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This work describes the implementation of a data-driven approach for the reduction of the complexity of parametrical partial differential equations (PDEs) employing Proper Orthogonal Decomposition (POD) and Gaussian Process Regression…

Numerical Analysis · Mathematics 2024-01-22 Giulio Ortali , Nicola Demo , Gianluigi Rozza

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

The present works is focused on studying bifurcating solutions in compressible fluid dynamics. On one side, the physics of the problem is thoroughly investigated using high-fidelity simulations of the compressible Navier-Stokes equations…

Numerical Analysis · Mathematics 2022-12-21 Niccolò Tonicello , Andrea Lario , Gianluigi Rozza , Gianmarco Mengaldo

This paper describes the numerical implementation in a high-performance computing environment of an open-source library for model order reduction in fluid dynamics. This library, called pyLOM, contains the algorithms of proper orthogonal…

We propose a new algorithm to compute a shifted proper orthogonal decomposition (sPOD) for systems dominated by multiple transport velocities. The sPOD is a recently proposed mode decomposition technique which overcomes the poor performance…

Numerical Analysis · Mathematics 2018-03-06 Philipp Schulze , Julius Reiss , Volker Mehrmann

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

In this work we propose reduced order methods as a reliable strategy to efficiently solve parametrized optimal control problems governed by shallow waters equations in a solution tracking setting. The physical parametrized model we deal…

Numerical Analysis · Mathematics 2023-08-08 Maria Strazzullo , Francesco Ballarin , Gianluigi Rozza

In this paper, we propose novel proper orthogonal decomposition (POD)--based model reduction methods that effectively address the issue of inverse crime in solving parabolic inverse problems. Both the inverse initial value problems and…

Numerical Analysis · Mathematics 2024-06-05 Wenlong Zhang , Zhiwen Zhang

We present a low-order modeling technique for actuated flows based on the regularization of an inverse problem. The inverse problem aims at minimizing the error between the model predictions and some reference simulations. The parameters to…

Fluid Dynamics · Physics 2009-11-13 Jessie Weller , Edoardo Lombardi , Angelo Iollo

In this contribution we propose reduced order methods to fast and reliably solve parametrized optimal control problems governed by time dependent nonlinear partial differential equations. Our goal is to provide a tool to deal with the time…

Numerical Analysis · Mathematics 2023-08-08 Francesco Ballarin , Gianluigi Rozza , Maria Strazzullo

Turbulent flows, despite their apparent randomness, exhibit coherent structures that underpin their dynamics. Proper orthogonal decomposition (POD) has been widely used to extract these structures from experimental data. While periodic…

Fluid Dynamics · Physics 2026-03-02 Shaun Davey , Callum Atkinson , Julio Soria

We present a formulation of proper orthogonal decomposition (POD) producing a velocity-temperature basis optimized with respect to an $H^1$ dissipation norm. This decomposition is applied, along with a conventional POD optimized with…

In this paper we utilize the Proper Orthogonal Decomposition (POD) method for model order reduction in application to Smoluchowski aggregation equations with source and sink terms. In particular, we show in practice that there exists a…

Numerical Analysis · Mathematics 2024-03-06 Ivan V. Timokhin , Sergey A. Matveev , Eugene E. Tyrtyshnikov , Alexander P. Smirnov

Vortex shedding around circular cylinders is a well known and studied phenomenon that appears in many engineering fields. A Reduced Order Model (ROM) of the incompressible flow around a circular cylinder is presented in this work. The ROM…

Numerical Analysis · Mathematics 2018-02-06 Giovanni Stabile , Saddam Hijazi , Andrea Mola , Stefano Lorenzi , Gianluigi Rozza

This paper presents a structure-exploiting nonlinear model reduction method for systems with general nonlinearities. First, the nonlinear model is lifted to a model with more structure via variable transformations and the introduction of…

Numerical Analysis · Computer Science 2019-07-30 Boris Kramer , Karen Willcox

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

We present a method to construct reduced-order models for duct flows of Bingham media. Our method is based on proper orthogonal decomposition (POD) to find a low-dimensional approximation to the velocity and artificial neural network to…

Numerical Analysis · Mathematics 2018-11-14 E. Muravleva , I. Oseledets , D. Koroteev

A parametric, hybrid reduced order model approach based on the Proper Orthogonal Decomposition with both Galerkin projection and interpolation based on Radial Basis Functions method is presented. This method is tested against a case of…

Numerical Analysis · Mathematics 2019-12-02 Sokratia Georgaka , Giovanni Stabile , Kelbij Star , Gianluigi Rozza , Michael J Bluck

This paper studies the numerical approximation of parametric time-dependent partial differential equations (PDEs) by proper orthogonal decomposition reduced order models (POD-ROMs). Although many papers in the literature consider reduced…

Numerical Analysis · Mathematics 2025-04-28 Bosco García-Arcilla , Alicia García-Mascaraque , Julia Novo

This paper presents a model order reduction (MOR) approach for high dimensional problems in the analysis of financial risk. To understand the financial risks and possible outcomes, we have to perform several thousand simulations of the…

Computational Finance · Quantitative Finance 2021-06-15 Andreas Binder , Onkar Jadhav , Volker Mehrmann