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Traditional reduced order modeling techniques such as the reduced basis (RB) method (relying, e.g., on proper orthogonal decomposition (POD)) suffer from severe limitations when dealing with nonlinear time-dependent parametrized PDEs,…

Numerical Analysis · Mathematics 2020-01-14 Stefania Fresca , Luca Dede , Andrea Manzoni

Kinetic equations are crucial for modeling non-equilibrium phenomena, but their computational complexity is a challenge. This paper presents a data-driven approach using reduced order models (ROM) to efficiently model non-equilibrium flows…

Fluid Dynamics · Physics 2023-10-09 Julian Koellermeier , Philipp Krah , Julius Reiss , Zachary Schellin

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

Numerical simulations are crucial for comprehending how engineering structures behave under extreme conditions, particularly when dealing with thermo-mechanically coupled issues compounded by damage-induced material softening. However, such…

Analysis of PDEs · Mathematics 2024-07-03 Qinghua Zhang , Stephan Ritzert , Jian Zhang , Jannick Kehls , Stefanie Reese , Tim Brepols

In this paper, we study numerically the linear damped second-order hyperbolic partial differential equation (PDE) with affine parameter dependence using a goal-oriented approach by finite element (FE) and reduced basis (RB) methods. The…

Computational Physics · Physics 2013-09-17 Khac Chi Hoang , Pierre Kerfriden , Stephane P. A. Bordas

In this work, the space-time MORe DWR (Model Order Reduction with Dual-Weighted Residual error estimates) framework is extended and further developed for single-phase flow problems in porous media. Specifically, our problem statement is the…

Numerical Analysis · Mathematics 2023-11-16 Hendrik Fischer , Julian Roth , Ludovic Chamoin , Amelie Fau , Mary F. Wheeler , Thomas Wick

In this work, we propose a Proper Orthogonal Decomposition-Reduced Order Model (POD-ROM) applied to time-splitting schemes for solving the Navier-Stokes equations with open boundary conditions. In this method, we combine three strategies to…

Numerical Analysis · Mathematics 2025-06-13 Mejdi Azaïez , Tomás Chacón Rebollo , Carlos Núñez Fernández , Samuele Rubino

Non-intrusive reduced-order models (ROMs) have recently generated considerable interest for constructing computationally efficient counterparts of nonlinear dynamical systems emerging from various domain sciences. They provide a…

Computational Physics · Physics 2020-12-30 Romit Maulik , Themistoklis Botsas , Nesar Ramachandra , Lachlan Robert Mason , Indranil Pan

We present a model reduction approach for the real-time solution of time-dependent nonlinear partial differential equations (PDEs) with parametric dependencies. The approach integrates several ingredients to develop efficient and accurate…

Numerical Analysis · Mathematics 2024-10-04 Ngoc Cuong Nguyen

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

We propose a technique for performing spectral (in time) analysis of spatially-resolved flowfield data, without needing any temporal resolution or information. This is achieved by combining projection-based reduced-order modeling with…

Fluid Dynamics · Physics 2023-07-31 Katherine J. Asztalos , Abdulrahman Almashjary , Scott T. M. Dawson

We propose a component-based (CB) parametric model order reduction (pMOR) formulation for parameterized {nonlinear} elliptic partial differential equations (PDEs). CB-pMOR is designed to deal with large-scale problems for which full-order…

Numerical Analysis · Mathematics 2022-02-22 Kathrin Smetana , Tommaso Taddei

Despite advancements in high-performance computing and modern numerical algorithms, computational cost remains prohibitive for multi-query kinetic plasma simulations. In this work, we develop data-driven reduced-order models (ROMs) for…

Numerical Analysis · Mathematics 2025-02-05 Ping-Hsuan Tsai , Seung Whan Chung , Debojyoti Ghosh , John Loffeld , Youngsoo Choi , Jonathan L. Belof

In this paper, we investigate tensor based nonintrusive reduced-order models (ROMs) for parametric cross-diffusion equations. The full-order model (FOM) consists of ordinary differential equations (ODEs) in matrix or tensor form resulting…

Numerical Analysis · Mathematics 2022-08-01 Bulent Karasozen , Murat Uzunca , Gulden Mulayim

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

The computational cost of parametric studies currently represents the major limitation to the application of simulation-based engineering techniques in a daily industrial environment. This work presents the first nonintrusive implementation…

Numerical Analysis · Mathematics 2020-02-05 Vasileios Tsiolakis , Matteo Giacomini , Ruben Sevilla , Carsten Othmer , Antonio Huerta

A space-time-parameters structure of parametric parabolic PDEs motivates the application of tensor methods to define reduced order models (ROMs). Within a tensor-based ROM framework, the matrix SVD - a traditional dimension reduction…

Numerical Analysis · Mathematics 2024-08-22 Alexander V. Mamonov , Maxim A. Olshanskii

The present work proposes a framework for nonlinear model order reduction based on a Graph Convolutional Autoencoder (GCA-ROM). In the reduced order modeling (ROM) context, one is interested in obtaining real-time and many-query evaluations…

Numerical Analysis · Mathematics 2023-11-08 Federico Pichi , Beatriz Moya , Jan S. Hesthaven

In this study, we present a non-intrusive reduced order modeling (ROM) framework for large-scale quasi-stationary systems. The framework proposed herein exploits the time series prediction capability of long short-term memory (LSTM)…

Computational Engineering, Finance, and Science · Computer Science 2019-11-20 Sk. Mashfiqur Rahman , Suraj Pawar , Omer San , Adil Rasheed , Traian Iliescu

Subspace-valued functions arise in a wide range of problems, including parametric reduced order modeling (PROM). In PROM, each parameter point can be associated with a subspace, which is used for Petrov-Galerkin projections of large system…

Statistics Theory · Mathematics 2021-07-13 Ruda Zhang , Simon Mak , David Dunson