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We propose a new method in which a generative network (GN) integrate into a reduced-order model (ROM) framework is used to solve inverse problems for partial differential equations (PDE). The aim is to match available measurements and…

Machine Learning · Computer Science 2025-06-17 Vinicius L. S. Silva , Claire E. Heaney , Nenko Nenov , Christopher C. Pain

In this work we propose a novel method to ensure important entropy inequalities are satisfied semi-discretely when constructing reduced order models (ROMs) on nonlinear reduced manifolds. We are in particular interested in ROMs of systems…

Numerical Analysis · Mathematics 2024-07-18 Robin Klein , Benjamin Sanderse , Pedro Costa , Rene Pecnik , Ruud Henkes

Reduced Order Models (ROMs) have been regarded as an efficient alternative to conventional high-fidelity Computational Fluid Dynamics (CFD) for accelerating the design and optimization processes in engineering applications. Many industrial…

Numerical Analysis · Mathematics 2026-01-15 Shenhui Ruan , Andreas G. Class , Gianluigi Rozza

In this article, we develop a set-oriented numerical methodology which allows to perform uncertainty quantification (UQ) for dynamical systems from a global point of view. That is, for systems with uncertain parameters we approximate the…

Dynamical Systems · Mathematics 2018-08-29 Michael Dellnitz , Stefan Klus , Adrian Ziessler

A nonlinear-manifold reduced order model (NM-ROM) is a great way of incorporating underlying physics principles into a neural network-based data-driven approach. We combine NM-ROMs with domain decomposition (DD) for efficient computation.…

Numerical Analysis · Mathematics 2023-12-04 Alejandro N. Diaz , Youngsoo Choi , Matthias Heinkenschloss

A previously developed quantum reduced-order model is revised and applied, together with the domain decomposition, to develop the quantum element method (QEM), a methodology for fast and accurate simulation of quantum eigenvalue problems.…

Computational Physics · Physics 2023-04-18 Ming-C. Cheng

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

Reduced order modeling (ROM) is a field of techniques that approximates complex physics-based models of real-world processes by inexpensive surrogates that capture important dynamical characteristics with a smaller number of degrees of…

Machine Learning · Computer Science 2021-08-30 Rachel Cooper , Andrey A. Popov , Adrian Sandu

Model predictive controllers use dynamics models to solve constrained optimal control problems. However, computational requirements for real-time control have limited their use to systems with low-dimensional models. Nevertheless,…

Systems and Control · Electrical Eng. & Systems 2024-10-30 Joseph Lorenzetti , Andrew McClellan , Charbel Farhat , Marco Pavone

This work presents a technique for statistically modeling errors introduced by reduced-order models. The method employs Gaussian-process regression to construct a mapping from a small number of computationally inexpensive `error indicators'…

Numerical Analysis · Computer Science 2015-04-16 Martin Drohmann , Kevin Carlberg

We develop a method for numerical time-domain wave propagation based on the model order reduction approach. The method is built with high-performance computing (HPC) implementation in mind that implies a high level of parallelism and…

Numerical Analysis · Mathematics 2014-06-27 Vladimir Druskin , Alexander V. Mamonov , Mikhail Zaslavsky

Kinetic transport equations are notoriously difficult to simulate because of their complex multiscale behaviors and the need to numerically resolve a high dimensional probability density function. Past literature has focused on building…

Numerical Analysis · Mathematics 2022-11-10 Zhichao Peng , Yanlai Chen , Yingda Cheng , Fengyan Li

Linear reduced-order modeling (ROM) is widely used for efficient simulation of deformation dynamics, but its accuracy is often limited by the fixed linearization of the reduced mapping. We propose a new adaptive strategy for linear ROM that…

Graphics · Computer Science 2025-10-01 Yutian Tao , Maurizio Chiaramonte , Pablo Fernandez

This paper addresses uncertainty quantification (UQ) for problems where scalar (or low-dimensional vector) response quantities are insufficient and, instead, full-field (very high-dimensional) responses are of interest. To do so, an…

Probability · Mathematics 2018-04-18 D. G Giovanis , M. D. Shields

A novel reduced order model (ROM) for incompressible flows is developed by performing a Galerkin projection based on a fully (space and time) discrete full order model (FOM) formulation. This 'discretize-then-project' approach requires no…

Deep learning is gaining increasing popularity for spatiotemporal forecasting. However, prior works have mostly focused on point estimates without quantifying the uncertainty of the predictions. In high stakes domains, being able to…

Artificial Intelligence · Computer Science 2021-06-15 Dongxia Wu , Liyao Gao , Xinyue Xiong , Matteo Chinazzi , Alessandro Vespignani , Yi-An Ma , Rose Yu

We present a globally convergent method to accelerate density-based topology optimization using projection-based reduced-order models (ROMs) and trust-region methods. To accelerate topology optimization, we replace the large-scale finite…

Numerical Analysis · Mathematics 2021-02-03 Masayuki Yano , Tianci Huang , Matthew J. Zahr

We present a comparative computational study of two stabilized Reduced Order Models (ROMs) for the simulation of convection-dominated incompressible flow (Reynolds number of the order of a few thousands). Representative solutions in the…

Fluid Dynamics · Physics 2024-05-01 Pierfrancesco Siena , Michele Girfoglio , Annalisa Quaini , Gianluigi Rozza

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

Partitioned methods allow one to build a simulation capability for coupled problems by reusing existing single-component codes. In so doing, partitioned methods can shorten code development and validation times for multiphysics and…

Numerical Analysis · Mathematics 2022-06-13 Amy de Castro , Paul Kuberry , Irina Tezaur , Pavel Bochev