English
Related papers

Related papers: Operator inference for non-intrusive model reducti…

200 papers

Learning dynamical models from data plays a vital role in engineering design, optimization, and predictions. Building models describing dynamics of complex processes (e.g., weather dynamics, or reactive flows) using empirical knowledge or…

Machine Learning · Computer Science 2024-09-21 Pawan Goyal , Peter Benner

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

This work presents a tensorial approach to constructing data-driven reduced-order models corresponding to semi-discrete partial differential equations with canonical Hamiltonian structure. By expressing parameter-varying operators with…

Numerical Analysis · Mathematics 2025-05-14 Arjun Vijaywargiya , Shane A. McQuarrie , Anthony Gruber

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

In this study, we present a tensor--train framework for nonintrusive operator inference aimed at learning discrete operators and using them to predict solutions of physical governing equations. Our framework comprises three approaches:…

Numerical Analysis · Mathematics 2025-09-11 Engin Danis , Duc Truong , Kim Ø. Rasmussen§ , Boian S. Alexandrov

Traditional projection-based reduced-order modeling approximates the full-order model by projecting it onto a linear subspace. With a fast-decaying Kolmogorov $n$-width of the solution manifold, the resulting reduced-order model (ROM) can…

Numerical Analysis · Mathematics 2026-03-27 Lijie Ji , Sabrina Rashid , Yanlai Chen , Zhu Wang

The increasing size and complexity of modern power systems have led to a high-dimensional mathematical model for transient stability studies, rendering full-scale simulations computationally burdensome. While dimensionality reduction is…

Dynamical Systems · Mathematics 2025-12-08 Farhana Farooq , Danish Rafiq

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

On the basis of input-output time-domain data collected from a complex simulator, this paper proposes a constructive methodology to infer a reduced-order linear, bilinear or quadratic time invariant dynamical model reproducing the…

Dynamical Systems · Mathematics 2020-12-15 Charles Poussot-Vassal , Tiphaine Sabatier , Claire Sarrat , Pierre Vuillemin

A nonintrusive model order reduction method for bilinear stochastic differential equations with additive noise is proposed. A reduced order model (ROM) is designed in order to approximate the statistical properties of high-dimensional…

Numerical Analysis · Mathematics 2025-06-11 M. A. Freitag , J. M. Nicolaus , M. Redmann

Many-query computations, in which a computational model for an engineering system must be evaluated many times, are crucial in design and control. For systems governed by partial differential equations (PDEs), typical high-fidelity…

Numerical Analysis · Mathematics 2024-02-09 Tomoki Koike , Elizabeth Qian

In this paper, we address an extension of the Loewner framework for learning quadratic control systems from input-output data. The proposed method first constructs a reduced-order linear model from measurements of the classical transfer…

Optimization and Control · Mathematics 2020-12-04 Ion Victor Gosea , Dimitrios S. Karachalios , Athanasios C. Antoulas

Projection-based model reduction has become a popular approach to reduce the cost associated with integrating large-scale dynamical systems so they can be used in many-query settings such as optimization and uncertainty quantification. For…

Numerical Analysis · Mathematics 2020-08-26 Han Gao , Jian-Xun Wang , Matthew J. Zahr

Multiple model reduction techniques have been proposed to tackle linear and non linear problems. Intrusive model order reduction techniques exhibit high accuracy levels, however, they are rarely used as a standalone industrial tool, because…

Computational Engineering, Finance, and Science · Computer Science 2025-04-10 Mikhael Tannous , Chady Ghnatios , Eivind Fonn , Trond Kvamsdal , Francisco Chinesta

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

Analyzing signals arising from dynamical systems typically requires many modeling assumptions and parameter estimation. In high dimensions, this modeling is particularly difficult due to the "curse of dimensionality". In this paper, we…

Systems and Control · Computer Science 2016-12-21 Tal Shnitzer , Ronen Talmon , Jean-Jacques Slotine

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

We propose a kernel-spectral embedding algorithm for learning low-dimensional nonlinear structures from high-dimensional and noisy observations, where the datasets are assumed to be sampled from an intrinsically low-dimensional manifold and…

Machine Learning · Statistics 2023-07-07 Xiucai Ding , Rong Ma

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

Recently developed reduced-order modeling techniques aim to approximate nonlinear dynamical systems on low-dimensional manifolds learned from data. This is an effective approach for modeling dynamics in a post-transient regime where the…

Dynamical Systems · Mathematics 2023-09-27 Samuel E. Otto , Gregory R. Macchio , Clarence W. Rowley