Past Event: CSEM Student Forum

Parallel in Time Algorithms for Multiscale Dynamical Systems using Interpolation and Neural Networks

Gopal R. Yalla, ICES, UT Austin

Abstract

We present a novel coarse scale solver for the parareal computation of dynamical systems. The coarse scale solver can be de ned through interpolation or as the output of a neural network, and accounts for slow scale motion in the system. When pairing this coarse solver with a ne scale solver that corrects for fast scale motion through a parareal scheme, we are able to achieve the accuracy of the ne solver at the ef ciency of the coarse solver. Successful tests for smaller but challenging problems are presented, which cover both highly oscillatory solutions and problems with strong forces localized in time. The results suggest signi cant speed up can be gained for multiscale problems when using a parareal scheme with this new coarse solver as opposed to the traditional parareal setup.