Symbolic Regression of Data-Driven Reduced Order Model Closures for Under-Resolved, Convection-Dominated Flows

TL;DR

This paper introduces a novel symbolic regression approach for data-driven reduced order model closures, improving interpretability, accuracy, and robustness in simulating under-resolved, convection-dominated flows.

Contribution

The paper proposes a symbolic regression-based closure strategy that combines advantages of existing methods and overcomes their limitations, leading to more effective ROMs.

Findings

SR closures outperform structural closures in accuracy.

SR closures are more robust across different flow regimes.

SR closures generalize better to unseen data.

Abstract

Data-driven closures correct the standard reduced order models (ROMs) to increase their accuracy in under-resolved, convection-dominated flows. There are two types of data-driven ROM closures in current use: (i) structural, with simple ansatzes (e.g., linear or quadratic); and (ii) machine learning-based, with neural network ansatzes. We propose a novel symbolic regression (SR) data-driven ROM closure strategy, which combines the advantages of current approaches and eliminates their drawbacks. As a result, the new data-driven SR closures yield ROMs that are interpretable, parsimonious, accurate, generalizable, and robust. To compare the data-driven SR-ROM closures with the structural and machine learning-based ROM closures, we consider the data-driven variational multiscale ROM framework and two under-resolved, convection-dominated test problems: the flow past a cylinder and the lid-driven cavity flow at Reynolds numbers Re = 10000, 15000, and 20000. This numerical investigation shows that the new data-driven SR-ROM closures yield more accurate and robust ROMs than the structural and machine learning ROM closures.