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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

In this paper, we present a generic approach of a dynamical data-driven model order reduction technique for three-dimensional fluid-structure interaction problems. A low-order continuous linear differential system is identified from…

Computational Engineering, Finance, and Science · Computer Science 2023-01-25 Claire Dupont , Florian De Vuyst , Anne-Virginie Salsac

The parametric radiative transfer equation (RTE) arises in multi-query applications, such as design optimization, inverse problems, and uncertainty quantification, which require solving the RTE multiple times for various parameters.…

Numerical Analysis · Mathematics 2025-09-08 Ning Tang , Zhichao Peng

This paper presents a method for the numerical treatment of reaction-convection-diffusion problems with parameter-dependent coefficients that are arbitrary rough and possibly varying at a very fine scale. The presented technique combines…

Numerical Analysis · Mathematics 2022-11-29 Francesca Bonizzoni , Moritz Hauck , Daniel Peterseim

In this work, a numerical simulation of 1D Burgers' equation is developed using finite difference method and a reduced order model (ROM) of the simulation is developed using proper orthogonal decomposition (POD). The objective of this work…

Numerical Analysis · Mathematics 2023-03-14 Neelakantan Padmanabhan

Highly accurate simulations of complex phenomena governed by partial differential equations (PDEs) typically require intrusive methods and entail expensive computational costs, which might become prohibitive when approximating steady-state…

Machine Learning · Computer Science 2023-05-17 Paolo Conti , Giorgio Gobat , Stefania Fresca , Andrea Manzoni , Attilio Frangi

One of the principal barriers in developing accurate and tractable predictive models in turbulent flows with a large number of species is to track every species by solving a separate transport equation, which can be computationally…

Computational Engineering, Finance, and Science · Computer Science 2021-05-19 Donya Ramezanian , Arash G. Nouri , Hessam Babaee

Data-driven reduced order models (ROMs) recently emerged as powerful tool for the solution of inverse scattering problems. The main drawback of this approach is that it was limited to the measurement arrays with reciprocally collocated…

Numerical Analysis · Mathematics 2022-07-27 Vladimir Druskin , Shari Moskow , Mikhail Zaslavsky

In this paper, we propose an equation-based parametric Reduced Order Model (ROM), whose accuracy is improved with data-driven terms added into the reduced equations. These additions have the aim of reintroducing contributions that in…

Numerical Analysis · Mathematics 2024-06-07 Anna Ivagnes , Giovanni Stabile , Gianluigi Rozza

This work introduces a reduced order modeling (ROM) framework for the solution of parameterized second-order linear elliptic partial differential equations formulated on unfitted geometries. The goal is to construct efficient…

Numerical Analysis · Mathematics 2025-10-14 Margarita Chasapi , Pablo Antolin , Annalisa Buffa

We extend our previous work [F. Henr'iquez and J. S. Hesthaven, arXiv:2403.02847 (2024)] to the linear, second-order wave equation in bounded domains. This technique uses two widely known mathematical tools to construct a fast and efficient…

Numerical Analysis · Mathematics 2026-04-13 Fernando Henriquez , Jan S. Hesthaven

The direct monitoring of a rotating detonation engine (RDE) combustion chamber has enabled the observation of combustion front dynamics that are composed of a number of co- and/or counter-rotating coherent traveling shock waves whose…

Dynamical Systems · Mathematics 2021-05-19 Ariana Mendible , James Koch , Henning Lange , Steven L. Brunton , J. Nathan Kutz

Image modeling and simulation are critical to extending the limits of leading edge lithography technologies used for IC making. Simultaneous source mask optimization (SMO) has become an important objective in the field of computational…

Probabilistic variants of Model Order Reduction (MOR) methods have recently emerged for improving stability and computational performance of classical approaches. In this paper, we propose a probabilistic Reduced Basis Method (RBM) for the…

Numerical Analysis · Mathematics 2023-12-06 Marie Billaud-Friess , Arthur Macherey , Anthony Nouy , Clémentine Prieur

Computational fluid dynamics (CFD) simulations play an important role in engineering science and applications, however, it is not applicable for problems requiring a large number of repeated calculations. Accordingly, many reduced-order…

Fluid Dynamics · Physics 2026-05-28 Shan Ding , Yongfu Tian , Rui Yang

Maximum distance separable (MDS) codes are widely used in distributed storage, but naively repairing a single failure in an $(n,k)$ MDS code requires downloading the full contents of $k$ surviving nodes. Minimum storage regenerating (MSR)…

Information Theory · Computer Science 2026-05-26 Jing Qiu , Weijun Fang , Shu-Tao Xia , Fang-Wei Fu

The onerous task of repeatedly resolving certain parametrized partial differential equations (pPDEs) in, e.g. the optimization context, makes it imperative to design vastly more efficient numerical solvers without sacrificing any accuracy.…

Numerical Analysis · Mathematics 2019-06-19 Yanlai Chen , Sigal Gottlieb , Lijie Ji , Yvon Maday , Zhenli Xu

The investigation of fluid-solid systems is very important in a lot of industrial processes. From a computational point of view, the simulation of such systems is very expensive, especially when a huge number of parametric configurations…

Reduced order modeling lowers the computational cost of solving PDEs by learning a low-order spatial representation from data and dynamically evolving these representations using manifold projections of the governing equations. While…

Fluid Dynamics · Physics 2024-07-10 Vedant Puri , Aviral Prakash , Levent Burak Kara , Yongjie Jessica Zhang

The Reduced Basis (RB) method is a well established method for the model order reduction of problems formulated as parametrized partial differential equations. One crucial requirement for the application of RB schemes is the availability of…

Numerical Analysis · Mathematics 2016-11-25 Andreas Buhr , Christian Engwer , Mario Ohlberger , Stephan Rave