Linear multistep methods for learning dynamics

School of Mathematics Colloquium
Thursday, March 11, 2021 - 11:00am for 1 hour (actually 50 minutes)
Qiang Du – Columbia University – qd2125@columbia.edu
Anton Bernshteyn

Numerical integration of given dynamic systems can be viewed as a forward problem with the learning of unknown dynamics from available state observations as an inverse problem. The latter has been around in various settings such as the model reduction of multiscale processes. It has received particular attention recently in the data-driven modeling via deep/machine learning. Indeed, solving both forward and inverse problems forms the loop of informative and intelligent scientific computing. A natural question is whether a good numerical integrator for discretizing prescribed dynamics is also good for discovering unknown dynamics. This lecture presents a study in the context of Linear multistep methods (LMMs).