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For nonlinear reduced-order models, especially for those with non-polynomial nonlinearities, the computational complexity still depends on the dimension of the original dynamical system. As a result, the reduced-order model loses its…

Numerical Analysis · Mathematics 2013-04-30 Zhu Wang

This thesis presents recent advances in model order reduction methods with the primary aim to construct online-efficient reduced surrogate models for parameterized multiscale phenomena and accelerate large-scale PDE-constrained parameter…

Numerical Analysis · Mathematics 2022-11-18 Tim Keil

In this contribution we develop an efficient reduced order model for solving parametrized linear-quadratic optimal control problems with linear time-varying state system. The fully reduced model combines reduced basis approximations of the…

Numerical Analysis · Mathematics 2024-08-29 Hendrik Kleikamp , Lukas Renelt

The Reduced Basis Method (RBM) is a popular certified model reduction approach for solving parametrized partial differential equations. One critical stage of the \textit{offline} portion of the algorithm is a greedy algorithm, requiring…

Numerical Analysis · Mathematics 2017-03-17 Jiahua Jiang , Yanlai Chen , Akil Narayan

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

Real-time simulation of elastic structures is essential in many applications, from computer-guided surgical interventions to interactive design in mechanical engineering. The Finite Element Method is often used as the numerical method of…

Machine Learning · Computer Science 2021-09-21 Alban Odot , Ryadh Haferssas , Stéphane Cotin

We present a method for computing reduced-order models of parameterized partial differential equation solutions. The key analytical tool is the singular value expansion of the parameterized solution, which we approximate with a singular…

Numerical Analysis · Mathematics 2014-11-03 Paul G. Constantine , David F. Gleich , Yangyang Hou , Jeremy Templeton

Reduced Order Models (ROMs) form essential tools across engineering domains by virtue of their function as surrogates for computationally intensive digital twinning simulators. Although purely data-driven methods are available for ROM…

Computational Engineering, Finance, and Science · Computer Science 2025-04-14 Konstantinos Vlachas , Thomas Simpson , Anthony Garland , D. Dane Quinn , Charbel Farhat , Eleni Chatzi

A bottleneck for computational lithography and optical metrology are long computational times for near field simulations. For design, optimization, and inverse scatterometry usually the same basic layout has to be simulated multiple times…

Optics · Physics 2010-11-12 J. Pomplun , L. Zschiedrich , S. Burger , F. Schmidt

The Reduced Basis Method (RBM) is a rigorous model reduction approach for solving parametrized partial differential equations. It identifies a low-dimensional subspace for approximation of the parametric solution manifold that is embedded…

Numerical Analysis · Mathematics 2018-09-25 Yanlai Chen , Jiahua Jiang , Akil Narayan

In this contribution we consider localized, robust and efficient a-posteriori error estimation of the localized reduced basis multi-scale (LRBMS) method for parametric elliptic problems with possibly heterogeneous diffusion coefficient. The…

Numerical Analysis · Mathematics 2019-10-30 Mario Ohlberger , Felix Schindler

In this work, we present a parallel, fully-distributed finite element numerical framework to simulate the low-frequency electromagnetic response of superconducting devices, which allows to efficiently exploit HPC platforms. We select the…

Computational Engineering, Finance, and Science · Computer Science 2018-04-13 Marc Olm , Santiago Badia , Alberto F. Martín

The efficient condition assessment of engineered systems requires the coupling of high fidelity models with data extracted from the state of the system `as-is'. In enabling this task, this paper implements a parametric Model Order Reduction…

Numerical Analysis · Mathematics 2024-07-25 Konstantinos Vlachas , Konstantinos Tatsis , Konstantinos Agathos , Adam R. Brink , Eleni Chatzi

We propose a nonlinear registration-based model reduction procedure for rapid and reliable solution of parameterized two-dimensional steady conservation laws. This class of problems is challenging for model reduction techniques due to the…

Numerical Analysis · Mathematics 2022-03-14 Andrea Ferrero , Tommaso Taddei , Lei Zhang

In this work, we bridge standard adaptive mesh refinement and coarsening on scalable octree background meshes and robust unfitted finite element formulations for the automatic and efficient solution of large-scale nonlinear solid mechanics…

Numerical Analysis · Mathematics 2021-09-01 Santiago Badia , Manuel Caicedo , Alberto F. Martín , Javier Principe

This paper proposes a dynamical Variable-separation method for solving parameter-dependent dynamical systems. To achieve this, we establish a dynamical low-rank approximation for the solutions of these dynamical systems by successively…

Numerical Analysis · Mathematics 2025-02-13 Liang Chen , Yaru Chen , Qiuqi Li , Tao Zhou

The dynamic behavior of jointed assemblies exhibiting friction nonlinearities features amplitude-dependent dissipation and stiffness. To develop numerical simulations for predictive and design purposes, macro-scale High Fidelity Models…

Computational Engineering, Finance, and Science · Computer Science 2022-04-27 Ahmed Amr Morsy , Mariella Kast , Paolo Tiso

For constrained linear systems with bounded disturbances and parametric uncertainty, we propose a robust adaptive model predictive control strategy with online parameter estimation. Constraints enforcing persistently exciting closed loop…

Optimization and Control · Mathematics 2023-03-08 Xiaonan Lu , Mark Cannon

Efficient structural reanalysis for high-rank modification plays an important role in engineering computations which require repeated evaluations of structural responses, such as structural optimization and probabilistic analysis. To…

Computational Engineering, Finance, and Science · Computer Science 2025-05-20 Wenxiong Li , Suiyin Chen , Huan Huang

We consider a randomised implementation of the finite element method (FEM) for elliptic partial differential equations on high-dimensional models. This is motivated by applications where model predictions are essential for real-time process…

Numerical Analysis · Mathematics 2019-07-30 Yue Wu , Dimitris Kamilis , Nick Polydorides