Research Day – April 5
On this week’s Research Day we have a public program item:
Wednesday, April 5, 2023:
14:00 Mohanamuraly Pavanakumar (CERFACS)
Learning stable and accurate numerical schemes for time dependent PDEs (abstract below)
Abstract:
Machine learning (ML) has begun to deeply penetrate the field of numerical computation of partial differential equations(PDEs), especially time-dependent
ones. There is significant buzz around completely replacing traditional numerical
schemes with ML. Yet we find no objective or systematic study on why ML is superior
to existing numerical methods. The scepticism of pure ML approaches revolves around
the problem of stability/generalisability and numerical analysis is an indispensable
tool to address both. In this talk, I will outline our work on the Machine-Learned
Two-step Taylor Galerkin Convection (ML-TTGC) scheme developed at CERFACS. Using a
hybrid approach of coupling standard numerical schemes (TTGC) with ML, we achieve
better stability and generalisability and can explain our improved results based
on numerical analysis. Results from the application of ML-TTGC to solve convection
and Burgers’ equation shows the value ML brings to the numerical PDE community.
The Research Day will be hybrid. If you like to attend on Zoom, please write a short e-mail to cs10-support@fau.de to receive the credentials.