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In this work, a new hybrid predictive Reduced Order Model (ROM) is proposed to solve reacting flow problems. This algorithm is based on a dimensionality reduction using Proper Orthogonal Decomposition (POD) combined with deep learning…

Machine Learning · Computer Science 2023-01-25 Adrián Corrochano , Rodolfo S. M. Freitas , Alessandro Parente , Soledad Le Clainche

We investigate model order reduction (MOR) strategies for simulating unsteady hemodynamics within cerebrovascular systems, contrasting a physics-based intrusive approach with a data-driven non-intrusive framework. High-fidelity 3D…

Numerical Analysis · Mathematics 2026-03-20 Rahul Halder , Arash Hajisharifi , Kabir Bakhshaei , Gianluigi Rozza

We are interested in numerically approximating the solution ${\bf U}(t)$ of the large dimensional semilinear matrix differential equation $\dot{\bf U}(t) = { \bf A}{\bf U}(t) + {\bf U}(t){ \bf B} + {\cal F}({\bf U},t)$, with appropriate…

Numerical Analysis · Mathematics 2021-05-26 Gerhard Kirsten , Valeria Simoncini

In this work, the space-time MORe DWR (Model Order Reduction with Dual-Weighted Residual error estimates) framework is extended and further developed for single-phase flow problems in porous media. Specifically, our problem statement is the…

Numerical Analysis · Mathematics 2023-11-16 Hendrik Fischer , Julian Roth , Ludovic Chamoin , Amelie Fau , Mary F. Wheeler , Thomas Wick

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

We apply the Proper Orthogonal Decomposition (POD) method for the efficient simulation of several scenarios undergone by Micro-Electro-Mechanical-Systems, involving nonlinearites of geometric and electrostatic nature. The former type of…

Numerical Analysis · Mathematics 2022-02-22 Gobat G. , Opreni A. , Fresca S. , Manzoni A. , Frangi A

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

Solving optimal control problems for transport-dominated partial differential equations (PDEs) can become computationally expensive, especially when dealing with high-dimensional systems. To overcome this challenge, we focus on developing…

Optimization and Control · Mathematics 2026-03-31 Tobias Breiten , Shubhaditya Burela , Philipp Schulze

In this paper, we consider the problem of model reduction of large scale systems, such as those obtained through the discretization of PDEs. We propose a randomized proper orthogonal decomposition (RPOD) technique to obtain the reduced…

Dynamical Systems · Mathematics 2013-12-17 Dan Yu , Suman Chakravorty

POD-DL-ROMs have been recently proposed as an extremely versatile strategy to build accurate and reliable reduced order models (ROMs) for nonlinear parametrized partial differential equations, combining (i) a preliminary dimensionality…

Numerical Analysis · Mathematics 2023-05-09 Simone Brivio , Stefania Fresca , Nicola Rares Franco , Andrea Manzoni

In this paper we discuss a projection model order reduction (MOR) method for a class of parametric linear evolution PDEs, which is based on the application of the Laplace transform. The main advantage of this approach consists in the fact…

Numerical Analysis · Mathematics 2022-09-02 Nicola Guglielmi , Mattia Manucci

In this paper we consider the numerical approximation of a semilinear reaction-diffusion model problem (PDEs) by means of reduced order methods (ROMs) based on proper orthogonal decomposition (POD). We focus on the time integration of the…

Numerical Analysis · Mathematics 2026-03-05 Bosco García-Archilla , Alicia García-Mascaraque , Julia Novo

A reduced-order model based on Proper Orthogonal Decomposition (POD) is proposed for the bidomain equations of cardiac electrophysiology. Its accuracy is assessed through electrocardiograms in various configurations, including myocardium…

Numerical Analysis · Mathematics 2012-07-23 Muriel Boulakia , Elisa Schenone , Jean-Frédéric Gerbeau

In this paper, we propose a network model, the multiclass classification-based reduced order model (MC-ROM), for solving time-dependent parametric partial differential equations (PPDEs). This work is inspired by the observation of applying…

Numerical Analysis · Mathematics 2022-10-11 Chen Cui , Kai Jiang , Shi Shu

Clinical oriented applications of computational electrocardiology require efficient and reliable identification of patient-specific parameters of mathematical models based on available measures. In particular, the estimation of cardiac…

Numerical Analysis · Mathematics 2016-11-01 Huanhuan Yang , Alessandro Veneziani

Modelling of physical systems may be a challenging task when it requires solving large sets of numerical equations. This is the case of photovoltaic (PV) systems which contain many PV modules, each module containing several silicon cells.…

Materials Science · Physics 2015-05-21 S. O. Ojo , S. Grivet-Talocia , M. Paggi

In this work, the dual-weighted residual (DWR) method is applied to obtain a certified incremental proper orthogonal decomposition (POD) based reduced order model. A novel approach called MORe DWR (Model Order Rduction with Dual-Weighted…

Numerical Analysis · Mathematics 2023-04-04 Hendrik Fischer , Julian Roth , Thomas Wick , Ludovic Chamoin , Amelie Fau

Efficient modeling of High Temperature Superconductors (HTSs) is crucial for real-time quench monitoring; however, full-order electromagnetic simulations remain prohibitively costly due to the strong nonlinearities. Conventional…

Computational Engineering, Finance, and Science · Computer Science 2026-02-17 Riccardo Basei , Francesco Pase , Francesco Lucchini , Francesco Toso , Riccardo Torchio

Deep learning-based reduced order models (DL-ROMs) have been recently proposed to overcome common limitations shared by conventional reduced order models (ROMs) - built, e.g., through proper orthogonal decomposition (POD) - when applied to…

Numerical Analysis · Mathematics 2021-11-03 Stefania Fresca , Andrea Manzoni

We are interested in the numerical solution of coupled nonlinear partial differential equations (PDEs) in two and three dimensions. Under certain assumptions on the domain, we take advantage of the Kronecker structure arising in standard…

Numerical Analysis · Mathematics 2021-07-21 Gerhard Kirsten