Non-intrusive Nonlinear Model Reduction via Machine Learning Approximations to Low-dimensional Operators

TL;DR

This paper introduces a machine learning-based method to approximate low-dimensional operators in reduced-order models, enabling non-intrusive, efficient simulations of nonlinear dynamical systems with minimal code modifications.

Contribution

It presents a novel non-intrusive approach to model reduction by using machine learning to approximate operators, reducing implementation complexity and computational cost.

Findings

Achieves up to 1000x reduction in run time.

Effectively applied to two types of PDEs.

Enables non-intrusive reduced-order modeling.

Abstract

Although projection-based reduced-order models (ROMs) for parameterized nonlinear dynamical systems have demonstrated exciting results across a range of applications, their broad adoption has been limited by their intrusivity: implementing such a reduced-order model typically requires significant modifications to the underlying simulation code. To address this, we propose a method that enables traditionally intrusive reduced-order models to be accurately approximated in a non-intrusive manner. Specifically, the approach approximates the low-dimensional operators associated with projection-based reduced-order models (ROMs) using modern machine-learning regression techniques. The only requirement of the simulation code is the ability to export the velocity given the state and parameters as this functionality is used to train the approximated low-dimensional operators. In addition to enabling nonintrusivity, we demonstrate that the approach also leads to very low computational complexity, achieving up to $1000\times$ reduction in run time. We demonstrate the effectiveness of the proposed technique on two types of PDEs.