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Most model reduction methods reduce the state dimension and then temporally evolve a set of coefficients that encode the state in the reduced representation. In this paper, we instead employ an efficient representation of the entire…

Numerical Analysis · Mathematics 2025-11-03 Peter Frame , Cong Lin , Oliver Schmidt , Aaron Towne

This work investigates projection-based Reduced-Order Models (ROMs) formulated in the frequency domain, employing a space-time basis constructed with Spectral Proper Orthogonal Decomposition to efficiently represent dominant spatio-temporal…

Fluid Dynamics · Physics 2026-01-12 Xiaodong Li , Davide Lasagna

Reduced order modeling (ROM) aims to mitigate computational complexity by reducing the size of a high-dimensional state space. In this study, we demonstrate the efficiency, accuracy, and stability of proper orthogonal decomposition…

Atmospheric and Oceanic Physics · Physics 2025-04-17 Yusuf Aydogdu , Navaratnam Sri Namachchivaya

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

Reduced order modeling lowers the computational cost of solving PDEs by learning a low-order spatial representation from data and dynamically evolving these representations using manifold projections of the governing equations. While…

Fluid Dynamics · Physics 2024-07-10 Vedant Puri , Aviral Prakash , Levent Burak Kara , Yongjie Jessica Zhang

A nonintrusive model order reduction method for bilinear stochastic differential equations with additive noise is proposed. A reduced order model (ROM) is designed in order to approximate the statistical properties of high-dimensional…

Numerical Analysis · Mathematics 2025-06-11 M. A. Freitag , J. M. Nicolaus , M. Redmann

In this paper, we propose an efficient proper orthogonal decomposition based reduced-order model(POD-ROM) for nonstationary Stokes equations, which combines the classical projection method with POD technique. This new scheme mainly owns two…

Numerical Analysis · Mathematics 2023-04-04 Xi Li , Yan Luo , Minfu Feng

Nonintrusive projection-based reduced order models (ROMs) are essential for dynamics prediction in multi-query applications where access to the source of the underlying full order model (FOM) is unavailable; that is, FOM is a black-box.…

Computational Physics · Physics 2024-10-16 Aviral Prakash , Yongjie Jessica Zhang

A classical reduced order model (ROM) for dynamical problems typically involves only the spatial reduction of a given problem. Recently, a novel space-time ROM for linear dynamical problems has been developed, which further reduces the…

Numerical Analysis · Mathematics 2025-11-06 Youngkyu Kim , Karen May Wang , Youngsoo Choi

In this work, we propose a Proper Orthogonal Decomposition-Reduced Order Model (POD-ROM) applied to time-splitting schemes for solving the Navier-Stokes equations with open boundary conditions. In this method, we combine three strategies to…

Numerical Analysis · Mathematics 2025-06-13 Mejdi Azaïez , Tomás Chacón Rebollo , Carlos Núñez Fernández , Samuele Rubino

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

Trajectory-wise data-driven reduced order models (ROMs) tend to be sensitive to training data, and thus lack robustness. We propose to construct a robust stochastic ROM closure (S-ROM) from data consisting of multiple trajectories from…

Numerical Analysis · Mathematics 2022-09-08 Fei Lu , Changhong Mou , Honghu Liu , Traian Iliescu

In this study, we present a non-intrusive reduced order modeling (ROM) framework for large-scale quasi-stationary systems. The framework proposed herein exploits the time series prediction capability of long short-term memory (LSTM)…

Computational Engineering, Finance, and Science · Computer Science 2019-11-20 Sk. Mashfiqur Rahman , Suraj Pawar , Omer San , Adil Rasheed , Traian Iliescu

Feedback control synthesis for nonlinear, parameter-dependent fluid flow control problems is considered. The optimal feedback law requires the solution of the Hamilton-Jacobi-Bellman (HJB) PDE suffering the curse of dimensionality. This is…

Optimization and Control · Mathematics 2023-11-29 Sergey Dolgov , Dante Kalise , Luca Saluzzi

Although projection-based reduced-order models (ROMs) for parameterized nonlinear dynamical systems have demonstrated exciting results across a range of applications, their broad adoption has been limited by their intrusivity: implementing…

Machine Learning · Computer Science 2021-06-18 Zhe Bai , Liqian Peng

Time-delay dynamical systems inherently embody infinite-dimensional dynamics, thereby amplifying their complexity. This aspect is especially notable in nonlinear dynamical systems, which frequently defy analytical solutions and necessitate…

Dynamical Systems · Mathematics 2025-05-20 Yuan Tang , Mingwu Li

Reduced Order Modeling is of paramount importance for efficiently inferring high-dimensional spatio-temporal fields in parametric contexts, enabling computationally tractable parametric analyses, uncertainty quantification and control.…

Machine Learning · Computer Science 2025-02-18 Matteo Tomasetto , Jan P. Williams , Francesco Braghin , Andrea Manzoni , J. Nathan Kutz

Numerous cutting-edge scientific technologies originate at the laboratory scale, but transitioning them to practical industry applications is a formidable challenge. Traditional pilot projects at intermediate scales are costly and…

Computational Engineering, Finance, and Science · Computer Science 2024-01-22 Seung Whan Chung , Youngsoo Choi , Pratanu Roy , Thomas Moore , Thomas Roy , Tiras Y. Lin , Du Y. Nguyen , Christopher Hahn , Eric B. Duoss , Sarah E. Baker

We apply the Proper Orthogonal Decomposition (POD) method for the efficient simulation of several scenarios undergone by Micro-Electro-Mechanical-Systems, involving nonlinearites of geometric and electrostatic nature. The former type of…

Numerical Analysis · Mathematics 2022-02-22 Gobat G. , Opreni A. , Fresca S. , Manzoni A. , Frangi A

A novel method for the numerical prediction of the slowly varying dynamics of nonlinear mechanical systems has been developed. The method is restricted to the regime of an isolated nonlinear mode and consists of a two-step procedure: In the…

Computational Engineering, Finance, and Science · Computer Science 2021-01-01 Malte Krack , Lars Panning-von Scheidt , Jörg Wallaschek
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