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

2025-02-07

AI Summary

Conventional reduced-order model (ROM) closures struggle to simultaneously achieve accuracy, interpretability, and generalizability for low-resolution, convection-dominated, high-Reynolds-number flows (Re = 10⁴–2×10⁴). Method: This work introduces symbolic regression (SR) into ROM closure construction for the first time, embedding it within a variational multiscale ROM framework that synergistically integrates physical constraints and data-driven learning—yielding an interpretable, lightweight, and robust SR-ROM closure. The approach overcomes the limited expressivity of structured closures and the opacity and poor generalization of neural-network-based closures. Contribution/Results: Evaluated on canonical benchmarks—including flow past a circular cylinder and lid-driven cavity flow—SR-ROM achieves markedly improved predictive accuracy and numerical stability. Compared to linear and quadratic structured closures as well as neural-network closures, it reduces prediction error by 30%–50% and demonstrates strong cross-regime generalization capability.

Technology Category

• Cognitive Modeling & Cognitive Systems: Symbolic Representations
• Machine Learning: Neuro-Symbolic Learning
• Computer Vision: Visual Reasoning & Symbolic Representations

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs

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.

Problem

• Enhances ROM accuracy in convection-dominated flows
• Proposes symbolic regression for interpretable ROM closures
• Compares SR-ROM with structural and ML-based closures

Innovation

• Symbolic regression for ROM closures
• Combines structural and ML advantages
• Enhances accuracy and robustness