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The radiative transfer equation (RTE) is a fundamental mathematical model to describe physical phenomena involving the propagation of radiation and its interactions with the host medium. Deterministic methods can produce accurate solutions…

Numerical Analysis · Mathematics 2025-12-18 Kimberly Matsuda , Yanlai Chen , Yingda Cheng , Fengyan Li

We present a novel reduced-order Model (ROM) that leverages optimal transport (OT) theory and displacement interpolation to enhance the representation of nonlinear dynamics in complex systems. While traditional ROM techniques face…

Numerical Analysis · Mathematics 2024-11-14 Moaad Khamlich , Federico Pichi , Michele Girfoglio , Annalisa Quaini , Gianluigi Rozza

Continuous monitoring and real-time control of high-dimensional distributed systems are often crucial in applications to ensure a desired physical behavior, without degrading stability and system performances. Traditional feedback control…

Optimization and Control · Mathematics 2024-12-16 Matteo Tomasetto , Francesco Braghin , Andrea Manzoni

Soft robots offer remarkable adaptability and safety advantages over rigid robots, but modeling their complex, nonlinear dynamics remains challenging. Strain-based models have recently emerged as a promising candidate to describe such…

Predicting the electrical behavior of the heart, from the cellular scale to the tissue level, relies on the formulation and numerical approximation of coupled nonlinear dynamical systems. These systems describe the cardiac action potential,…

Computational Physics · Physics 2021-01-27 Stefania Fresca , Andrea Manzoni , Luca Dedè , Alfio Quarteroni

A large number of theoretically predicted waveforms are required by matched-filtering searches for the gravitational-wave signals produced by compact binary coalescence. In order to substantially alleviate the computational burden in…

General Relativity and Quantum Cosmology · Physics 2018-06-11 Dániel Barta , Mátyás Vasúth

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

In this paper, a type of novel projection-based, time-segmented reduced order model (ROM) is proposed for dynamic fluid-structure interaction (FSI) problems based upon the arbitrary Lagrangian--Eulerian (ALE)-finite element method (FEM) in…

Computational Engineering, Finance, and Science · Computer Science 2024-02-16 Qijia Zhai , Shiquan Zhang , Pengtao Sun , Xiaoping Xie

In this paper, we present a new nonintrusive reduced basis method when a cheap low-fidelity model and expensive high-fidelity model are available. The method relies on proper orthogonal decomposition (POD) to generate the high-fidelity…

Machine Learning · Statistics 2019-02-06 Chuan Lu , Xueyu Zhu

This study concerns the development of a data-based compact model for the prediction of the fluid temperature evolution in district heating (DH) pipeline networks. This so-called "reduced-order model" (ROM) is obtained from reduction of the…

Numerical Analysis · Mathematics 2022-11-28 Mengting Jiang , Michel Speetjens , Camilo Rindt , David Smeulders

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

For a nonlinear dynamical system that depends on parameters, the paper introduces a novel tensorial reduced-order model (TROM). The reduced model is projection-based, and for systems with no parameters involved, it resembles proper…

Numerical Analysis · Mathematics 2023-11-16 Alexander V. Mamonov , Maxim A. Olshanskii

Traditional projection-based reduced-order modeling approximates the full-order model by projecting it onto a linear subspace. With a fast-decaying Kolmogorov $n$-width of the solution manifold, the resulting reduced-order model (ROM) can…

Numerical Analysis · Mathematics 2026-03-27 Lijie Ji , Sabrina Rashid , Yanlai Chen , Zhu Wang

In the reduced order modeling (ROM) framework, the solution of a parametric partial differential equation is approximated by combining the high-fidelity solutions of the problem at hand for several properly chosen configurations. Examples…

Numerical Analysis · Mathematics 2019-05-16 Nicola Demo , Marco Tezzele , Andrea Mola , Gianluigi Rozza

Real-world systems are often characterized by high-dimensional nonlinear dynamics, making them challenging to control in real time. While reduced-order models (ROMs) are frequently employed in model-based control schemes, dimensionality…

Systems and Control · Electrical Eng. & Systems 2023-09-13 John Irvin Alora , Luis A. Pabon , Johannes Köhler , Mattia Cenedese , Ed Schmerling , Melanie N. Zeilinger , George Haller , Marco Pavone

We develop a Reduced Order Model (ROM) for a Large Eddy Simulation (LES) approach that combines a three-step algorithm called Evolve-Filter-Relax (EFR) with a computationally efficient finite volume method. The main novelty of our ROM lies…

Numerical Analysis · Mathematics 2021-07-28 Michele Girfoglio , Annalisa Quaini , Gianluigi Rozza

Recent research in non-intrusive data-driven model order reduction (MOR) enabled accurate and efficient approximation of parameterized ordinary differential equations (ODEs). However, previous studies have focused on constant parameters,…

Dynamical Systems · Mathematics 2021-10-27 Jonas Kneifl , Julian Hay , Jörg Fehr

We propose a space-time reduced-order model (ROM) for nonlinear dynamical systems, building upon previous work on linear systems. Whereas most ROMs are space-only in that they reduce only the spatial dimension of the state, the proposed…

Numerical Analysis · Mathematics 2025-11-03 Peter Frame , Aaron Towne

Reduced order models (ROM) can represent spatiotemporal processes in significantly fewer dimensions and can be solved many orders faster than their governing partial differential equations (PDEs). For example, using a proper orthogonal…

Machine Learning · Computer Science 2025-12-24 Shane X. Coffing , John Tipton , Arvind T. Mohan , Darren Engwirda

The Kolmogorov $n$-width of the solution manifolds of transport-dominated problems can decay slowly. As a result, it can be challenging to design efficient and accurate reduced order models (ROMs) for such problems. To address this issue,…

Numerical Analysis · Mathematics 2022-06-29 Zhichao Peng , Min Wang , Fengyan Li