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The nuclear community has coupled several three-dimensional Computational Fluid Dynamics (CFD) solvers with one-dimensional system thermal-hydraulic (STH) codes. This work proposes to replace the CFD solver by a reduced order model (ROM) to…

Fluid Dynamics · Physics 2020-10-21 S. Kelbij Star , Giuseppe Spina , Francesco Belloni , Joris Degroote

Traditional linear subspace reduced order models (LS-ROMs) are able to accelerate physical simulations, in which the intrinsic solution space falls into a subspace with a small dimension, i.e., the solution space has a small Kolmogorov…

Numerical Analysis · Mathematics 2025-11-06 Youngkyu Kim , Youngsoo Choi , David Widemann , Tarek Zohdi

Autoencoder techniques find increasingly common use in reduced order modeling as a means to create a latent space. This reduced order representation offers a modular data-driven modeling approach for nonlinear dynamical systems when…

Fluid Dynamics · Physics 2021-12-15 Shady E. Ahmed , Omer San , Adil Rasheed , Traian Iliescu

The two-layer quasi-geostrophic equations (2QGE) is a simplified model that describes the dynamics of a stratified, wind-driven ocean in terms of potential vorticity and stream function. Its numerical simulation is plagued by a high…

Numerical Analysis · Mathematics 2024-08-30 Lander Besabe , Michele Girfoglio , Annalisa Quaini , Gianluigi Rozza

Rapid simulations of advection-dominated problems are vital for multiple engineering and geophysical applications. In this paper, we present a long short-term memory neural network to approximate the nonlinear component of the reduced-order…

Machine Learning · Computer Science 2019-11-04 Romit Maulik , Vishwas Rao , Sandeep Madireddy , Bethany Lusch , Prasanna Balaprakash

Galerkin reduced order models (ROMs), e.g., based on proper orthogonal decomposition (POD) or reduced basis methods, have achieved significant success in the numerical simulation of fluid flows. The ROM numerical analysis, however, is still…

Numerical Analysis · Mathematics 2024-09-04 Francesco Ballarin , Traian Iliescu

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

We consider model order reduction based on proper orthogonal decomposition (POD) for unsteady incompressible Navier-Stokes problems, assuming that the snapshots are given by spatially adapted finite element solutions. We propose two…

Numerical Analysis · Mathematics 2019-08-02 Carmen Gräßle , Michael Hinze , Jens Lang , Sebastian Ullmann

We propose a new hyper-reduction method for a recently introduced nonlinear model reduction framework based on dynamically transformed basis functions and especially well-suited for advection-dominated systems. Furthermore, we discuss…

Numerical Analysis · Mathematics 2021-08-30 Felix Black , Philipp Schulze , Benjamin Unger

A major goal for reduced-order models of unsteady fluid flows is to uncover and exploit latent low-dimensional structure. Proper orthogonal decomposition (POD) provides an energy-optimal linear basis to represent the flow kinematics, but…

Fluid Dynamics · Physics 2022-03-23 Jared L. Callaham , Steven L. Brunton , Jean-Christophe Loiseau

This work presents a novel reduced-order model (ROM) for the incompressible Navier-Stokes equations with time-dependent boundary conditions. This ROM is velocity-only, i.e. the simulation of the velocity does not require the computation of…

Numerical Analysis · Mathematics 2022-12-26 Henrik Rosenberger , Benjamin Sanderse

An adaptive approach to using reduced-order models as surrogates in PDE-constrained optimization is introduced that breaks the traditional offline-online framework of model order reduction. A sequence of optimization problems constrained by…

Optimization and Control · Mathematics 2014-07-30 Matthew J. Zahr , Charbel Farhat

Nearly all model-reduction techniques project the governing equations onto a linear subspace of the original state space. Such subspaces are typically computed using methods such as balanced truncation, rational interpolation, the…

Numerical Analysis · Computer Science 2019-06-07 Kookjin Lee , Kevin Carlberg

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

This work presents a non-intrusive reduced-order modeling framework for dynamical systems with spatially localized features characterized by slow singular value decay. The proposed approach builds upon two existing methodologies for reduced…

Dynamical Systems · Mathematics 2025-06-16 Leonidas Gkimisis , Nicole Aretz , Marco Tezzele , Thomas Richter , Peter Benner , Karen E. Willcox

Reduced order models (ROM) are commonly employed to solve parametric problems and to devise inexpensive response surfaces to evaluate quantities of interest in real-time. There are many families of ROMs in the literature and choosing among…

Numerical Analysis · Mathematics 2021-06-28 Matteo Giacomini , Luca Borchini , Ruben Sevilla , Antonio Huerta

This paper formulates, analyzes, and demonstrates numerically a method for the partitioned solution of coupled interface problems involving combinations of projection-based reduced order models (ROM) and/or full order methods (FOMs). The…

Numerical Analysis · Mathematics 2023-08-29 Amy de Castro , Pavel Bochev , Paul Kuberry , Irina Tezaur

A Finite-Volume based POD-Galerkin reduced order modeling strategy for steady-state Reynolds averaged Navier--Stokes (RANS) simulation is extended for low-Prandtl number flow. The reduced order model is based on a full order model for which…

Fluid Dynamics · Physics 2020-08-04 Kelbij Star , Giovanni Stabile , Gianluigi Rozza , Joris Degroote

Proper orthogonal decomposition (POD) allows reduced-order modeling of complex dynamical systems at a substantial level, while maintaining a high degree of accuracy in modeling the underlying dynamical systems. Advances in machine learning…

Machine Learning · Computer Science 2023-03-13 Justin Baker , Elena Cherkaev , Akil Narayan , Bao Wang

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