Machine Learning-based quadratic closures for non-intrusive Reduced Order Models
For practitioners of reduced-order modeling in fluid dynamics, this method offers a more generalizable quadratic closure than least-squares approaches, though it is incremental in nature.
The authors introduce a data-driven quadratic closure for non-intrusive Reduced Order Models (ROMs) using a MIONet to learn the quadratic operator, improving accuracy in under-resolved regimes. On two fluid dynamics benchmarks, the correction term enhances standard POD-based ROM accuracy.
In the present work, we introduce a data-driven approach to enhance the accuracy of non-intrusive Reduced Order Models (ROMs). In particular, we focus on ROMs built using Proper Orthogonal Decomposition (POD) in an under-resolved and marginally-resolved regime, i.e. when the number of modes employed is not enough to capture the system dynamics. We propose a method to re-introduce the contribution of neglected modes through a quadratic correction term, given by the action of a quadratic operator on the POD coefficients. Differently from the state-of-the-art methodologies, where the operator is learned via least-squares optimisation, we propose to parametrise the operator by a Multi-Input Operators Network (MIONet). This way, we are able to build models with higher generalisation capabilities, where the operator itself is continuous in space -- thus agnostic of the domain discretisation -- and parameter-dependent. We test our model on two standard benchmarks in fluid dynamics and show that the correction term improves the accuracy of standard POD-based ROMs.