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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…

Machine Learning · Computer Science 2026-03-10 Eric Parish , Anthony Gruber , Patrick Blonigan , Irina Tezaur

Non-intrusive methods have been used since two decades to derive reduced-order models for geometrically nonlinear structures, with a particular emphasis on the so-called STiffness Evaluation Procedure (STEP), relying on the static…

Computational Engineering, Finance, and Science · Computer Science 2022-05-26 Alessandra Vizzaccaro , Arthur Givois , Pierluigi Longobardi , Yichang Shen , Jean-François Deü , Loïc Salles , Cyril Touzé , Olivier Thomas

This work presents a non-intrusive reduced-order modeling framework for dynamical systems with spatially localized features characterized by slow singular value decay. The proposed approach builds upon two existing methodologies for reduced…

Dynamical Systems · Mathematics 2025-06-16 Leonidas Gkimisis , Nicole Aretz , Marco Tezzele , Thomas Richter , Peter Benner , Karen E. Willcox

Identifying differential operators from data is essential for the mathematical modeling of complex physical and biological systems where massive datasets are available. These operators must be stable for accurate predictions for dynamics…

Numerical Analysis · Mathematics 2024-05-02 Aviral Prakash , Yongjie Jessica Zhang

Noise poses a challenge for learning dynamical-system models because already small variations can distort the dynamics described by trajectory data. This work builds on operator inference from scientific machine learning to infer…

Machine Learning · Computer Science 2021-07-27 Wayne Isaac Tan Uy , Yuepeng Wang , Yuxiao Wen , Benjamin Peherstorfer

This work proposes novel techniques for the efficient numerical simulation of parameterized, unsteady partial differential equations. Projection-based reduced order models (ROMs) such as the reduced basis method employ a (Petrov-)Galerkin…

Numerical Analysis · Mathematics 2023-12-05 Nicholas Mueller , Santiago Badia

This paper focuses on the problem of quantifying the effects of model-structure uncertainty in the context of time-evolving dynamical systems. This is motivated by multi-model uncertainty in computer physics simulations: developers often…

Dynamical Systems · Mathematics 2019-02-01 Anthony M. DeGennaro , Nathan M. Urban , Balasubramanya T. Nadiga , Terry Haut

We propose a general dynamic reduced-order modeling framework for typical experimental data: time-resolved sensor data and optional non-time-resolved PIV snapshots. This framework contains four steps. First, the sensor signals are lifted to…

Fluid Dynamics · Physics 2018-05-09 Jean-Christophe Loiseau , Bernd R. Noack , Steven L. Brunton

Sparse regression has emerged as a popular technique for learning dynamical systems from temporal data, beginning with the SINDy (Sparse Identification of Nonlinear Dynamics) framework proposed by arXiv:1509.03580. Quantifying the…

Methodology · Statistics 2023-08-21 Sara Venkatraman , Sumanta Basu , Martin T. Wells

Non-intrusive model reduction is a promising solution to system dynamics prediction, especially in cases where data are collected from experimental campaigns or proprietary software simulations. In this work, we present a method for…

Fluid Dynamics · Physics 2024-04-04 Leonidas Gkimisis , Thomas Richter , Peter Benner

This work primarily focuses on an operator inference methodology aimed at constructing low-dimensional dynamical models based on a priori hypotheses about their structure, often informed by established physics or expert insights. Stability…

Machine Learning · Computer Science 2024-03-04 Igor Pontes Duff , Pawan Goyal , Peter Benner

This paper presents a probabilistic approach to represent and quantify model-form uncertainties in the reduced-order modeling of complex systems using operator inference techniques. Such uncertainties can arise in the selection of an…

Machine Learning · Statistics 2024-11-08 Jin Yi Yong , Rudy Geelen , Johann Guilleminot

Characterizing and controlling nonlinear, multi-scale phenomena play important roles in science and engineering. Cluster-based reduced-order modeling (CROM) was introduced to exploit the underlying low-dimensional dynamics of complex…

Data Analysis, Statistics and Probability · Physics 2017-01-03 Eurika Kaiser , Marek Morzynski , Guillaume Daviller , J Nathan Kutz , Bingni W Brunton , Steven L Brunton

This work presents a nonintrusive physics-preserving method to learn reduced-order models (ROMs) of Lagrangian systems, which includes nonlinear wave equations. Existing intrusive projection-based model reduction approaches construct…

Numerical Analysis · Mathematics 2024-04-05 Harsh Sharma , Boris Kramer

Projection-based nonlinear model order reduction methods can be used to reduce simulation times for the solution of many PDE-constrained problems. It has been observed in literature that such nonlinear reduced-order models (ROMs) based on…

Numerical Analysis · Computer Science 2018-07-02 C. Bach , L. Song , T. Erhart , F. Duddeck

Time-dependent partial differential equations are ubiquitous in physics-based modeling, but they remain computationally intensive in many-query scenarios, such as real-time forecasting, optimal control, and uncertainty quantification.…

Machine Learning · Computer Science 2026-01-26 Sven Dummer , Dongwei Ye , Christoph Brune

Nonlinear aeroelastic reduced-order models (ROMs) based on machine learning or artificial intelligence algorithms can be complex and computationally demanding to train, meaning that for practical aeroelastic applications, the conservative…

Derivation of reduced order representations of dynamical systems requires the modeling of the truncated dynamics on the retained dynamics. In its most general form, this so-called closure model has to account for memory effects. In this…

Dynamical Systems · Mathematics 2020-06-12 Shaowu Pan , Karthik Duraisamy

We present a new scientific machine learning method that learns from data a computationally inexpensive surrogate model for predicting the evolution of a system governed by a time-dependent nonlinear partial differential equation (PDE), an…

Numerical Analysis · Mathematics 2022-02-28 Elizabeth Qian , Ionut-Gabriel Farcas , Karen Willcox

Reduced order models (ROMs) play a critical role in fluid mechanics by providing low-cost predictions, making them an attractive tool for engineering applications. However, for ROMs to be widely applicable, they must not only generalise…

Machine Learning · Computer Science 2025-05-06 Ismaël Zighed , Nicolas Thome , Patrick Gallinari , Taraneh Sayadi