Nonintrusive projection-based reduced order modeling using stable learned differential operators

TL;DR

This paper introduces a nonintrusive reduced order modeling approach that learns stable differential operators from data and integrates them into existing projection-based ROMs for accurate and stable dynamics prediction.

Contribution

It proposes a learn-then-project method using stable sparse learned differential operators for nonintrusive model reduction in black-box scenarios.

Findings

Accurate and stable predictions for 1-D advection, Burgers, and 2-D advection equations.

Compatible with Galerkin and LSPG projection methods.

Demonstrates effectiveness in multiple numerical experiments.

Abstract

Nonintrusive projection-based reduced order models (ROMs) are essential for dynamics prediction in multi-query applications where access to the source of the underlying full order model (FOM) is unavailable; that is, FOM is a black-box. This article proposes a learn-then-project approach for nonintrusive model reduction. In the first step of this approach, high-dimensional stable sparse learned differential operators (S-LDOs) are determined using the generated data. In the second step, the ordinary differential equations, comprising these S-LDOs, are used with suitable dimensionality reduction and low-dimensional subspace projection methods to provide equations for the evolution of reduced states. This approach allows easy integration into the existing intrusive ROM framework to enable nonintrusive model reduction while allowing the use of Petrov-Galerkin projections. The applicability of the proposed approach is demonstrated for Galerkin and LSPG projection-based ROMs through three numerical experiments: 1-D advection equation, 1-D Burgers equation and 2-D advection equation. The results indicate that the proposed nonintrusive ROM strategy provides accurate and stable dynamics prediction.