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Recent research in non-intrusive data-driven model order reduction (MOR) enabled accurate and efficient approximation of parameterized ordinary differential equations (ODEs). However, previous studies have focused on constant parameters,…

Dynamical Systems · Mathematics 2021-10-27 Jonas Kneifl , Julian Hay , Jörg Fehr

The integration of reduced-order models (ROMs) with high-performance computing (HPC) is critical for developing digital twins, particularly for real-time monitoring and predictive maintenance of industrial systems. This paper presents a…

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

In this effort we propose a data-driven learning framework for reduced order modeling of fluid dynamics. Designing accurate and efficient reduced order models for nonlinear fluid dynamic problems is challenging for many practical…

Computational Physics · Physics 2018-12-05 Xuping Xie , Guannan Zhang , Clayton G. Webster

We present a novel technique to significantly reduce the offline cost associated to non-intrusive nonlinear tensors identification in reduced order models (ROMs) of geometrically nonlinear, finite elements (FE)-discretized structural…

Numerical Analysis · Mathematics 2024-11-22 Alexander Saccani , Paolo Tiso

The present work proposes a framework for nonlinear model order reduction based on a Graph Convolutional Autoencoder (GCA-ROM). In the reduced order modeling (ROM) context, one is interested in obtaining real-time and many-query evaluations…

Numerical Analysis · Mathematics 2023-11-08 Federico Pichi , Beatriz Moya , Jan S. Hesthaven

In recent years, data-driven deep learning models have gained significant interest in the analysis of turbulent dynamical systems. Within the context of reduced-order models (ROMs), convolutional autoencoders (CAEs) pose a universally…

Vortex-induced vibrations (VIV) pose computationally expensive problems of high practical interest to several engineering fields. In this work we develop a non-intrusive, reduced-order modelling methodology for two-dimensional (2D) VIV…

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

This contribution describes the implementation of a data--driven shape optimization pipeline in a naval architecture application. We adopt reduced order models (ROMs) in order to improve the efficiency of the overall optimization, keeping a…

Numerical Analysis · Mathematics 2024-01-22 Nicola Demo , Giulio Ortali , Gianluca Gustin , Gianluigi Rozza , Gianpiero Lavini

Reduced order models (ROM) can represent spatiotemporal processes in significantly fewer dimensions and can be solved many orders faster than their governing partial differential equations (PDEs). For example, using a proper orthogonal…

Machine Learning · Computer Science 2025-12-24 Shane X. Coffing , John Tipton , Arvind T. Mohan , Darren Engwirda

The current study aims to evaluate and investigate the development of projection-based reduced-order models (ROMs) for efficient and accurate RDE simulations. Specifically, we focus on assessing the projection-based ROM construction…

Fluid Dynamics · Physics 2024-08-29 Ryan Camacho , Cheng Huang

The continuous casting tundish plays a critical role as a metallurgical reactor in the continuous casting process, with its flow characteristics serving as a key parameter in the production of high-quality steel. These characteristics are…

Statistical tools are crucial for studying and modeling turbulent flows, where chaotic velocity fluctuations span a wide range of spatial and temporal scales. Advances in image velocimetry, especially in tracking-based methods, now allow…

Fluid Dynamics · Physics 2025-02-19 Miguel A. Mendez , Manuel Ratz , Damien Rigutto

Reduced-order models (ROMs) are essential for rapid simulation of complex biomechanical systems and for bridging the gap between high fidelity models and clinical application. However, ROMs for tissue growth and remodeling (G&R) remain…

Computational Engineering, Finance, and Science · Computer Science 2026-04-16 Joel Laudo , Adrian Buganza Tepole

We apply reduced-order modeling (ROM) techniques to single-phase flow in faulted porous media, accounting for changing rock properties and fault geometry variations using a radial basis function mesh deformation method. This approach…

Numerical Analysis · Mathematics 2024-03-07 Enrico Ballini , Luca Formaggia , Alessio Fumagalli , Anna Scotti , Paolo Zunino

Establishing appropriate mathematical models for complex systems in natural phenomena not only helps deepen our understanding of nature but can also be used for state estimation and prediction. However, the extreme complexity of natural…

Machine Learning · Computer Science 2024-03-27 Cheng Fang , Jinqiao Duan

Reduced-order models are indispensable for multi-query or real-time problems. However, there are still many challenges to constructing efficient ROMs for time-dependent parametrized problems. Using a linear reduced space is inefficient for…

Numerical Analysis · Mathematics 2023-11-17 Junming Duan , Jan S. Hesthaven

The paper presents a Projection-Based Reduced-Order Model for simulations of high Reynolds turbulent flows. The PBROM are enhanced by incorporating various models of turbulent viscosity and residual closures to model the effects of…

Computational Engineering, Finance, and Science · Computer Science 2021-05-25 My Ha Dao , Hoang Huy Nguyen

Unsteady fluid systems are nonlinear high-dimensional dynamical systems that may exhibit multiple complex phenomena both in time and space. Reduced Order Modeling (ROM) of fluid flows has been an active research topic in the recent decade…

Fluid Dynamics · Physics 2020-10-05 Hamidreza Eivazi , Hadi Veisi , Mohammad Hossein Naderi , Vahid Esfahanian

Reduced Order Models (ROMs) form essential tools across engineering domains by virtue of their function as surrogates for computationally intensive digital twinning simulators. Although purely data-driven methods are available for ROM…

Computational Engineering, Finance, and Science · Computer Science 2025-04-14 Konstantinos Vlachas , Thomas Simpson , Anthony Garland , D. Dane Quinn , Charbel Farhat , Eleni Chatzi