Prof. Dr. Benjamin Peherstorfer- Learning Context -aware Reduced Models for Multifidelity Computations

Courant Institute of Mathematical Sciences, New York University, USA

Abstract

Traditional model reduction constructs reduced models with the aim of replacing expensive, high-fidelity models to speed up computations. However, reduced and high-fidelity models are increasingly used together in multifidelity methods, which means that the purpose of reduced models becomes supporting computations with the high-fidelity models rather than approximating and replacing them. In this presentation, we propose context-aware reduced models that are explicitly constructed for being used together with high-fidelity models in multifidelity computations. In the first part of the presentation, we introduce the adaptive multifidelity Monte Carlo (AMFMC) method that constructs reduced models that optimally support the multifidelity estimation of statistics of high-fidelity model outputs. Our analysis shows that our context-aware reduced models optimally reduce the runtime of multifidelity estimation, even though they are less accurate in the sense of traditional model reduction. In the second part, we present a multifidelity approach to dynamically couple reduced models with high-fidelity models, where the reduced models are adapted in a context-aware sense with sparse data from the high-fidelity model. Our numerical examples demonstrate that the dynamic coupling is particularly beneficial in case of convection-dominated problems, where our context-aware approach achieves significant speedups, whereas traditional reduced models are even more costly to evaluate than the high-fidelity models.