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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

Partial differential equations can be used to model many problems in several fields of application including, e.g., fluid mechanics, heat and mass transfer, and electromagnetism. Accurate discretization methods (e.g., finite element or…

Numerical Analysis · Mathematics 2022-03-18 Pierfrancesco Siena , Michele Girfoglio , Gianluigi Rozza

A state-space representation of water quality dynamics describing disinfectant (e.g., chlorine) transport dynamics in drinking water distribution networks has been recently proposed. Such representation is a byproduct of space- and…

Systems and Control · Electrical Eng. & Systems 2022-06-15 Shen Wang , Ahmad F. Taha , Ankush Chakrabarty , Lina Sela , Ahmed Abokifa

This paper deals with model-order reduction of parametric partial differential equations (PPDE). More specifically, we consider the problem of finding a good approximation subspace of the solution manifold of the PPDE when only partial…

Numerical Analysis · Mathematics 2017-07-04 C. Herzet , P. Héas , A. Drémeau

Numerical simulations of contaminant dispersion, as after a gas leakage incident on a chemical plant, can provide valuable insights for both emergency response and preparedness. Simulation approaches combine incompressible Navier-Stokes…

Computational Engineering, Finance, and Science · Computer Science 2026-03-05 Lisa Kühn , Jacopo Bonari , Max von Danwitz , Alexander Popp

High-fidelity numerical simulations of partial differential equations (PDEs) given a restricted computational budget can significantly limit the number of parameter configurations considered and/or time window evaluated for modeling a given…

Machine Learning · Computer Science 2023-09-04 Paolo Conti , Mengwu Guo , Andrea Manzoni , Attilio Frangi , Steven L. Brunton , J. Nathan Kutz

Deep learning-based reduced order models (DL-ROMs) have been recently proposed to overcome common limitations shared by conventional reduced order models (ROMs) - built, e.g., through proper orthogonal decomposition (POD) - when applied to…

Numerical Analysis · Mathematics 2021-11-03 Stefania Fresca , Andrea Manzoni

In dynamical system theory, the process of obtaining a reduced-order approximation of the high-order model is called model order reduction. The closeness of the reduced-order model to the original model is generally gauged by using system…

Systems and Control · Electrical Eng. & Systems 2023-03-07 Umair Zulfiqar , Xin Dua , Qiuyan Song , Muwahida Liaquat , Victor Sreeram

A method for adaptive model order reduction for nonsmooth discrete element simulation is developed and analysed in numerical experiments. Regions of the granular media that collectively move as rigid bodies are substituted with rigid bodies…

Computational Physics · Physics 2015-12-02 Martin Servin , Da Wang

pyMOR is a free software library for model order reduction that includes both reduced basis and system-theoretic methods. All methods are implemented in terms of abstract vector and operator interfaces, which allows direct integration of…

Mathematical Software · Computer Science 2022-04-01 Petar Mlinarić , Stephan Rave , Jens Saak

This paper proposes a non-intrusive, data-driven reduced-order modeling framework for stochastic optimal control problems governed by partial differential equations. The control problem is formulated with a quadratic cost functional and…

Optimization and Control · Mathematics 2026-05-20 Lingling Ma , Jingyi Zhang , Qiuqi Li

In the present work, we introduce a novel approach to enhance the precision of reduced order models by exploiting a multi-fidelity perspective and DeepONets. Reduced models provide a real-time numerical approximation by simplifying the…

Numerical Analysis · Mathematics 2023-11-21 Nicola Demo , Marco Tezzele , Gianluigi Rozza

This paper is concerned with the design of a non-intrusive model order reduction (MOR) for the system of parametric time-domain Maxwell equations. A time- and parameter-independent reduced basis (RB) is constructed by using a two-step…

Numerical Analysis · Mathematics 2021-03-24 Ying Zhao , Liang Li , Kun Li

An adaptive projection-based reduced-order model (ROM) formulation is presented for model-order reduction of problems featuring chaotic and convection-dominant physics. An efficient method is formulated to adapt the basis at every time-step…

Computational Physics · Physics 2023-08-09 Cheng Huang , Karthik Duraisamy

This work introduces a new method to efficiently solve optimization problems constrained by partial differential equations (PDEs) with uncertain coefficients. The method leverages two sources of inexactness that trade accuracy for speed:…

Optimization and Control · Mathematics 2019-05-20 Matthew J. Zahr , Kevin T. Carlberg , Drew P. Kouri

Orthogonal projection-based reduced order models (PROM) are the output of widely-used model reduction methods. In this work, a novel product form is derived for the reduction error system of these reduced models, and it is shown that any…

Systems and Control · Electrical Eng. & Systems 2022-01-03 Noam Leiter , Daniel Zelazo

Clinical oriented applications of computational electrocardiology require efficient and reliable identification of patient-specific parameters of mathematical models based on available measures. In particular, the estimation of cardiac…

Numerical Analysis · Mathematics 2016-11-01 Huanhuan Yang , Alessandro Veneziani

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

Accurate simulations are essential for engineering applications, and intricate continuum mechanical material models are constructed to achieve this goal. However, the increasing complexity of the material models and geometrical properties…

Computational Engineering, Finance, and Science · Computer Science 2023-11-30 Steffen Kastian , Jannick Kehls , Tim Brepols , Stefanie Reese

In this contribution, we coupled the isogeometric analysis to a reduced order modelling technique in order to provide a computationally efficient solution in parametric domains. In details, we adopt the free-form deformation method to…

Numerical Analysis · Mathematics 2020-11-23 Fabrizio Garotta , Nicola Demo , Marco Tezzele , Massimo Carraturo , Alessandro Reali , Gianluigi Rozza