Symbolic Regression of Data-Driven Reduced Order Model Closures for Under-Resolved, Convection-Dominated Flows
This work addresses the challenge of accurate modeling in fluid dynamics for researchers and engineers, but it is incremental as it builds on existing data-driven closure methods.
The paper tackled the problem of improving reduced order model (ROM) accuracy for under-resolved, convection-dominated flows by proposing a symbolic regression (SR) data-driven closure strategy, which resulted in more accurate and robust ROMs compared to existing structural and machine learning-based closures, as demonstrated in test problems like flow past a cylinder and lid-driven cavity flow at Reynolds numbers up to 20000.
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.