The PDE Prior
October 5, 2022 at 5 pm CEST
There is an interesting new field developing at the intersection of the physical sciences and deep learning, sometimes called AI4Science. In one direction, tools developed in the AI community are used to solve problems in science, such as protein folding, molecular simulation, and so on. But also in the other direction, deep insights from mathematics and physics are inspiring new DL architectures, such as Neural ODE solvers, and equivariance. In this talk, I will start with mapping out some of the opportunities at this intersection and subsequently dive a little deeper into PDE solving. Also, in this subfield, cross fertilization has already happened both ways: people have used DL tools to successfully solve PDE equations much faster than with traditional solvers. But reversely, there are also efforts to use PDEs as “infinite width”, functional representations of layers in a deep NN architecture. The latter is helpful for instance to become independent of gridding choices. In the second half of this talk, I will explain our most recent efforts to solve PDEs faster and more accurately using DL, and reversely, new ways to use PDEs as an approximate equivariance prior.
Prof. Dr. Max Welling is a full professor and research chair in machine learning at the University of Amsterdam. He is also a Distinguished Scientist at MSR. He is a fellow at the Canadian Institute for Advanced Research (CIFAR) and the European Lab for Learning and Intelligent Systems (ELLIS) where he serves on the founding board. His previous appointments include VP at Qualcomm Technologies, professor at UC Irvine, postdoc at U. Toronto and UCL under supervision of Prof. Geoffrey Hinton, and postdoc at Caltech under supervision of Prof. Pietro Perona. He finished his PhD in theoretical high energy physics under supervision of Nobel laureate Prof. Gerard ‘t Hooft.
Max Welling has served as associate editor in chief of IEEE TPAMI from 2011-2015, he serves on the advisory board of the Neurips foundation since 2015 and has been program chair and general chair of Neurips in 2013 and 2014, respectively. He was also program chair of AISTATS in 2009 and ECCV in 2016 and general chair and co-founder of MIDL 2018. Max Welling is recipient of the ECCV Koenderink Prize in 2010 and the ICML Test of Time award in 2021.