A Trust Region RB-ML-ROM Approach for Parabolic PDE Constrained Optimization

Klein, Benedikt; Ohlberger, Mario

Abstract

Optimization problems constrained by parabolic PDEs are common in science and engineering, involving challenges like optimal control and inverse problems. Traditional methods require numerous iterations to solve discretized PDEs, often creating a computational bottleneck. Surrogate models, especially reduced order models (ROM) obtained from reduced basis (RB) methods, offer increased efficiency by approximating these high-fidelity solutions.This contribution explores how machine learning (ML) can enhance surrogate model construction in the framework of error aware trust region (TR) optimization methods.