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In this paper, the modelling strategy of a Cosserat rod element (CRE) is addressed systematically for 3-dimensional dynamical analysis of slender structures. We employ the exact nonlinear kinematic relationships in the sense of Cosserat…

Functional Analysis · Mathematics 2007-05-23 D. Q. Cao , Dongsheng Liu , Charles H. -T. Wang

This paper presents a new data-driven non-intrusive reduced-order model(NIROM) that outperforms the traditional Proper orthogonal decomposition (POD) based reducedorder model. This is achieved by using Auto-Encoder(AE) and attention-based…

Computational Physics · Physics 2021-09-07 R. Fu , D. Xiao , I. M. Navon , C. Wang

Given a set of solution snapshots of a hyperbolic PDE, we are interested in learning a reduced order model (ROM). To this end, we propose a novel decompose then learn approach. We decompose the solution by expressing it as a composition of…

Numerical Analysis · Mathematics 2021-09-14 Neeraj Sarna , Peter Benner

In this paper we present a novel approach for the design of high order general boundary conditions when approximating solutions of the Euler equations on domains with curved boundaries, using meshes which may not be boundary conformal. When…

Numerical Analysis · Mathematics 2023-12-13 Mirco Ciallella , Stephane Clain , Elena Gaburro , Mario Ricchiuto

Steering a system towards a desired target in a very short amount of time is challenging from a computational standpoint. Indeed, the intrinsically iterative nature of optimal control problems requires multiple simulations of the physical…

Optimization and Control · Mathematics 2025-05-16 Matteo Tomasetto , Andrea Manzoni , Francesco Braghin

Autoencoder techniques find increasingly common use in reduced order modeling as a means to create a latent space. This reduced order representation offers a modular data-driven modeling approach for nonlinear dynamical systems when…

Fluid Dynamics · Physics 2021-12-15 Shady E. Ahmed , Omer San , Adil Rasheed , Traian Iliescu

The two-field vibroacoustic finite-element (FE) model requires a relatively large number of degrees of freedom compared to the monophysics model, and the conventional force identification method for structural vibration can be adjusted for…

Computational Engineering, Finance, and Science · Computer Science 2022-11-23 Seungin Oh , Chang-uk Ahn , Kwanghyun Ahn , Jin-Gyun Kim

We propose an efficient retraining strategy for a parameterized Reduced Order Model (ROM) that attains accuracy comparable to full retraining while requiring only a fraction of the computational time and relying solely on sparse…

Machine Learning · Computer Science 2026-02-27 Ismaël Zighed , Andrea Nóvoa , Luca Magri , Taraneh Sayadi

We investigate the sensitivity of reduced order models (ROMs) to training data resolution as well as sampling rate. In particular, we consider proper orthogonal decomposition (POD), coupled with Galerkin projection (POD-GP), as an intrusive…

Fluid Dynamics · Physics 2020-07-15 Shady E. Ahmed , Omer San , Diana A. Bistrian , Ionel M. Navon

A novel approach to full waveform inversion (FWI), based on a data driven reduced order model (ROM) of the wave equation operator is introduced. The unknown medium is probed with pulses and the time domain pressure waveform data is recorded…

Numerical Analysis · Mathematics 2022-08-03 Alexander V. Mamonov , Liliana Borcea , Josselin Garnier , Jörn Zimmerling

We explore the recently-proposed Virtual Element Method (VEM) for numerical solution of boundary value problems on arbitrary polyhedral meshes. More specifically, we focus on the elasticity equations in three-dimensions and elaborate upon…

Numerical Analysis · Mathematics 2015-07-22 Arun L. Gain , Cameron Talischi , Glaucio H. Paulino

Complex mechanical systems often exhibit strongly nonlinear behavior due to the presence of nonlinearities in the energy dissipation mechanisms, material constitutive relationships, or geometric/connectivity mechanics. Numerical modeling of…

Computational Engineering, Finance, and Science · Computer Science 2024-04-09 Harsh Sharma , David A. Najera-Flores , Michael D. Todd , Boris Kramer

Inferring unknown initial states in shock-dominated compressible flows from sparse and noisy measurements is a challenging ill-posed inverse problem due to nonlinear wave interactions and limited sensing. In this work, we develop a…

Machine Learning · Computer Science 2026-05-20 Bipin Tiwari , Muhammad Abid , Omer San

A seismic wavefield reconstruction framework based on compressed sensing using the data-driven reduced-order model (ROM) is proposed and its characteristics are investigated through numerical experiments. The data-driven ROM is generated…

The finite element method (FEM) is a well-established numerical method for solving partial differential equations (PDEs). However, its mesh-based nature gives rise to substantial computational costs, especially for complex multiscale…

Computational Engineering, Finance, and Science · Computer Science 2025-06-24 Weihang Ouyang , Yeonjong Shin , Si-Wei Liu , Lu Lu

We study an inverse scattering problem for a generic hyperbolic system of equations with an unknown coefficient called the reflectivity. The solution of the system models waves (sound, electromagnetic or elastic), and the reflectivity…

Numerical Analysis · Mathematics 2020-02-03 Liliana Borcea , Vladimir Druskin , Alexander V. Mamonov , Mikhail Zaslavsky , Jörn Zimmerling

Projection-based Reduced Order Models (ROMs) are often deployed as static surrogates, which limits their practical utility once a system leaves the training manifold. We formalize and study adaptive non-intrusive ROMs that update both the…

Machine Learning · Computer Science 2026-02-13 Amirpasha Hedayat , Alberto Padovan , Karthik Duraisamy

A refined a priori error analysis of the lowest order (linear) nonconforming Virtual Element Method (VEM) for approximating a model Poisson problem is developed in both 2D and 3D. A set of new geometric assumptions is proposed on shape…

Numerical Analysis · Mathematics 2019-05-17 Shuhao Cao , Long Chen

We propose a new hyper-reduction method for a recently introduced nonlinear model reduction framework based on dynamically transformed basis functions and especially well-suited for advection-dominated systems. Furthermore, we discuss…

Numerical Analysis · Mathematics 2021-08-30 Felix Black , Philipp Schulze , Benjamin Unger

The simulation of many complex phenomena in engineering and science requires solving expensive, high-dimensional systems of partial differential equations (PDEs). To circumvent this, reduced-order models (ROMs) have been developed to speed…

Machine Learning · Computer Science 2025-10-27 Paolo Conti , Jonas Kneifl , Andrea Manzoni , Attilio Frangi , Jörg Fehr , Steven L. Brunton , J. Nathan Kutz