Graduate Student / Postdoc Seminar

Scientific machine learning for solving high-dimensional evolution equations

Speaker: Benjamin Peherstorfer, Courant

Location: Warren Weaver Hall 1302

Date: Friday, February 18, 2022, 11:15 a.m.


While machine learning methods have been shown to provide accurate
predictions when trained on sufficient data, many of the
scientifically most interesting phenomena happen in regimes where
there is no data available a priori and where it is even unclear how
to collect informative data at all. In this work, we propose the
Neural Galerkin methodology that integrates data acquisition into the
process of solving partial differential equations with deep learning
so that new data samples are collected in a self-informed manner that
is guided by the dynamics of the solution itself. Numerical
experiments demonstrate that the adaptive data collection of Neural
Galerkin is key to providing accurate approximations of solutions in
high dimensions, especially if features of the solutions are local
such as in interacting particle systems described by kinetic equations
and when advecting coherent structures and waves in high dimensions.