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Related papers: Data-driven model reduction via non-intrusive opti…

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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

In this work we present an integrated computational pipeline involving several model order reduction techniques for industrial and applied mathematics, as emerging technology for product and/or process design procedures. Its data-driven…

Numerical Analysis · Mathematics 2022-04-05 Marco Tezzele , Nicola Demo , Andrea Mola , Gianluigi Rozza

In the construction of reduced-order models for dynamical systems, linear projection methods, such as proper orthogonal decompositions, are commonly employed. However, for many dynamical systems, the lower dimensional representation of the…

Dynamical Systems · Mathematics 2021-08-31 Sreeram Venkat , Ralph C. Smith , Carl T. Kelley

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

Dissipative partial differential equations that exhibit chaotic dynamics tend to evolve to attractors that exist on finite-dimensional manifolds. We present a data-driven reduced order modeling method that capitalizes on this fact by…

Machine Learning · Computer Science 2022-07-20 Alec J. Linot , Michael D. Graham

We present an efficient data-driven regression approach for constructing reduced-order models (ROMs) of reaction-diffusion systems exhibiting pattern formation. The ROMs are learned non-intrusively from available training data of physically…

Pattern Formation and Solitons · Physics 2025-08-12 Alessandro Alla , Rudy Geelen , Hannah Lu

Reduced-order models are indispensable for multi-query or real-time problems. However, there are still many challenges to constructing efficient ROMs for time-dependent parametrized problems. Using a linear reduced space is inefficient for…

Numerical Analysis · Mathematics 2023-11-17 Junming Duan , Jan S. Hesthaven

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 paper presents a novel non-linear model reduction method: Probabilistic Manifold Decomposition (PMD), which provides a powerful framework for constructing non-intrusive reduced-order models (ROMs) by embedding a high-dimensional system…

Numerical Analysis · Mathematics 2026-01-09 Jiaming Guo , Dunhui Xiao

Autoencoder techniques find increasingly common use in reduced order modeling as a means to create a latent space. This reduced order representation offers a modular data-driven modeling approach for nonlinear dynamical systems when…

Fluid Dynamics · Physics 2021-12-15 Shady E. Ahmed , Omer San , Adil Rasheed , Traian Iliescu

In this paper, we investigate projection-based intrusive and data-driven non-intrusive model order reduction methods in numerical simulation of rotating thermal shallow water equation (RTSWE) in parametric and non-parametric form.…

Numerical Analysis · Mathematics 2023-07-19 Süleyman Yıldız , Murat Uzunca , Bülent Karasözen

Reduced Order Models (ROMs) have gained a great attention by the scientific community in the last years thanks to their capabilities of significantly reducing the computational cost of the numerical simulations, which is a crucial objective…

Numerical Analysis · Mathematics 2024-06-05 Guglielmo Padula , Michele Girfoglio , Gianluigi Rozza

Generally, reduced order models of fluid flows are obtained by projecting the Navier-Stokes equations onto a reduced subspace spanned by vector functions that carry the meaningful information of the dynamics. A common method to generate…

Fluid Dynamics · Physics 2023-09-22 M. Oulghelou , A. Ammar , R. Ayoub

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

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 presents a methodology that enables projection-based model reduction for black-box high-fidelity models such as commercial CFD codes. The methodology specifically addresses the situation where the high-fidelity model may be a…

Analysis of PDEs · Mathematics 2017-10-18 S. Ashwin Renganathan , Yingjie Liu , Dimitri N. Mavris

Reduced-order modeling techniques, including balanced truncation and $\mathcal{H}_2$-optimal model reduction, exploit the structure of linear dynamical systems to produce models that accurately capture the dynamics. For nonlinear systems…

Optimization and Control · Mathematics 2022-01-17 Samuel E. Otto , Alberto Padovan , Clarence W. Rowley

In the present work, we introduce a data-driven approach to enhance the accuracy of non-intrusive Reduced Order Models (ROMs). In particular, we focus on ROMs built using Proper Orthogonal Decomposition (POD) in an under-resolved and…

Numerical Analysis · Mathematics 2026-05-26 Gabriele Codega , Anna Ivagnes , Nicola Demo , Gianluigi Rozza

A data-driven closure modeling based on proper orthogonal decomposition (POD) temporal modes is used to obtain stable and accurate reduced order models (ROMs) of unsteady compressible flows. Model reduction is obtained via Galerkin and…

Fluid Dynamics · Physics 2021-09-22 Victor Zucatti , William Wolf

One of the major challenges in the Bayesian solution of inverse problems governed by partial differential equations (PDEs) is the computational cost of repeatedly evaluating numerical PDE models, as required by Markov chain Monte Carlo…

Computation · Statistics 2016-05-03 Tiangang Cui , Youssef M. Marzouk , Karen E. Willcox