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Model order reduction (MOR) techniques play a crucial role in the computer-aided design of modern integrated circuits, where they are used to reduce the size of parasitic networks. Unfortunately, the efficient reduction of passive networks…

Computational Engineering, Finance, and Science · Computer Science 2016-06-29 Denis Oyaro , Piero Triverio

The reduced basis method (RBM) empowers repeated and rapid evaluation of parametrized partial differential equations through an offline-online decomposition, a.k.a. a learning-execution process. A key feature of the method is a greedy…

Numerical Analysis · Mathematics 2020-09-16 Jiahua Jiang , Yanlai Chen

In this contribution we investigate in mathematical modeling and efficient simulation of biological cells with a particular emphasis on effective modeling of structural properties that originate from active forces generated from…

Numerical Analysis · Mathematics 2021-11-02 Tobias Leibner , Maja Matis , Mario Ohlberger , Stephan Rave

In the context of simulation-based methods, multiple challenges arise, two of which are considered in this work. As a first challenge, problems including time-dependent phenomena with complex domain deformations, potentially even with…

Numerical Analysis · Mathematics 2023-12-06 Fabian Key , Max von Danwitz , Francesco Ballarin , Gianluigi Rozza

Topology Optimization (TO) provides a systematic approach for obtaining structure design with optimum performance of interest. However, the process requires numerical evaluation of objective function and constraints at each iteration, which…

Machine Learning · Computer Science 2022-03-22 Ren Kai Tan , Chao Qian , Dan Xu , Wenjing Ye

Generally, reduced order models of fluid flows are obtained by projecting the Navier-Stokes equations onto a reduced subspace spanned by vector functions that carry the meaningful information of the dynamics. A common method to generate…

Fluid Dynamics · Physics 2023-09-22 M. Oulghelou , A. Ammar , R. Ayoub

We investigate a suitable application of Model Order Reduction (MOR) techniques for the numerical approximation of Turing patterns, that are stationary solutions of reaction-diffusion PDE (RD-PDE) systems. We show that solutions of…

Numerical Analysis · Mathematics 2022-03-18 Alessandro Alla , Angela Monti , Ivonne Sgura

This paper introduces multivariate input-output models to predict the errors and bases dimensions of local parametric Proper Orthogonal Decomposition reduced-order models. We refer to these multivariate mappings as the MP-LROM models. We…

Numerical Analysis · Computer Science 2017-01-16 Azam Moosavi , Razvan Stefanescu , Adrian Sandu

This article describes a bridge between POD-based model order reduction techniques and the classical Newton/Krylov solvers. This bridge is used to derive an efficient algorithm to correct, "on-the-fly", the reduced order modelling of highly…

Classical Physics · Physics 2011-09-23 Pierre Kerfriden , Pierre Gosselet , Sondipon Adhikari , Stéphane Bordas

We consider the elastic scattering problem by multiple disjoint arcs or \emph{cracks} in two spatial dimensions. A key aspect of our approach lies in the parametric description of each arc's shape, which is controlled by a potentially…

Numerical Analysis · Mathematics 2024-03-19 Fernando Henríquez , José Pinto

This paper introduces tensorial calculus techniques in the framework of Proper Orthogonal Decomposition (POD) to reduce the computational complexity of the reduced nonlinear terms. The resulting method, named tensorial POD, can be applied…

Numerical Analysis · Computer Science 2015-06-18 Răzvan Ştefănescu , Adrian Sandu , Ionel M. Navon

We develop a variant of a tensor reduced-order model (tROM) for the parameterized shallow-water dam-break problem. This hyperbolic system presents multiple challenges for model reduction, including a slow decay of the Kolmogorov $N$-width…

Numerical Analysis · Mathematics 2025-12-11 Md Rezwan Bin Mizan , Maxim Olshanskii , Ilya Timofeyev

In this paper, a reduced-order model (ROM) based on the proper orthogonal decomposition and the discrete empirical interpolation method is proposed for efficiently simulating time-fractional partial differential equations (TFPDEs). Both…

Numerical Analysis · Mathematics 2024-02-07 Hongfei Fu , Hong Wang , Zhu Wang

We present a comparative computational study of two stabilized Reduced Order Models (ROMs) for the simulation of convection-dominated incompressible flow (Reynolds number of the order of a few thousands). Representative solutions in the…

Fluid Dynamics · Physics 2024-05-01 Pierfrancesco Siena , Michele Girfoglio , Annalisa Quaini , Gianluigi Rozza

Quantum computing is a promising technology for accelerating partial differential equation solvers applied to large-scale real-world problems. However, reconstructing a classical representation of the solution from the quantum state remains…

In the study of micro-swimmers, both artificial and biological ones, many-query problems arise naturally. Even with the use of advanced high performance computing (HPC), it is not possible to solve this kind of problems in an acceptable…

Numerical Analysis · Mathematics 2020-08-04 Nicola Giuliani , Martin W. Hess , Antonio DeSimone , Gianluigi Rozza

An adaptive projection-based reduced-order model (ROM) formulation is presented for model-order reduction of problems featuring chaotic and convection-dominant physics. An efficient method is formulated to adapt the basis at every time-step…

Computational Physics · Physics 2023-08-09 Cheng Huang , Karthik Duraisamy

Dynamic Mode Decomposition (DMD) yields a linear, approximate model of a system's dynamics that is built from data. We seek to reduce the order of this model by identifying a reduced set of modes that best fit the output. We adopt a model…

Machine Learning · Statistics 2020-01-20 John Graff , Xianzhang Xu , Francis D. Lagor , Tarunraj Singh

We present a two-level parameterized Model Order Reduction (pMOR) technique for the linear hyperbolic Partial Differential Equation (PDE) of time-domain elastodynamics. In order to approximate the frequency-domain PDE, we take advantage of…

Numerical Analysis · Mathematics 2020-10-08 Mohamed Aziz Bhouri , Anthony T. Patera

We present a novel reduced order model (ROM) approach for parameterized time-dependent PDEs based on modern learning. The ROM is suitable for multi-query problems and is nonintrusive. It is divided into two distinct stages: A nonlinear…

Numerical Analysis · Mathematics 2020-11-24 Nikolaj T. Mücke , Sander M. Bohté , Cornelis W. Oosterlee