Operator Inference Aware Quadratic Manifolds with Isotropic Reduced Coordinates for Nonintrusive Model Reduction

TL;DR

This paper introduces a greedy training method for quadratic manifolds in nonintrusive model reduction that optimizes both reconstruction and prediction errors, significantly improving reduced model accuracy.

Contribution

The proposed greedy training procedure jointly minimizes reconstruction and prediction errors, resulting in more accurate and smooth quadratic manifolds for reduced modeling.

Findings

Achieves up to 100x higher accuracy in reduced models.

Avoids oscillatory and non-smooth embeddings.

Effective on transport and turbulent flow problems.

Abstract

Quadratic manifolds for nonintrusive reduced modeling are typically trained to minimize the reconstruction error on snapshot data, which means that the error of models fitted to the embedded data in downstream learning steps is ignored. In contrast, we propose a greedy training procedure that takes into account both the reconstruction error on the snapshot data and the prediction error of reduced models fitted to the data. Because our procedure learns quadratic manifolds with the objective of achieving accurate reduced models, it avoids oscillatory and other non-smooth embeddings that can hinder learning accurate reduced models. Numerical experiments on transport and turbulent flow problems show that quadratic manifolds trained with the proposed greedy approach lead to reduced models with up to two orders of magnitude higher accuracy than quadratic manifolds trained with respect to the reconstruction error alone.