NN-OpInf: an operator inference approach using structure-preserving composable neural networks

TL;DR

NN-OpInf introduces a structure-preserving neural network framework for non-intrusive reduced-order modeling, enhancing accuracy and stability in capturing complex dynamical systems compared to polynomial-based methods.

Contribution

It develops a novel neural operator inference method that enforces physical structure and supports complex dynamics, improving over existing polynomial approaches.

Findings

Demonstrates improved accuracy and robustness in nonlinear problems

Outperforms polynomial OpInf and prior neural ROMs in stability

Enables modeling of non-polynomial nonlinearities with higher fidelity

Abstract

We propose neural network operator inference (NN-OpInf): a structure-preserving, composable, and minimally restrictive operator inference framework for the non-intrusive reduced-order modeling of dynamical systems. The approach learns latent dynamics from snapshot data, enforcing local operator structure such as skew-symmetry, (semi-)positive definiteness, and gradient preservation, while also reflecting complex dynamics by supporting additive compositions of heterogeneous operators. We present practical training strategies and analyze computational costs relative to linear and quadratic polynomial OpInf (P-OpInf). Numerical experiments across several nonlinear and parametric problems demonstrate improved accuracy, stability, and robustness over P-OpInf and prior NN-ROM formulations, particularly when the dynamics are not well represented by polynomial models. These results suggest that NN-OpInf can serve as an effective drop-in replacement for P-OpInf when the dynamics to be modeled contain non-polynomial nonlinearities, offering potential gains in accuracy and out-of-distribution performance at the expense of higher training computational costs and a more difficult, non-convex learning problem.