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

2026-03-09

AI Summary

This work addresses the challenge of accurately representing non-polynomial nonlinear dynamics in non-intrusive reduced-order modeling by proposing a structure-preserving and composable neural operator inference framework. The method learns latent-space dynamics directly from snapshot data and, for the first time, integrates physical structure constraints—such as skew-symmetry and positive definiteness—into a composable neural network architecture. This enables additive composition of heterogeneous operators to capture complex dynamical behaviors. Compared to conventional polynomial operator inference and existing neural-network-based reduced-order models, the proposed framework demonstrates significantly improved accuracy, numerical stability, and out-of-distribution generalization across multiple nonlinear and parametric problems.

Technology Category

• Search and Optimization: Non-convex Optimization
• Machine Learning: Structured Learning
• Constraint Satisfaction and Optimization: Constraint Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

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.

Problem

• non-intrusive reduced-order modeling
• non-polynomial nonlinearities
• operator inference
• dynamical systems
• structure-preserving

Innovation

• operator inference
• structure-preserving neural networks
• non-intrusive reduced-order modeling
• composable dynamics
• non-polynomial nonlinearities