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The domain decomposition (DD) nonlinear-manifold reduced-order model (NM-ROM) represents a computationally efficient method for integrating underlying physics principles into a neural network-based, data-driven approach. Compared to linear…

Numerical Analysis · Mathematics 2024-12-03 Ivan Zanardi , Alejandro N. Diaz , Seung Whan Chung , Marco Panesi , Youngsoo Choi

The paper introduces a reduced order model (ROM) for numerical integration of a dynamical system which depends on multiple parameters. The ROM is a projection of the dynamical system on a low dimensional space that is both problem-dependent…

Numerical Analysis · Mathematics 2022-06-08 Alexander V. Mamonov , Maxim A. Olshanskii

The need for multiple interactive, real-time simulations using different parameter values has driven the design of fast numerical algorithms with certifiable accuracies. The reduced basis method (RBM) presents itself as such an option. RBM…

Numerical Analysis · Mathematics 2021-01-18 Yanlai Chen , Sigal Gottlieb , Lijie Ji , Yvon Maday

The task of repeatedly solving parametrized partial differential equations (pPDEs) in, e.g. optimization or interactive applications, makes it imperative to design highly efficient and equally accurate surrogate models. The reduced basis…

Numerical Analysis · Mathematics 2020-09-11 Yanlai Chen , Lijie Ji , Akil Narayan , Zhenli Xu

Fractional Laplace equations are becoming important tools for mathematical modeling and prediction. Recent years have shown much progress in developing accurate and robust algorithms to numerically solve such problems, yet most solvers for…

Numerical Analysis · Mathematics 2018-08-03 Harbir Antil , Yanlai Chen , Akil Narayan

We present a reduced order modeling (ROM) technique for subsurface multi-phase flow problems building on the recently introduced deep residual recurrent neural network (DR-RNN) [1]. DR-RNN is a physics aware recurrent neural network for…

Computational Engineering, Finance, and Science · Computer Science 2018-10-25 J. Nagoor Kani , Ahmed H. Elsheikh

Dynamic mechanical metamaterials (MMs) are artificial media composed of periodic micro-structures, designed to manipulate wave propagation. Modeling and designing these materials can be computationally demanding due to the broad design…

Applied Physics · Physics 2023-07-04 Weidi Wang , Alireza Amirkhizi

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

The vast majority of reduced-order models (ROMs) first obtain a low dimensional representation of the problem from high-dimensional model (HDM) training data which is afterwards used to obtain a system of reduced complexity. Unfortunately,…

Numerical Analysis · Mathematics 2023-09-14 Victor Zucatti , Matthew J. Zahr

An adaptive approach to using reduced-order models as surrogates in PDE-constrained optimization is introduced that breaks the traditional offline-online framework of model order reduction. A sequence of optimization problems constrained by…

Optimization and Control · Mathematics 2014-07-30 Matthew J. Zahr , Charbel Farhat

In numerical simulations of many charged systems at the micro/nano scale, a common theme is the repeated solution of the Poisson-Boltzmann equation. This task proves challenging, if not entirely infeasible, largely due to the nonlinearity…

Numerical Analysis · Mathematics 2018-08-29 Lijie Ji , Yanlai Chen , Zhenli Xu

Reduced order modeling (ROM) provides an efficient framework to compute solutions of parametric problems. Basically, it exploits a set of precomputed high-fidelity solutions --- computed for properly chosen parameters, using a full-order…

Numerical Analysis · Mathematics 2019-11-19 Nicola Demo , Marco Tezzele , Gianluigi Rozza

In gradient-based time domain topology optimization, design sensitivity analysis (DSA) of the dynamic response is essential, and requires high computational cost to directly differentiate, especially for high-order dynamic system. To…

Numerical Analysis · Mathematics 2023-08-22 Shuhao Li , Hu Wang , Jichao Yin , Xinchao Jiang , Yaya Zhang

We consider model order reduction of parameterized Hamiltonian systems describing nondissipative phenomena, like wave-type and transport dominated problems. The development of reduced basis methods for such models is challenged by two main…

Numerical Analysis · Mathematics 2021-05-27 Cecilia Pagliantini

Digital twins have emerged as a key technology for optimizing the performance of engineering products and systems. High-fidelity numerical simulations constitute the backbone of engineering design, providing an accurate insight into the…

Machine Learning · Computer Science 2023-06-28 G. I. Drakoulas , T. V. Gortsas , G. C. Bourantas , V. N. Burganos , D. Polyzos

Reduced Order Modelling (ROM) has been widely used to create lower order, computationally inexpensive representations of higher-order dynamical systems. Using these representations, ROMs can efficiently model flow fields while using…

Fluid Dynamics · Physics 2021-10-13 Pranshu Pant , Ruchit Doshi , Pranav Bahl , Amir Barati Farimani

Reduced-order models are indispensable for multi-query or real-time problems. However, there are still many challenges to constructing efficient ROMs for time-dependent parametrized problems. Using a linear reduced space is inefficient for…

Numerical Analysis · Mathematics 2023-11-17 Junming Duan , Jan S. Hesthaven

Time domain simulations are crucial for analyzing transient behavior and broadband responses in electromagnetic problems. However, conventional numerical methods such as finite element method in time domain (FEMTD) and finite difference…

Computational Physics · Physics 2025-02-19 Ruth Medeiros , Valentín de la Rubia

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

In this work we combine the framework of the Reduced Basis method (RB) with the framework of the Localized Orthogonal Decomposition (LOD) in order to solve parametrized elliptic multiscale problems. The idea of the LOD is to split a high…

Numerical Analysis · Mathematics 2015-05-20 Assyr Abdulle , Patrick Henning