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We present a framework for parametric proper orthogonal decomposition (POD)-Galerkin reduced-order modeling (ROM) of fluid flows that accommodates variations in flow parameters and control inputs. As an initial step, to explore how the…

Fluid Dynamics · Physics 2025-11-10 Shintaro Sato , Oliver T. Schmidt

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

This paper focuses on reduced-order models (ROMs) built for the efficient treatment of PDEs having solutions that bifurcate as the values of multiple input parameters change. First, we consider a method called local ROM that uses k-means…

Numerical Analysis · Mathematics 2022-01-03 Martin W. Hess , Annalisa Quaini , Gianluigi Rozza

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

Soft robots offer remarkable adaptability and safety advantages over rigid robots, but modeling their complex, nonlinear dynamics remains challenging. Strain-based models have recently emerged as a promising candidate to describe such…

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

We present a novel reduced-order Model (ROM) that leverages optimal transport (OT) theory and displacement interpolation to enhance the representation of nonlinear dynamics in complex systems. While traditional ROM techniques face…

Numerical Analysis · Mathematics 2024-11-14 Moaad Khamlich , Federico Pichi , Michele Girfoglio , Annalisa Quaini , Gianluigi Rozza

This paper presents a new data-driven non-intrusive reduced-order model(NIROM) that outperforms the traditional Proper orthogonal decomposition (POD) based reducedorder model. This is achieved by using Auto-Encoder(AE) and attention-based…

Computational Physics · Physics 2021-09-07 R. Fu , D. Xiao , I. M. Navon , C. Wang

We provide an introduction to POD-MOR with focus on (nonlinear) parametric PDEs and (nonlinear) time-dependent PDEs, and PDE constrained optimization with POD surrogate models as application. We cover the relation of POD and SVD, POD from…

Numerical Analysis · Mathematics 2020-08-04 Carmen Gräßle , Michael Hinze , Stefan Volkwein

Reduced-order models (ROMs) provide a powerful means of synthesizing dynamic walking gaits on legged robots. Yet this approach lacks the formal guarantees enjoyed by methods that utilize the full-order model (FOM) for gait synthesis, e.g.,…

Systems and Control · Electrical Eng. & Systems 2025-09-03 Sergio A. Esteban , Max H. Cohen , Adrian B. Ghansah , Aaron D. Ames

We propose a data-driven filtered reduced order model (DDF-ROM) framework for the numerical simulation of fluid flows. The novel DDF-ROM framework consists of two steps: (i) In the first step, we use explicit ROM spatial filtering of the…

Fluid Dynamics · Physics 2017-09-14 X. Xie , M. Mohebujjaman , L. G. Rebholz , T. Iliescu

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

Cardiovascular diseases are a leading cause of death in the world, driving the development of patient-specific and benchmark models for blood flow analysis. This chapter provides a theoretical overview of the main categories of Reduced…

Numerical Analysis · Mathematics 2025-10-21 Pierfrancesco Siena , Pasquale Claudio Africa , Michele Girfoglio , Gianluigi Rozza

The use of reduced-order models (ROMs) in physics-based modeling and simulation almost always involves the use of linear reduced basis (RB) methods such as the proper orthogonal decomposition (POD). For some nonlinear problems, linear RB…

Numerical Analysis · Mathematics 2022-04-19 Rakesh Halder , Krzysztof Fidkowski , Kevin Maki

Reduced-order plasma models that can efficiently predict plasma behavior across various settings and configurations are highly sought after yet elusive. The demand for such models has surged in the past decade due to their potential to…

Plasma Physics · Physics 2024-03-05 Farbod Faraji , Maryam Reza , Aaron Knoll , J. Nathan Kutz

One predominant challenge in additive manufacturing (AM) is to achieve specific material properties by manipulating manufacturing process parameters during the runtime. Such manipulation tends to increase the computational load imposed on…

Machine Learning · Computer Science 2023-10-24 Mahmoud Yaseen , Dewen Yushu , Peter German , Xu Wu

We develop a variant of a tensor reduced-order model (tROM) for the parameterized shallow-water dam-break problem. This hyperbolic system presents multiple challenges for model reduction, including a slow decay of the Kolmogorov $N$-width…

Numerical Analysis · Mathematics 2025-12-11 Md Rezwan Bin Mizan , Maxim Olshanskii , Ilya Timofeyev

While data-driven techniques are powerful tools for reduced-order modeling of systems with chaotic dynamics, great potential remains for leveraging known physics (i.e. a full-order model (FOM)) to improve predictive capability. We develop a…

Machine Learning · Computer Science 2025-07-30 Alex Guo , Michael D. Graham

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

This paper deals with the numerical modeling of flow around and through a porous obstacle by a reduced order model (ROM) obtained by Galerkin projection of the Navier-Stokes equations onto a Proper Orthogonal Decomposition (POD) reduced…

Fluid Dynamics · Physics 2023-07-24 Cyrille Allery , Claudine Beghein , Claire Dubot , Fabien Dubot