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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

This work formulates a new approach to reduced modeling of parameterized, time-dependent partial differential equations (PDEs). The method employs Operator Inference, a scientific machine learning framework combining data-driven learning…

Computational Engineering, Finance, and Science · Computer Science 2025-06-16 Shane A McQuarrie , Parisa Khodabakhshi , Karen E Willcox

This work explores the physics-driven machine learning technique Operator Inference (OpInf) for predicting the state of chaotic dynamical systems. OpInf provides a non-intrusive approach to infer approximations of polynomial operators in…

Model-order reduction techniques allow the construction of low-dimensional surrogate models that can accelerate engineering design processes. Often, these techniques are intrusive, meaning that they require direct access to underlying…

Dynamical Systems · Mathematics 2023-08-16 Yevgeniya Filanova , Igor Pontes Duff , Pawan Goyal , Peter Benner

Numerical simulations of complex multiphysics systems, such as char combustion considered herein, yield numerous state variables that inherently exhibit physical constraints. This paper presents a new approach to augment Operator Inference…

Computational Physics · Physics 2026-05-15 Hyeonghun Kim , Boris Kramer

Reduced-order modeling has a long tradition in computational fluid dynamics. The ever-increasing significance of data for the synthesis of low-order models is well reflected in the recent successes of data-driven approaches such as Dynamic…

Dynamical Systems · Mathematics 2020-12-09 Peter Benner , Pawan Goyal , Jan Heiland , Igor Pontes Duff

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

Constrained mechanical systems occur in many applications, such as modeling of robots and other multibody systems. In this case, the motion is governed by a system of differential-algebraic equations (DAE), often with large and sparse…

Dynamical Systems · Mathematics 2025-07-09 Peter Benner , Yevgeniya Filanova , Igor Pontes Duff , Jens Saak

This paper proposes a novel approach for learning a data-driven quadratic manifold from high-dimensional data, then employing this quadratic manifold to derive efficient physics-based reduced-order models. The key ingredient of the approach…

Numerical Analysis · Mathematics 2022-12-29 Rudy Geelen , Stephen Wright , Karen Willcox

This work develops a non-intrusive, data-driven surrogate modeling framework based on Operator Inference (OpInf) for rapidly solving parameter-dependent matrix equations in many-query settings. Motivated by the requirements of the OpInf…

Numerical Analysis · Mathematics 2025-11-21 Xuelian Wen , Qiuqi Li , Juan Zhang

Recent years have witnessed the promise of coupling machine learning methods and physical domain-specific insights for solving scientific problems based on partial differential equations (PDEs). However, being data-intensive, these methods…

Machine Learning · Computer Science 2025-06-03 Wuyang Chen , Jialin Song , Pu Ren , Shashank Subramanian , Dmitriy Morozov , Michael W. Mahoney

This work presents structure-preserving Lift & Learn, a scientific machine learning method that employs lifting variable transformations to learn structure-preserving reduced-order models for nonlinear partial differential equations (PDEs)…

Machine Learning · Computer Science 2026-01-09 Harsh Sharma , Juan Diego Draxl Giannoni , Boris Kramer

In this work, we investigate a skew-symmetric parameterization for energy-preserving quadratic operators. Earlier, [Goyal et al., 2023] proposed this parameterization to enforce energy-preservation for quadratic terms in the context of…

Numerical Analysis · Mathematics 2025-03-17 Leonidas Gkimisis , Igor Pontes Duff , Pawan Goyal , Peter Benner

This paper presents an energy-preserving machine learning method for inferring reduced-order models (ROMs) by exploiting the multi-symplectic form of partial differential equations (PDEs). The vast majority of energy-preserving…

Machine Learning · Computer Science 2024-09-17 Süleyman Yıldız , Pawan Goyal , Peter Benner

Mechanical systems are often characterized only by their response to certain loads known from experiments or simulations. The obtained data can be used for various purposes: system analysis, design of mathematical models, or construction of…

Dynamical Systems · Mathematics 2026-01-05 Yevgeniya Filanova , Igor Pontes Duff , Pawan Goyal , Peter Benner

Existing model reduction techniques for high-dimensional models of conservative partial differential equations (PDEs) encounter computational bottlenecks when dealing with systems featuring non-polynomial nonlinearities. This work presents…

Numerical Analysis · Mathematics 2025-10-21 Harsh Sharma , Juan Diego Draxl Giannoni , Boris Kramer

In this work, we address the challenge of efficiently modeling dynamical systems in process engineering. We use reduced-order model learning, specifically operator inference. This is a non-intrusive, data-driven method for learning…

Numerical Analysis · Mathematics 2024-07-31 Ion Victor Gosea , Luisa Peterson , Pawan Goyal , Jens Bremer , Kai Sundmacher , Peter Benner

This paper presents a block-structured formulation of Operator Inference as a way to learn structured reduced-order models for multiphysics systems. The approach specifies the governing equation structure for each physics component and the…

Computational Engineering, Finance, and Science · Computer Science 2026-02-20 Benjamin G. Zastrow , Anirban Chaudhuri , Karen E. Willcox , Anthony Ashley , Michael Chamberlain Henson

This paper presents a data-driven, nested Operator Inference (OpInf) approach for learning physics-informed reduced-order models (ROMs) from snapshot data of high-dimensional dynamical systems. The approach exploits the inherent hierarchy…

Machine Learning · Computer Science 2025-08-18 Nicole Aretz , Karen Willcox

This paper derives predictive reduced-order models for rocket engine combustion dynamics via Operator Inference, a scientific machine learning approach that blends data-driven learning with physics-based modeling. The non-intrusive nature…

Computational Engineering, Finance, and Science · Computer Science 2021-10-19 Shane A. McQuarrie , Cheng Huang , Karen E. Willcox
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