# Operator inference for non-intrusive model reduction of systems with non-polynomial nonlinear terms

arXiv: https://arxiv.org/abs/2002.09726 · HTML: https://mlsanity.com/paper/2002.09726/

## Key facts

- Cited by 32 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Feb 2020.

## Built on by (most cited first, 30 of 32)

- [Modern Koopman Theory for Dynamical Systems](https://mlsanity.com/paper/2102.12086/) (2021)
- [Enhancing Computational Fluid Dynamics with Machine Learning](https://mlsanity.com/paper/2110.02085/) (2021)
- [gLaSDI: Parametric Physics-informed Greedy Latent Space Dynamics Identification](https://mlsanity.com/paper/2204.12005/) (2022)
- [Machine Learning for Partial Differential Equations](https://mlsanity.com/paper/2303.17078/) (2023)
- [Physics-informed regularization and structure preservation for learning stable reduced models from data with operator inference](https://mlsanity.com/paper/2107.02597/) (2021)
- [Canonical and Noncanonical Hamiltonian Operator Inference](https://mlsanity.com/paper/2304.06262/) (2023)
- [Physics-informed active learning with simultaneous weak-form latent space dynamics identification](https://mlsanity.com/paper/2407.00337/) (2024)
- [Operator inference with roll outs for learning reduced models from scarce and low-quality data](https://mlsanity.com/paper/2212.01418/) (2022)
- [Guaranteed Stable Quadratic Models and their applications in SINDy and Operator Inference](https://mlsanity.com/paper/2308.13819/) (2023)
- [Thermodynamically Consistent Latent Dynamics Identification for Parametric Systems](https://mlsanity.com/paper/2506.08475/) (2025)
- [Deep-HyROMnet: A deep learning-based operator approximation for hyper-reduction of nonlinear parametrized PDEs](https://mlsanity.com/paper/2202.02658/) (2022)
- [Digital Twins in Wind Energy: Emerging Technologies and Industry-Informed Future Directions](https://mlsanity.com/paper/2304.11405/) (2023)
- [Operator inference of non-Markovian terms for learning reduced models from partially observed state trajectories](https://mlsanity.com/paper/2103.01362/) (2021)
- [textitFastSVD-ML-ROM: A Reduced-Order Modeling Framework based on Machine Learning for Real-Time Applications](https://mlsanity.com/paper/2207.11842/) (2022)
- [LQResNet: A Deep Neural Network Architecture for Learning Dynamic Processes](https://mlsanity.com/paper/2103.02249/) (2021)
- [Certified data-driven physics-informed greedy auto-encoder simulator](https://mlsanity.com/paper/2211.13698/) (2022)
- [Nested Operator Inference for Adaptive Data-Driven Learning of Reduced-order Models](https://mlsanity.com/paper/2508.11542/) (2025)
- [Toward Adaptive Non-Intrusive Reduced-Order Models: Design and Challenges](https://mlsanity.com/paper/2602.11378/) (2026)
- [Learning Low-Dimensional Quadratic-Embeddings of High-Fidelity Nonlinear Dynamics using Deep Learning](https://mlsanity.com/paper/2111.12995/) (2021)
- [Distributed computing for physics-based data-driven reduced modeling at scale: Application to a rotating detonation rocket engine](https://mlsanity.com/paper/2407.09994/) (2024)
- [Physically consistent predictive reduced-order modeling by enhancing Operator Inference with state constraints](https://mlsanity.com/paper/2502.03672/) (2025)
- [mLaSDI: Multi-stage latent space dynamics identification](https://mlsanity.com/paper/2506.09207/) (2025)
- [Operator Inference Aware Quadratic Manifolds with Isotropic Reduced Coordinates for Nonintrusive Model Reduction](https://mlsanity.com/paper/2507.20463/) (2025)
- [Sequential decoder training for improved latent space dynamics identification](https://mlsanity.com/paper/2510.03535/) (2025)
- [Rank-Minimizing and Structured Model Inference](https://mlsanity.com/paper/2302.09521/) (2023)
- [FTL: Transfer Learning Nonlinear Plasma Dynamic Transitions in Low Dimensional Embeddings via Deep Neural Networks](https://mlsanity.com/paper/2404.17466/) (2024)
- [SODAs: Sparse Optimization for the Discovery of Differential and Algebraic Equations](https://mlsanity.com/paper/2503.05993/) (2025)
- [Learning reduced-order Quadratic-Linear models in Process Engineering using Operator Inference](https://mlsanity.com/paper/2402.17698/) (2024)
- [Structure-preserving learning for multi-symplectic PDEs](https://mlsanity.com/paper/2409.10432/) (2024)
- [Nonlinear Model Order Reduction of Dynamical Systems in Process Engineering: Review and Comparison](https://mlsanity.com/paper/2506.12819/) (2025)

## Abstract (arXiv)

This work presents a non-intrusive model reduction method to learn low-dimensional models of dynamical systems with non-polynomial nonlinear terms that are spatially local and that are given in analytic form. In contrast to state-of-the-art model reduction methods that are intrusive and thus require full knowledge of the governing equations and the operators of a full model of the discretized dynamical system, the proposed approach requires only the non-polynomial terms in analytic form and learns the rest of the dynamics from snapshots computed with a potentially black-box full-model solver. The proposed method learns operators for the linear and polynomially nonlinear dynamics via a least-squares problem, where the given non-polynomial terms are incorporated in the right-hand side. The least-squares problem is linear and thus can be solved efficiently in practice. The proposed method is demonstrated on three problems governed by partial differential equations, namely the diffusion-reaction Chafee-Infante model, a tubular reactor model for reactive flows, and a batch-chromatography model that describes a chemical separation process. The numerical results provide evidence that the proposed approach learns reduced models that achieve comparable accuracy as models constructed with state-of-the-art intrusive model reduction methods that require full knowledge of the governing equations.