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A nonlinear-manifold reduced order model (NM-ROM) is a great way of incorporating underlying physics principles into a neural network-based data-driven approach. We combine NM-ROMs with domain decomposition (DD) for efficient computation.…

Numerical Analysis · Mathematics 2023-12-04 Alejandro N. Diaz , Youngsoo Choi , Matthias Heinkenschloss

Generating a digital twin of any complex system requires modeling and computational approaches that are efficient, accurate, and modular. Traditional reduced order modeling techniques are targeted at only the first two but the novel…

Fluid Dynamics · Physics 2020-01-29 Shady E. Ahmed , Sk. Mashfiqur Rahman , Omer San , Adil Rasheed , Ionel M. Navon

Nonintrusive projection-based reduced order models (ROMs) are essential for dynamics prediction in multi-query applications where access to the source of the underlying full order model (FOM) is unavailable; that is, FOM is a black-box.…

Computational Physics · Physics 2024-10-16 Aviral Prakash , Yongjie Jessica Zhang

Trajectory-wise data-driven reduced order models (ROMs) tend to be sensitive to training data, and thus lack robustness. We propose to construct a robust stochastic ROM closure (S-ROM) from data consisting of multiple trajectories from…

Numerical Analysis · Mathematics 2022-09-08 Fei Lu , Changhong Mou , Honghu Liu , Traian Iliescu

This paper presents a novel, more efficient proper orthogonal decomposition (POD) based reduced-order model (ROM) for compressible flows. In this POD model the governing equations, i.e., the conservation of mass, momentum, and energy…

Computational Physics · Physics 2021-02-03 Elizabeth H. Krath , Forrest L. Carpenter , Paul G. A. Cizmas , David A. Johnston

This study investigates the generalization capabilities and robustness of purely deep learning (DL) models and hybrid models based on physical principles in fluid dynamics applications, specifically focusing on iteratively forecasting the…

Linear reduced-order modeling (ROM) simplifies complex simulations by approximating the behavior of a system using a simplified kinematic representation. Typically, ROM is trained on input simulations created with a specific spatial…

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 propose a new reduced order modeling strategy for tackling parametrized Partial Differential Equations (PDEs) with linear constraints, in particular Darcy flow systems in which the constraint is given by mass conservation. Our approach…

Numerical Analysis · Mathematics 2023-11-27 Wietse M. Boon , Nicola R. Franco , Alessio Fumagalli , Paolo Zunino

We propose a three-tier machine learning framework based on the next-generation Equation-Free algorithm for learning the spatio-temporal dynamics of mass-constrained complex systems with hidden states, whose dynamics can in principle be…

Numerical Analysis · Mathematics 2026-02-10 Gianmaria Viola , Alessandro Della Pia , Lucia Russo , Ioannis Kevrekidis , Constantinos Siettos

We propose a space-time reduced-order model (ROM) for nonlinear dynamical systems, building upon previous work on linear systems. Whereas most ROMs are space-only in that they reduce only the spatial dimension of the state, the proposed…

Numerical Analysis · Mathematics 2025-11-03 Peter Frame , Aaron Towne

Dynamic mode decomposition (DMD) has recently become a popular tool for the non-intrusive analysis of dynamical systems. Exploiting Proper Orthogonal Decomposition (POD) as a dimensionality reduction technique, DMD is able to approximate a…

Numerical Analysis · Mathematics 2024-01-17 Francesco Andreuzzi , Nicola Demo , Gianluigi Rozza

The direct parametrisation method for invariant manifold is a model-order reduction technique that can be applied to nonlinear systems described by PDEs and discretised e.g. with a finite element procedure in order to derive efficient…

Numerical Analysis · Mathematics 2024-03-19 Alessandra Vizzaccaro , Giorgio Gobat , Attilio Frangi , Cyril Touzé

Solving complex partial differential equations is vital in the physical sciences, but often requires computationally expensive numerical methods. Reduced-order models (ROMs) address this by exploiting dimensionality reduction to create fast…

Machine Learning · Computer Science 2026-05-19 Robert Stephany , William Michael Anderson , Youngsoo Choi

The numerical treatment of fluid-particle systems is a very challenging problem because of the complex coupling phenomena occurring between the two phases. Although accurate mathematical modelling is available to address this kind of…

Numerical Analysis · Mathematics 2024-03-22 Arash Hajisharifi , Rahul Halder , Michele Girfoglio , Andrea Beccari , Domenico Bonanni , Gianluigi Rozza

In Laser Powder Bed Fusion (LPBF), the applied laser energy produces high thermal gradients that lead to unacceptable final part distortion. Accurate distortion prediction is essential for optimizing the 3D printing process and…

Machine Learning · Computer Science 2024-12-09 Indu Kant Deo , Youngsoo Choi , Saad A. Khairallah , Alexandre Reikher , Maria Strantza

Reduced-order models (ROMs) are often used to accelerate the simulation of large physical systems. However, traditional ROM techniques, such as those based on proper orthogonal decomposition (POD), often struggle with advection-dominated…

Numerical Analysis · Mathematics 2025-11-07 Toby van Gastelen , Wouter Edeling , Benjamin Sanderse

Latent ODE models provide flexible descriptions of dynamic systems, but they can struggle with extrapolation and predicting complicated non-linear dynamics. The latent ODE approach implicitly relies on encoders to identify unknown system…

Machine Learning · Computer Science 2024-10-14 Matt L. Sampson , Peter Melchior

Reduced-order models have long been used to understand the behavior of nonlinear partial differential equations (PDEs). Naturally, reduced-order modeling techniques come at the price of computational accuracy for a decrease in computation…

Numerical Analysis · Mathematics 2023-07-26 Jovan Žigić

We present a numerical methodology for construction of reduced order models, ROMs, of fluid flows through the combination of flow modal decomposition and regression analysis. Spectral proper orthogonal decomposition, SPOD, is applied to…

Fluid Dynamics · Physics 2019-07-24 Hugo F. S. Lui , William R. Wolf