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Reducing the computational time required by high-fidelity, full order models (FOMs) for the solution of problems in cardiac mechanics is crucial to allow the translation of patient-specific simulations into clinical practice. While FOMs,…

Numerical Analysis · Mathematics 2022-02-09 Ludovica Cicci , Stefania Fresca , Andrea Manzoni , Alfio Quarteroni

Linear reduced-order modeling (ROM) simplifies complex simulations by approximating the behavior of a system using a simplified kinematic representation. Typically, ROM is trained on input simulations created with a specific spatial…

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

One predominant challenge in additive manufacturing (AM) is to achieve specific material properties by manipulating manufacturing process parameters during the runtime. Such manipulation tends to increase the computational load imposed on…

Machine Learning · Computer Science 2023-10-24 Mahmoud Yaseen , Dewen Yushu , Peter German , Xu Wu

Cardiovascular diseases are a leading cause of death in the world, driving the development of patient-specific and benchmark models for blood flow analysis. This chapter provides a theoretical overview of the main categories of Reduced…

Numerical Analysis · Mathematics 2025-10-21 Pierfrancesco Siena , Pasquale Claudio Africa , Michele Girfoglio , Gianluigi Rozza

Accurate error estimation is crucial in model order reduction, both to obtain small reduced-order models and to certify their accuracy when deployed in downstream applications such as digital twins. In existing a posteriori error estimation…

Numerical Analysis · Mathematics 2023-07-24 Sridhar Chellappa , Lihong Feng , Peter Benner

The main goal of this work is to develop a data-driven Reduced Order Model (ROM) strategy from high-fidelity simulation result data of a Full Order Model (FOM). The goal is to predict at lower computational cost the time evolution of…

Computational Engineering, Finance, and Science · Computer Science 2024-09-02 Azzeddine Tiba , Thibault Dairay , Florian de Vuyst , Iraj Mortazavi , Juan-Pedro Berro Ramirez

Reduced Order Modelling (ROM) has been widely used to create lower order, computationally inexpensive representations of higher-order dynamical systems. Using these representations, ROMs can efficiently model flow fields while using…

Fluid Dynamics · Physics 2021-10-13 Pranshu Pant , Ruchit Doshi , Pranav Bahl , Amir Barati Farimani

In many applications, projection-based reduced-order models (ROMs) have demonstrated the ability to provide rapid approximate solutions to high-fidelity full-order models (FOMs). However, there is no a priori assurance that these…

Numerical Analysis · Computer Science 2020-04-22 Philip A. Etter , Kevin T. Carlberg

This paper presents a physics-based data-driven method to learn predictive reduced-order models (ROMs) from high-fidelity simulations, and illustrates it in the challenging context of a single-injector combustion process. The method…

Computational Physics · Physics 2020-07-14 Renee Swischuk , Boris Kramer , Cheng Huang , Karen Willcox

How to build an accurate reduced order model (ROM) for multidimensional time dependent partial differential equations (PDEs) is quite open. In this paper, we propose a new ROM for linear parabolic PDEs. We prove that our new method can be…

Numerical Analysis · Mathematics 2022-09-29 Noel Walkington , Franziska Weber , Yangwen Zhang

We propose a machine learning-based method to build a system of differential equations that approximates the dynamics of 3D electromechanical models for the human heart, accounting for the dependence on a set of parameters. Specifically,…

Numerical Analysis · Mathematics 2022-04-06 Francesco Regazzoni , Matteo Salvador , Luca Dedè , Alfio Quarteroni

This work proposes novel techniques for the efficient numerical simulation of parameterized, unsteady partial differential equations. Projection-based reduced order models (ROMs) such as the reduced basis method employ a (Petrov-)Galerkin…

Numerical Analysis · Mathematics 2023-12-05 Nicholas Mueller , Santiago Badia

In this paper we propose to use model reduction techniques for speeding up the diagonalization-based parallel-in-time (ParaDIAG) preconditioner, for iteratively solving all-at-once systems from evolutionary PDEs. In particular, we use the…

Numerical Analysis · Mathematics 2020-12-17 Jun Liu , Zhu Wang

To speed-up the solution to parametrized differential problems, reduced order models (ROMs) have been developed over the years, including projection-based ROMs such as the reduced-basis (RB) method, deep learning-based ROMs, as well as…

Numerical Analysis · Mathematics 2022-02-08 Ludovica Cicci , Stefania Fresca , Andrea Manzoni

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

Reduced order modeling (ROM) techniques are numerical methods that approximate the solution of parametric partial differential equation (PDE) by properly combining the high-fidelity solutions of the problem obtained for several…

Numerical Analysis · Mathematics 2023-08-08 M. Girfoglio , L. Scandurra , F. Ballarin , G. Infantino , F. Nicolò , A. Montalto , G. Rozza , R. Scrofani , M. Comisso , F. Musumeci

High-fidelity simulations of mixing and combustion processes are generally computationally demanding and time-consuming, hindering their wide application in industrial design and optimization. The present study proposes parametric reduced…

Fluid Dynamics · Physics 2023-08-29 Chenxu Ni , Siyu Ding , Xingjian Wang

Simulating fluid flows in different virtual scenarios is of key importance in engineering applications. However, high-fidelity, full-order models relying, e.g., on the finite element method, are unaffordable whenever fluid flows must be…

Fluid Dynamics · Physics 2021-11-24 Stefania Fresca , Andrea Manzoni

Reduced-order models (ROMs) are widely used in fluid engineering to enable rapid prediction of flow fields for parametric analysis, design optimization, and control applications. Proper orthogonal decomposition (POD) is commonly employed to…

Fluid Dynamics · Physics 2026-02-25 Yuto Nakamura , Shintaro Sato , Naofumi Ohnishi