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We propose a projection-based model order reduction procedure for a general class of parametric quasi-static problems in nonlinear mechanics with internal variables. The methodology is integrated in the industrial finite element code code…

Numerical Analysis · Mathematics 2023-01-02 Eki Agouzal , Jean-Philippe Argaud , Michel Bergmann , Guilhem Ferté , Tommaso Taddei

Partial differential equations can be used to model many problems in several fields of application including, e.g., fluid mechanics, heat and mass transfer, and electromagnetism. Accurate discretization methods (e.g., finite element or…

Numerical Analysis · Mathematics 2022-03-18 Pierfrancesco Siena , Michele Girfoglio , Gianluigi Rozza

The use of reduced-order models (ROMs) in physics-based modeling and simulation almost always involves the use of linear reduced basis (RB) methods such as the proper orthogonal decomposition (POD). For some nonlinear problems, linear RB…

Numerical Analysis · Mathematics 2022-04-19 Rakesh Halder , Krzysztof Fidkowski , Kevin Maki

Partial differential equation-based numerical solution frameworks for initial and boundary value problems have attained a high degree of complexity. Applied to a wide range of physics with the ultimate goal of enabling engineering…

Numerical Analysis · Mathematics 2021-05-11 Matthew Duschenes , Krishna Garikipati

We introduce a method for the fast numerical approximation of linear, second-order parabolic partial differential equations (PDEs for short) with time-independent coefficients based on model order reduction techniques and the Laplace…

Numerical Analysis · Mathematics 2026-01-06 Fernando Henríquez , Jan S. Hesthaven

This paper focuses on the efficient numerical algorithms of a three-field Biot's consolidation model. The approach begins with the introduction of innovative monolithic and global-in-time iterative decoupled algorithms, which incorporate…

Numerical Analysis · Mathematics 2025-08-07 Huipeng Gu , Francesco Ballarin , Mingchao Cai , Jingzhi Li

Recent developments in diagnostic and computing technologies offer to leverage numerous forms of nonintrusive modeling approaches from data where machine learning can be used to build computationally cheap and accurate surrogate models. To…

Computational Physics · Physics 2023-02-22 Saeed Akbari , Suraj Pawar , Omer San

In analyzing and assessing the condition of dynamical systems, it is necessary to account for nonlinearity. Recent advances in computation have rendered previously computationally infeasible analyses readily executable on common computer…

Computational Engineering, Finance, and Science · Computer Science 2021-09-24 Thomas Simpson , Nikolaos Dervilis , Eleni Chatzi

Computing reduced-order models using non-intrusive methods is particularly attractive for systems that are simulated using black-box solvers. However, obtaining accurate data-driven models can be challenging, especially if the underlying…

Mathematical Physics · Physics 2024-01-03 Alberto Padovan , Blaine Vollmer , Daniel J. Bodony

The increasing size and complexity of modern power systems have led to a high-dimensional mathematical model for transient stability studies, rendering full-scale simulations computationally burdensome. While dimensionality reduction is…

Dynamical Systems · Mathematics 2025-12-08 Farhana Farooq , Danish Rafiq

Although projection-based reduced-order models (ROMs) for parameterized nonlinear dynamical systems have demonstrated exciting results across a range of applications, their broad adoption has been limited by their intrusivity: implementing…

Machine Learning · Computer Science 2021-06-18 Zhe Bai , Liqian Peng

Model Order Reduction (MOR) based on Proper Orthogonal Decomposition (POD) and Smooth Particle Hydrodynamics (SPH) has proven effective in various applications. Most MOR methods utilizing POD are implemented within a pure Eulerian…

Computational Physics · Physics 2025-08-04 Lidong Fang , Zilong Song , Kirk Fraser , Huaxiong Huang

This paper introduces a multifidelity formulation that reduces the computational cost of the proper orthogonal decomposition (POD) of a high-fidelity model by leveraging data from cheaper, lower-fidelity models. POD is a prevalent technique…

Numerical Analysis · Mathematics 2026-05-29 Nicole Aretz , Karen Willcox

We introduce a novel nonlinear seismic imaging method based on model order reduction. The reduced order model (ROM) is an orthogonal projection of the wave equation propagator operator on the subspace of the snapshots of the solutions of…

Numerical Analysis · Mathematics 2015-09-16 Alexander V. Mamonov , Vladimir Druskin , Mikhail Zaslavsky

This work proposes a new framework of model reduction for parametric complex systems. The framework employs a popular model reduction technique dynamic mode decomposition (DMD), which is capable of combining data-driven learning and physics…

Numerical Analysis · Mathematics 2022-04-21 Hannah Lu , Daniel M. Tartakovsky

In this paper, we propose a computationally efficient iterative algorithm for proper orthogonal decomposition (POD) using random sampling based techniques. In this algorithm, additional rows and columns are sampled and a merging technique…

Numerical Analysis · Mathematics 2020-11-23 Charumathi V , M. Ramakrishna , Vinita Vasudevan

In this paper, we propose a computationally efficient iterative algorithm for proper orthogonal decomposition (POD) using random sampling based techniques. In this algorithm, additional rows and columns are sampled and a merging technique…

Numerical Analysis · Computer Science 2021-07-07 V. Charumathi , M. Ramakrishna , Vinita Vasudevan

We propose a non-intrusive reduced-order modeling method based on proper orthogonal decomposition (POD) and polynomial chaos expansion (PCE) for stochastic representations in uncertainty quantification (UQ) analysis. Firstly, POD provides…

Computational Physics · Physics 2021-07-02 Xiang Sun , Xiaomin Pan , Jung-Il Choi

The theory of nonlinear balanced truncation provides a system-theoretic framework for model reduction that preserves important properties such as stability, controllability, and observability. We present a scalable algorithm for computing…

Optimization and Control · Mathematics 2026-04-28 Nicholas A. Corbin , Boris Kramer

This work proposes a model-reduction methodology that preserves Lagrangian structure (equivalently Hamiltonian structure) and achieves computational efficiency in the presence of high-order nonlinearities and arbitrary parameter dependence.…

Computational Engineering, Finance, and Science · Computer Science 2015-04-16 Kevin Carlberg , Ray Tuminaro , Paul Boggs