative postdoctoral researcher. During his PhD, James developed the open-source Mutation++ library for modeling ionized gases in nonequilibrium. He recieved a M.S. degree in Aerospace Engineering and a graduate minor degree in Mathematics from North Carolina State University in 2011, where he also completed his undergraduate training with a B.S. in Aerospace Engineering in 2009. James was awarded a NOAA Ernest F. Hollings Scholarship in 2007 as well as a NASA Space Grant and Graduate Student Research Program Fellowhsip in 2009. He recently recieved a postdoctoral fellowship from the Labex Mathématiques Hadamard to study the solution of PDEs with deep learning. His interests included machine learning for predictive modeling, thermodynamic and transport theory for ionized and magnetized plasmas, hypersonic flows, and atmospheric entry.
Philippe von Wurstemberger
Overcoming the curse of dimensionality with DNNs: Theoretical approximation results for PDEs
Philippe von Wurstemberger is currently a Ph.D. student at ETH Zurich under the supervision of Dr. Arnulf Jentzen, where he also recieved his B.S. and M.S. degrees in Mathematics. In 2015, he completed a semester exchange program at Princeton University. His interests include approximation methods for high-dimensional PDEs, mathematical analysis of deep learning, and reinforcement learning.
Rémi Gribonval is a Research Director (Directeur de Recherche) with INRIA in Rennes, France, and the scientific leader of the PANAMA research group on sparse audio processing. In 2011, he was awarded the Blaise Pascal Award of the GAMNI-SMAI by the French Academy of Sciences, and a starting investigator grant from the European Research Council in 2011. He is an IEEE fellow and a EURASIP Fellow. He founded the series of international workshops SPARS on Signal Processing with Adaptive/Sparse Representations. Since 2002 he has been the coordinator of several national, bilateral and European research projects. He has been a member of the IEEE SPTM Technical Committee and of the SPARS steering committee.
Siamak Mehrkanoon received his Ph.D. degree in machine learning from KU Leuven, Belgium, in 2015. He was a Visiting Researcher with the Department of Automation, Tsinghua University, Beijing, China, in 2014, a Postdoctoral Research Fellow with the University of Waterloo, Canada, from 2015 to 2016, and a Visiting Postdoctoral Researcher with the Cognitive Systems Laboratory, University of Tubingen, Germany, in 2016. He was awarded the FWO postdoctoral fellowship in 2017. He is currently an assistant professor in the department of data science and knowledge engineering, Maastricht university. His current research interests encompass deep learning, neural networks, kernel-based models, unsupervised and semi-supervised learning, pattern recognition, numerical algorithms, and optimization.