Lookahead data-gathering strategies for online adaptive model reduction of transport-dominated problems

TL;DR

This paper introduces lookahead data-gathering strategies for online adaptive model reduction of transport-dominated problems, improving prediction accuracy, robustness, and stability over previous methods that only look back in time.

Contribution

The paper proposes novel lookahead data-gathering strategies that predict future states to enhance adaptive model reduction for transport-dominated problems.

Findings

Lookahead strategies improve model accuracy.

Enhanced robustness and stability of reduced models.

Outperform previous data-gathering methods in experiments.

Abstract

Online adaptive model reduction efficiently reduces numerical models of transport-dominated problems by updating reduced spaces over time, which leads to nonlinear approximations on latent manifolds that can achieve a faster error decay than classical linear model reduction methods that keep reduced spaces fixed. Critical for online adaptive model reduction is coupling the full and reduced model to judiciously gather data from the full model for adapting the reduced spaces so that accurate approximations of the evolving full-model solution fields can be maintained. In this work, we introduce lookahead data-gathering strategies that predict the next state of the full model for adapting reduced spaces towards dynamics that are likely to be seen in the immediate future. Numerical experiments demonstrate that the proposed lookahead strategies lead to accurate reduced models even for problems where previously introduced data-gathering strategies that look back in time fail to provide predictive models. The proposed lookahead strategies also improve the robustness and stability of online adaptive reduced models.