Numerical Analysis and Scientific Computing Seminar | Elizabeth Qian, Reduced operator inference for nonlinear PDEs

For Zoom Link please contact ddelreyfernandez@uwaterloo.ca  

Speaker

Assistant Professor Elizabeth Qian, Georgia Tech, Schools of Aerospace Engineering and Computational Science and Engineering

Title

Reduced operator inference for nonlinear PDEs

Abstract

This talk will present a scientific machine learning method that learns from data a computationally inexpensive surrogate model for a time-dependent nonlinear partial differential equation (PDE), an enabling technology for many computational algorithms used in engineering settings. The method brings together two main elements. First, ideas from projection-based model reduction are used to explicitly parametrize the learned model by low-dimensional polynomial operators which reflect the known form of the governing PDE. Second, supervised machine learning tools are used to infer from data the reduced operators of this physics-informed parametrization. For systems whose governing PDEs contain more general (non-polynomial) nonlinearities, the learned model performance can be improved through the use of lifting variable transformations which expose polynomial structure in the PDE. Numerical experiments on a three-dimensional rocket combustion simulation with over 18 million degrees of freedom demonstrate that the learned reduced models achieve accurate predictions with a dimension reduction of five orders of magnitude and model runtime reduction of up to nine orders of magnitude.