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Projection-based model order reduction on nonlinear manifolds has been recently proposed for problems with slowly decaying Kolmogorov n-width such as advection-dominated ones. These methods often use neural networks for manifold learning…

Computational Physics · Physics 2023-03-20 Jorio Cocola , John Tencer , Francesco Rizzi , Eric Parish , Patrick Blonigan

This paper aims at reviewing nonlinear methods for model order reduction of structures with geometric nonlinearity, with a special emphasis on the techniques based on invariant manifold theory. Nonlinear methods differ from linear based…

Numerical Analysis · Mathematics 2022-05-26 Cyril Touzé , Alessandra Vizzaccaro , Olivier Thomas

In this paper we propose a general algorithmic framework for first-order methods in optimization in a broad sense, including minimization problems, saddle-point problems and variational inequalities. This framework allows to obtain many…

This contribution introduces a model order reduction approach for an advection-reaction problem with a parametrized reaction function. The underlying discretization uses an ultraweak formulation with an $L^2$-like trial space and an…

Numerical Analysis · Mathematics 2024-07-01 Christian Engwer , Mario Ohlberger , Lukas Renelt

We develop a novel deep learning technique, termed Deep Orthogonal Decomposition (DOD), for dimensionality reduction and reduced order modeling of parameter dependent partial differential equations. The approach consists in the construction…

Numerical Analysis · Mathematics 2024-05-15 Nicola Rares Franco , Andrea Manzoni , Paolo Zunino , Jan S. Hesthaven

Regressions created from experimental or simulated data enable the construction of metamodels, widely used in a variety of engineering applications. Many engineering problems involve multi-parametric physics whose corresponding…

Computational Engineering, Finance, and Science · Computer Science 2021-03-10 Abel Sancarlos , Victor Champaney , Jean-Louis Duval , Elias Cueto , Francisco Chinesta

We consider model order reduction by proper orthogonal decomposition (POD) for parametrized partial differential equations, where the underlying snapshots are computed with adaptive finite elements. We address computational and theoretical…

Numerical Analysis · Mathematics 2016-09-21 Sebastian Ullmann , Marko Rotkvic , Jens Lang

Physics-based models often involve large systems of parametrized partial differential equations, where design parameters control various properties. However, high-fidelity simulations of such systems on large domains or with high grid…

Computational Physics · Physics 2025-05-15 Diba Behnoudfar

This work introduces a new approach for accelerating the numerical analysis of time-domain partial differential equations (PDEs) governing complex physical systems. The methodology is based on a combination of a classical reduced-order…

Machine Learning · Computer Science 2024-06-06 Victor Matray , Faisal Amlani , Frédéric Feyel , David Néron

This paper presents the first application of the direct parametrisation method for invariant manifolds to a fully coupled multiphysics problem involving the nonlinear vibrations of deformable structures subjected to an electrostatic field.…

Numerical Analysis · Mathematics 2023-12-25 Attilio Frangi , Alessio Colombo , Alessandra Vizzaccaro , Cyril Touzé

In recent years, there has been a growing interest in understanding complex microstructures and their effect on macroscopic properties. In general, it is difficult to derive an effective constitutive law for such microstructures with…

Computational Engineering, Finance, and Science · Computer Science 2023-10-18 Theron Guo , Ondřej Rokoš , Karen Veroy

This work introduces an empirical quadrature-based hyperreduction procedure and greedy training algorithm to effectively reduce the computational cost of solving convection-dominated problems with limited training. The proposed approach…

Numerical Analysis · Mathematics 2023-09-14 Marzieh Alireza Mirhoseini , Matthew J. Zahr

The paper proposes an approach for the efficient model order reduction of dynamic contact problems in linear elasticity. Instead of the augmented Lagrangian method that is widely used for mechanical contact problems, we prefer here the…

Numerical Analysis · Mathematics 2021-07-27 Diana Manvelyan , Bernd Simeon , Utz Wever

Theory and methods to obtain parametric reduced-order models by moment matching are presented. The definition of the parametric moment is introduced, and methods (model-based and data-driven) for the approximation of the parametric moment…

Systems and Control · Electrical Eng. & Systems 2025-06-13 Hanqing Zhang , Junyu Mao , Mohammad Fahim Shakib , Giordano Scarciotti

A non-intrusive model order reduction (MOR) method for solving parameterized electromagnetic scattering problems is proposed in this paper. A database collecting snapshots of high-fidelity solutions is built by solving the parameterized…

Numerical Analysis · Mathematics 2022-07-19 Xiao-Feng He , Liang Li , Stephane Lanteri , Kun Li

In this work we introduce an approach for modeling and analyzing collective behavior of a group of agents using moments. We represent the group of agents via their distribution and derive a method to estimate the dynamics of the moments. We…

Optimization and Control · Mathematics 2020-04-30 Silun Zhang , Axel Ringh , Xiaoming Hu , Johan Karlsson

Assessing IC manufacturing process fluctuations and their impacts on IC interconnect performance has become unavoidable for modern DSM designs. However, the construction of parametric interconnect models is often hampered by the rapid…

Hardware Architecture · Computer Science 2011-11-09 Peng Li , Frank Liu , Xin Li , Lawrence T. Pileggi , Sani R. Nassif

Orthogonal projection-based reduced order models (PROM) are the output of widely-used model reduction methods. In this work, a novel product form is derived for the reduction error system of these reduced models, and it is shown that any…

Systems and Control · Electrical Eng. & Systems 2022-01-03 Noam Leiter , Daniel Zelazo

In this paper we suggest a moment matching method for quadratic-bilinear dynamical systems. Most system-theoretic reduction methods for nonlinear systems rely on multivariate frequency representations. Our approach instead uses univariate…

Numerical Analysis · Mathematics 2021-06-07 Björn Liljegren-Sailer , Nicole Marheineke

The model reduction problem for high-order multi-input, multi-output (MIMO) polynomial nonlinear systems based on moment matching is addressed. The technique of power-series decomposition is exploited: this decomposes the solution of the…

Systems and Control · Electrical Eng. & Systems 2025-08-20 Chao Huang , Alessandro Astolfi