Nonlinear projection-based model order reduction with machine learning regression for closure error modeling in the latent space

TL;DR

This paper introduces a novel nonlinear model order reduction method using Gaussian process regression and RBF interpolation for closure error modeling, enhancing efficiency, interpretability, and applicability over neural network approaches.

Contribution

It presents a new approach combining GPR and RBFs for closure modeling in PMOR, surpassing neural networks in interpretability and data efficiency.

Findings

Achieves high accuracy in complex fluid dynamics problems.

Improves efficiency and interpretability over traditional methods.

Successfully applied to 2D Burgers and 3D turbulent flow simulations.

Abstract

A significant advancement in nonlinear projection-based model order reduction (PMOR) is presented through a highly effective methodology. This methodology employs Gaussian process regression (GPR) and radial basis function (RBF) interpolation for closure error modeling in the latent space, offering notable gains in efficiency and expanding the scope of PMOR. Moving beyond the limitations of deep artificial neural networks (ANNs), previously used for this task, this approach provides crucial advantages in terms of interpretability and a reduced demand for extensive training data. The capabilities of GPR and RBFs are showcased in two demanding applications: a two-dimensional parametric inviscid Burgers problem, featuring propagating shocks across the entire computational domain, and a complex three-dimensional turbulent flow simulation around an Ahmed body. The results demonstrate that this innovative approach preserves accuracy and achieves substantial improvements in efficiency and interpretability when contrasted with traditional PMOR and ANN-based closure modeling.