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Natural convection in porous media is a highly nonlinear multiphysical problem relevant to many engineering applications (e.g., the process of $\mathrm{CO_2}$ sequestration). Here, we present a non-intrusive reduced order model of natural…

Computational Engineering, Finance, and Science · Computer Science 2023-08-30 T. Kadeethum , F. Ballarin , Y. Choi , D. O'Malley , H. Yoon , N. Bouklas

Solving optimal control problems for transport-dominated partial differential equations (PDEs) can become computationally expensive, especially when dealing with high-dimensional systems. To overcome this challenge, we focus on developing…

Optimization and Control · Mathematics 2024-12-30 Tobias Breiten , Shubhaditya Burela , Philipp Schulze

Advection-dominated problems are predominantly noticed in nature, engineering systems, and various industrial processes. Traditional linear compression methods, such as proper orthogonal decomposition (POD) and reduced basis (RB) methods…

Numerical Analysis · Mathematics 2025-07-16 Harshith Gowrachari , Nicola Demo , Giovanni Stabile , Gianluigi Rozza

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

In this work, a novel method with an adaptive functional basis for reduced order models (ROM) based on proper orthogonal decomposition (POD) is introduced. The method is intended to be applied in particular to hydrocarbon reservoir…

Numerical Analysis · Mathematics 2021-06-23 Dmitry Voloskov , Dimitri Pissarenko

Computing reduced-order models using non-intrusive methods is particularly attractive for systems that are simulated using black-box solvers. However, obtaining accurate data-driven models can be challenging, especially if the underlying…

Mathematical Physics · Physics 2024-01-03 Alberto Padovan , Blaine Vollmer , Daniel J. Bodony

This paper presents a reduced order approach for transient modeling of multiple moving objects in nonlinear crossflows. The Proper Orthogonal Decomposition method and the Galerkin projection are used to construct a reduced version of the…

Fluid Dynamics · Physics 2021-06-07 My Ha Dao

POD-DL-ROMs have been recently proposed as an extremely versatile strategy to build accurate and reliable reduced order models (ROMs) for nonlinear parametrized partial differential equations, combining (i) a preliminary dimensionality…

Numerical Analysis · Mathematics 2023-05-09 Simone Brivio , Stefania Fresca , Nicola Rares Franco , Andrea Manzoni

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

We investigate the sensitivity of reduced order models (ROMs) to training data resolution as well as sampling rate. In particular, we consider proper orthogonal decomposition (POD), coupled with Galerkin projection (POD-GP), as an intrusive…

Fluid Dynamics · Physics 2020-07-15 Shady E. Ahmed , Omer San , Diana A. Bistrian , Ionel M. Navon

We introduce improved Reduced Order Models (ROM) for convection-dominated flows. These non-linear closure models are inspired from successful numerical stabilization techniques used in Large Eddy Simulations (LES), such as Local Projection…

Numerical Analysis · Mathematics 2017-11-28 Mejdi Azaïez , Tomás Chacón Rebollo , Samuele Rubino

Solving optimal control problems for transport-dominated partial differential equations (PDEs) can become computationally expensive, especially when dealing with high-dimensional systems. To overcome this challenge, we focus on developing…

Optimization and Control · Mathematics 2026-03-31 Tobias Breiten , Shubhaditya Burela , Philipp Schulze

This paper is concerned with the design of a non-intrusive model order reduction (MOR) for the system of parametric time-domain Maxwell equations. A time- and parameter-independent reduced basis (RB) is constructed by using a two-step…

Numerical Analysis · Mathematics 2021-03-24 Ying Zhao , Liang Li , Kun Li

Reduced order models play an important role in the design, optimization and control of dynamical systems. In recent years, there has been an increasing interest in the application of data-driven techniques for model reduction that can…

Fluid Dynamics · Physics 2021-02-23 Carlos J. G. Rojas , Andreas Dengel , Mateus Dias Ribeiro

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

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

Non-intrusive model reduction is a promising solution to system dynamics prediction, especially in cases where data are collected from experimental campaigns or proprietary software simulations. In this work, we present a method for…

Fluid Dynamics · Physics 2024-04-04 Leonidas Gkimisis , Thomas Richter , Peter Benner

In this paper, we compare the intrusive proper orthogonal decomposition (POD) with Galerkin projection and the data-driven dynamic mode decomposition (DMD), for Heston's option pricing model. The full order model is obtained by…

Numerical Analysis · Mathematics 2025-01-03 Sinem Kozpınar , Murat Uzunca , Bülent Karasözen

We present a reduced order method (ROM) based on proper orthogonal decomposition (POD) for the viscous Burgers' equation and the incompressible Navier-Stokes equations discretized using an implicit-explicit hybrid discontinuous…

Numerical Analysis · Mathematics 2020-04-21 Guosheng Fu , Zhu Wang

We present a fully non-intrusive parametric reduced-order modeling (PROM) framework for geometrically nonlinear structures subject to geometric variations. The method builds upon equation-driven Galerkin ROMs constructed from vibration…

Numerical Analysis · Mathematics 2025-12-09 Alexander Saccani , Paolo Tiso