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Galerkin-based reduced-order models (G-ROMs) offer efficient and accurate approximations for laminar flows but require hundreds to thousands of modes $N$ to capture the complex dynamics of turbulent flows. This makes standard G-ROMs…

Fluid Dynamics · Physics 2025-06-11 Ping-Hsuan Tsai , Paul Fischer , Edgar Solomonik

The impact of chemical reactions on the robustness and accuracy of projection-based Reduced-Order Models (ROMs) of fluid flows is investigated. Both Galerkin and Least-Squares Petrov Galerkin ROMs are shown to be less robust in reacting…

Computational Physics · Physics 2019-07-19 Cheng Huang , Karthik Duraisamy , Charles L. Merkle

In many applications, projection-based reduced-order models (ROMs) have demonstrated the ability to provide rapid approximate solutions to high-fidelity full-order models (FOMs). However, there is no a priori assurance that these…

Numerical Analysis · Computer Science 2020-04-22 Philip A. Etter , Kevin T. Carlberg

We propose a new method in which a generative network (GN) integrate into a reduced-order model (ROM) framework is used to solve inverse problems for partial differential equations (PDE). The aim is to match available measurements and…

Machine Learning · Computer Science 2025-06-17 Vinicius L. S. Silva , Claire E. Heaney , Nenko Nenov , Christopher C. Pain

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

Model order reduction (MOR) is an important step in the design process of integrated circuits. Specifically, the electromagnetic models extracted from modern complex designs result in a large number of passive elements that introduce…

Numerical Analysis · Mathematics 2023-11-16 Christos Giamouzis , Dimitrios Garyfallou , Anastasis Vagenas , Nestor Evmorfopoulos

Traditional reduced order modeling techniques such as the reduced basis (RB) method (relying, e.g., on proper orthogonal decomposition (POD)) suffer from severe limitations when dealing with nonlinear time-dependent parametrized PDEs,…

Numerical Analysis · Mathematics 2020-01-14 Stefania Fresca , Luca Dede , Andrea Manzoni

In many areas of engineering, nonlinear numerical analysis is playing an increasingly important role in supporting the design and monitoring of structures. Whilst increasing computer resources have made such formerly prohibitive analyses…

Numerical Analysis · Mathematics 2020-07-02 Thomas Simpson , Nikolaos Dervilis , Eleni Chatzi

In a recent work, we proposed a graph-based manifold learning scheme for the nonlinear Galerkin-reduction of quasi-static solid mechanical problems [1]. The resulting nonlinear approximation spaces can closely and flexibly represent…

Computational Engineering, Finance, and Science · Computer Science 2025-09-01 Erik Faust , Lisa Scheunemann

State estimation is key to both analyzing physical mechanisms and enabling real-time control of fluid flows. A common estimation approach is to relate sensor measurements to a reduced state governed by a reduced-order model (ROM). (When…

Fluid Dynamics · Physics 2020-06-10 Nirmal J. Nair , Andres Goza

We propose a computationally efficient framework to treat nonlinear partial differential equations having bifurcating solutions as one or more physical control parameters are varied. Our focus is on steady bifurcations. Plotting a…

Numerical Analysis · Mathematics 2020-06-11 Federico Pichi , Annalisa Quaini , Gianluigi Rozza

Non-intrusive reduced-order models (ROMs) have recently generated considerable interest for constructing computationally efficient counterparts of nonlinear dynamical systems emerging from various domain sciences. They provide a…

Computational Physics · Physics 2020-12-30 Romit Maulik , Themistoklis Botsas , Nesar Ramachandra , Lachlan Robert Mason , Indranil Pan

We present a non-intrusive model reduction framework for linear poroelasticity problems in heterogeneous porous media using proper orthogonal decomposition (POD) and neural networks, based on the usual offline-online paradigm. As the…

Numerical Analysis · Mathematics 2023-08-08 T. Kadeethum , F. Ballarin , N. Bouklas

This work presents a reduced order modelling technique built on a high fidelity embedded mesh finite element method. Such methods, and in particular the CutFEM method, are attractive in the generation of projection-based reduced order…

Numerical Analysis · Mathematics 2023-08-08 Efthymios N. Karatzas , Francesco Ballarin , Gianluigi Rozza

Model reduction by projection-based approaches is often associated with losing some of the important features that contribute towards the dynamics of the retained scales. As a result, a mismatch occurs between the predicted trajectories of…

Fluid Dynamics · Physics 2023-04-12 Shady E. Ahmed , Omer San

Model order reduction aims to determine a low-order approximation of high-order models with least possible approximation errors. For application to physical systems, it is crucial that the reduced order model (ROM) is robust to any…

Systems and Control · Electrical Eng. & Systems 2025-05-05 Shivam Bajaj , Carolyn L. Beck , Vijay Gupta

We describe a high order technique to generate quadrilateral decompositions and meshes for complex two dimensional domains using spectral elements in a field guided procedure. Inspired by cross field methods, we never actually compute…

Numerical Analysis · Mathematics 2019-10-02 Julian Marcon , David A. Kopriva , Spencer J. Sherwin , Joaquim Peiró

A parametric reduced order model based on proper orthogonal decomposition with Galerkin projection has been developed and applied for the modeling of heat transport in T-junction pipes which are widely found in nuclear power plants. Thermal…

Computational Physics · Physics 2019-01-29 Sokratia Georgaka , Giovanni Stabile , Gianluigi Rozza , Michael J Bluck

Reduced order models (ROMs) are widely used in scientific computing to tackle high-dimensional systems. However, traditional ROM methods may only partially capture the intrinsic geometric characteristics of the data. These characteristics…

Numerical Analysis · Mathematics 2025-01-13 Moaad Khamlich , Federico Pichi , Gianluigi Rozza

Linear reduced-order modeling (ROM) is widely used for efficient simulation of deformation dynamics, but its accuracy is often limited by the fixed linearization of the reduced mapping. We propose a new adaptive strategy for linear ROM that…

Graphics · Computer Science 2025-10-01 Yutian Tao , Maurizio Chiaramonte , Pablo Fernandez