Conference ID: 586-527-161
PIN Code: 367876
After its tremendous success in computer science, deep learning is increasingly used in the context of scientific computing. In this lecture, we will present different algorithms and results of our group on the application of deep learning algorithms in the computation of PDEs. We focus on two sets of problems in this talk. In the first part, we will consider the use of deep learning algorithms for computing observables of parametric PDEs and present two sets of techniques: training on low discrepancy sequences and a multi-level training algorithm to enhance the accuracy of deep learning algorithms in this data poor regime. Applications to uncertainty quantification, PDE constraint optimization and prediction of Tsunamis will be presented. In the second part of the talk, we will present rigorous error analysis of Physics informed Neural Networks (PINNs) that were recently proposed for solving PDEs. The algorithm and proposed theory will be illustrated with several numerical examples.
Siddhartha Mishra is currently Professor for Applied Mathematics at ETH (Swiss federal institute of technology) Zurich, Switzerland. His research interests are in numerical analysis, scientific computing, nonlinear partial differential equations, computational astrophysics, computational fluid dynamics, computational climate science, machine learning and modeling and simulation of biological systems. For his research contributions, he has been honored with the Collatz prize of international council of industrial and applied matheamatics (ICIAM) in 2019, the Infosys Prize of the Infosys science foundation in 2019, the Richard von-Mises prize of the international association of applied mathematics and mechanics (GAMM) in 2015, the Jacques Lious Lions award of the European community on computational methods in applied sciences (ECCOMAS) in 2018 and the highly competitive starting (2012) and consolidator grants (2018) of the European research council (ERC). He serves on the editorial board of several international journals on computational science and has been an invited speaker at many leading conferences, including the international congress of mathematicians (ICM) in Rio De Janeiro in 2018.