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Related papers: Reduced Order Model Closures: A Brief Tutorial

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This paper explores how to identify a reduced order model (ROM) from a physical system. A ROM captures an invariant subset of the observed dynamics. We find that there are four ways a physical system can be related to a mathematical model:…

Dynamical Systems · Mathematics 2023-07-05 Robert Szalai

The data-driven reduced order models (ROMs) have recently emerged as an efficient tool for the solution of the inverse scattering problems with applications to seismic and sonar imaging. One specification of this approach is that it…

Numerical Analysis · Mathematics 2022-11-16 V. Druskin , S. Moskow , M. Zaslavsky

In this work, a new hybrid predictive Reduced Order Model (ROM) is proposed to solve reacting flow problems. This algorithm is based on a dimensionality reduction using Proper Orthogonal Decomposition (POD) combined with deep learning…

Machine Learning · Computer Science 2023-01-25 Adrián Corrochano , Rodolfo S. M. Freitas , Alessandro Parente , Soledad Le Clainche

Model order reduction (MOR) is crucial for the design process of integrated circuits. Specifically, the vast amount of passive RLCk elements in electromagnetic models extracted from physical layouts exacerbates the extraction time, the…

Rapid simulations of advection-dominated problems are vital for multiple engineering and geophysical applications. In this paper, we present a long short-term memory neural network to approximate the nonlinear component of the reduced-order…

Machine Learning · Computer Science 2019-11-04 Romit Maulik , Vishwas Rao , Sandeep Madireddy , Bethany Lusch , Prasanna Balaprakash

Hybrid physics-machine learning models are increasingly being used in simulations of transport processes. Many complex multiphysics systems relevant to scientific and engineering applications include multiple spatiotemporal scales and…

Fluid Dynamics · Physics 2021-06-09 Shady E. Ahmed , Omer San , Kursat Kara , Rami Younis , Adil Rasheed

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

This paper develops an interpretable, non-intrusive reduced-order modeling technique using regularized kernel interpolation. Existing non-intrusive approaches approximate the dynamics of a reduced-order model (ROM) by solving a data-driven…

Computational Engineering, Finance, and Science · Computer Science 2026-01-26 Alejandro N Diaz , Shane A McQuarrie , John T Tencer , Patrick J Blonigan

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

We consider low-order controller design for large-scale linear time-invariant dynamical systems with inputs and outputs. Model order reduction is a popular technique, but controllers designed for reduced-order models may result in unstable…

Optimization and Control · Mathematics 2018-03-20 Peter Benner , Tim Mitchell , Michael L. Overton

Projection-based nonlinear model order reduction methods can be used to reduce simulation times for the solution of many PDE-constrained problems. It has been observed in literature that such nonlinear reduced-order models (ROMs) based on…

Numerical Analysis · Computer Science 2018-07-02 C. Bach , L. Song , T. Erhart , F. Duddeck

This work studies reduced order modeling (ROM) approaches to speed up the solution of variational data assimilation problems with large scale nonlinear dynamical models. It is shown that a key requirement for a successful reduced order…

Systems and Control · Computer Science 2015-05-20 Răzvan Ştefănescu , Adrian Sandu , Ionel Michael Navon

Moment closure methods appear in myriad scientific disciplines in the modelling of complex systems. The goal is to achieve a closed form of a large, usually even infinite, set of coupled differential (or difference) equations. Each equation…

Statistical Mechanics · Physics 2018-12-24 Christian Kuehn

Reduced order modeling has gained considerable attention in recent decades owing to the advantages offered in reduced computational times and multiple solutions for parametric problems. The focus of this manuscript is the application of…

Numerical Analysis · Mathematics 2018-11-21 Gianluigi Rozza , Haris Malik , Nicola Demo , Marco Tezzele , Michele Girfoglio , Giovanni Stabile , Andrea Mola

We develop an on-the-fly reduced-order model (ROM) integrated with a flow simulation, gradually replacing a corresponding full-order model (FOM) of a physics solver. Unlike offline methods requiring a separate FOM-only simulation prior to…

Fluid Dynamics · Physics 2023-12-01 Seung Won Suh , Seung Whan Chung , Peer-Timo Bremer , Youngsoo Choi

The vast majority of reduced-order models (ROMs) first obtain a low dimensional representation of the problem from high-dimensional model (HDM) training data which is afterwards used to obtain a system of reduced complexity. Unfortunately,…

Numerical Analysis · Mathematics 2023-09-14 Victor Zucatti , Matthew J. Zahr

The objective of this paper is to investigate how noisy and incomplete observations can be integrated in the process of building a reduced-order model. This problematic arises in many scientific domains where there exists a need for…

Machine Learning · Statistics 2018-05-18 Patrick Héas , Cédric Herzet

We examine nonlinear dynamical systems of ordinary differential equations or differential algebraic equations. In an uncertainty quantification, physical parameters are replaced by random variables. The inner variables as well as a quantity…

Numerical Analysis · Mathematics 2019-04-15 Roland Pulch

We present a reduced-order model (ROM) methodology for inverse scattering problems in which the reduced-order models are data-driven, i.e. they are constructed directly from data gathered by sensors. Moreover, the entries of the ROM contain…

Numerical Analysis · Mathematics 2023-06-16 Jörn Zimmerling , Vladimir Druskin , Murthy Guddati , Elena Cherkaev , Rob Remis

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