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Shape optimization is a challenging task in many engineering fields, since the numerical solutions of parametric system may be computationally expensive. This work presents a novel optimization procedure based on reduced order modeling,…

Numerical Analysis · Mathematics 2018-11-07 Nicola Demo , Marco Tezzele , Gianluca Gustin , Gianpiero Lavini , Gianluigi Rozza

In this paper, we propose a deep learning-based method, deep Euler method (DEM) to solve ordinary differential equations. DEM significantly improves the accuracy of the Euler method by approximating the local truncation error with deep…

Numerical Analysis · Mathematics 2020-03-24 Xing Shen , Xiaoliang Cheng , Kewei Liang

Simulations of many rigid bodies colliding with each other sometimes yield particularly interesting results if the colliding objects differ significantly in size and are non-spherical. The most expensive part within such a simulation code…

Computational Geometry · Computer Science 2022-10-21 Peter J. Noble , Tobias Weinzierl

The discrete element method (DEM) can provide detailed descriptions of sea ice dynamics that explicitly model floes and discontinuities in the ice, which can be challenging to represent accurately with current models. However, floe-scale…

Geophysics · Physics 2022-07-13 Brendan West , Devin O'Connor , Matthew Parno , Max Krackow , Chris Polashenski

We treat the accurate simulation of the calcination reaction in particles, where the particles are large and, thus, the inner-particle processes must be resolved. Because these processes need to be described with coupled partial…

Fluid Dynamics · Physics 2023-11-28 Lucas Reineking , Torben Bergold , Enric Illana , Viktor Scherer , Martin Mönnigmann

Modern multi-core systems have a large number of design parameters, most of which are discrete-valued, and this number is likely to keep increasing as chip complexity rises. Further, the accurate evaluation of a potential design choice is…

Distributed, Parallel, and Cluster Computing · Computer Science 2015-07-15 Neha V. Karanjkar , Madhav P. Desai

This paper presents a structure-exploiting nonlinear model reduction method for systems with general nonlinearities. First, the nonlinear model is lifted to a model with more structure via variable transformations and the introduction of…

Numerical Analysis · Computer Science 2019-07-30 Boris Kramer , Karen Willcox

Physics-informed neural networks (PINNs) have gained significant attention for solving forward and inverse problems related to partial differential equations (PDEs). While advancements in loss functions and network architectures have…

Machine Learning · Computer Science 2025-08-11 Adrian Celaya , David Fuentes , Beatrice Riviere

In this work we propose and analyze a novel Hybrid High-Order discretization of a class of (linear and) nonlinear elasticity models in the small deformation regime which are of common use in solid mechanics. The proposed method is valid in…

Numerical Analysis · Mathematics 2017-07-10 Michele Botti , Daniele Di Pietro , Pierre Sochala

The finite element method (FEM) is among the most commonly used numerical methods for solving engineering problems. Due to its computational cost, various ideas have been introduced to reduce computation times, such as domain decomposition,…

Computational Engineering, Finance, and Science · Computer Science 2019-11-07 Andrea Mendizabal , Pablo Márquez-Neila , Stéphane Cotin

Fluid-structure interactions are central to many bio-molecular processes, and they impose a great challenge for computational and modeling methods. In this paper, we consider the immersed boundary method (IBM) for biofluid systems, and to…

Numerical Analysis · Mathematics 2021-10-13 Yushuang Luo , Xiantao Li , Wenrui Hao

We present an adaptive reduced-order model for the efficient time-resolved simulation of fluid-structure interaction problems with complex and non-linear deformations. The model is based on repeated linearizations of the structural balance…

Fluid Dynamics · Physics 2020-04-13 Ali Thari , Vito Pasquariello , Niels Aage , Stefan Hickel

Accurate interpolation of seismic data is crucial for improving the quality of imaging and interpretation. In recent years, deep learning models such as U-Net and generative adversarial networks have been widely applied to seismic data…

Neuronal damage, in the form of both brain and spinal cord injuries, is one of the major causes of disability and death in young adults worldwide. One way to assess the direct damage occurring after a mechanical insult is the simulation of…

Neural and Evolutionary Computing · Computer Science 2024-09-20 Antonio LaTorre , Man Ting Kwong , Julián A. García-Grajales , Riyi Shi , Antoine Jérusalem , José-María Peña

Several nonlinear model reduction techniques are compared for the three cases of the non-parallel version of the Kuramoto-Sivashinsky equation, the transient regime of flow past a cylinder at $Re=100$ and fully developed flow past a…

Computational Physics · Physics 2020-05-08 Denis Sipp , Miguel Fosas de Pando , Peter J. Schmid

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

This paper focuses on a new framework for reduced order modelling of non-intrusive data with application to 2D flows. To overcome the shortcomings of intrusive model order reduction usually derived by combining the POD and the Galerkin…

Numerical Analysis · Mathematics 2016-11-16 D. A. Bistrian , I. M. Navon

While proper orthogonal decomposition (POD) is widely used for model reduction, its standard form does not take into account any parametric model structure. Extensions to POD have been proposed to address this, but these either require…

Numerical Analysis · Mathematics 2025-08-13 Sebastiaan P. C. van Schie , Boris Kramer , John T. Hwang

We extend the index-aware model-order reduction method to systems of nonlinear differential-algebraic equations with a special nonlinear term f(Ex), where E is a singular matrix. Such nonlinear differential-algebraic equations arise, for…

Numerical Analysis · Mathematics 2020-02-25 Nicodemus Banagaaya , Giuseppe Ali , Sara Grundel , Peter Benner

Objective: Inclusion of individualised electrical conductivities of head tissues is crucial for the accuracy of electrical source imaging techniques based on electro/magnetoencephalography and the efficacy of transcranial electrical…