Multiscale Model Reduction in Physics with Deep Networks

Mon, May 13, 2019, 4:15 pm
Department of Astrophysical Sciences


Approximating high-dimensional functionals with low-dimensional models is a central issue of machine learning and physics. This talk shows deep convolutional neural network architectures take advantage of scale separation, symmetries and sparse representations. We introduce simplified architectures which can be analyzed mathematically. Scale separations is performed with wavelets and scale interactions are captured through phase coherence. We show applications to modeling of astrophysical turbulences, regression of quantum molecular energies as
well as image classification and generation.


Stéphane Mallat received a Ph.D. from the University of Pennsylvania in 1988, after which he became a Professor at the Courant Institute of Mathematical Sciences. In 1995, he became Professor of Applied Mathematics at Ecole Polytechnique, Paris and Department Chair in 2001. From 2001 to 2007 he was co-founder and CEO of a semiconductor start-up company. From 2012 to 2017 he was Professor in the Computer Science Department of Ecole Normale Supérieure, in Paris. Since 2017, he has held the “Data Sciences” chair at the Collège de France.
Stéphane Mallat’s research interests include machine learning, signal processing, and harmonic analysis. He is a member of the French Academy of sciences, a foreign member of the US National Academy of Engineering, an IEEE Fellow and an EUSIPCO Fellow. In 1997, he received the Outstanding Achievement Award from the SPIE Society and was a plenary lecturer at the International Congress of Mathematicians in 1998. He also received the 2004 European IST Grand prize, the 2004 INIST-CNRS prize for most cited French researcher in engineering and computer science, the 2007 EADS grand prize of the French Academy of Sciences, the 2013 Innovation medal of the CNRS, and the 2015 IEEE Signal Processing best sustaining paper award.