June 6, 2024, 4:42 a.m. | Victor Matray (LMPS), Faisal Amlani (LMPS), Fr\'ed\'eric Feyel (LMPS), David N\'eron (LMPS)

cs.LG updates on arXiv.org arxiv.org

arXiv:2406.02615v1 Announce Type: new
Abstract: This work introduces a new approach for accelerating the numerical analysis of time-domain partial differential equations (PDEs) governing complex physical systems. The methodology is based on a combination of a classical reduced-order modeling (ROM) framework and recently-introduced Graph Neural Networks (GNNs), where the latter is trained on highly heterogeneous databases of varying numerical discretization sizes. The proposed techniques are shown to be particularly suitable for non-parametric geometries, ultimately enabling the treatment of a diverse range …

abstract analysis applications arxiv combination cs.ai cs.lg differential domain dynamics framework graph graph neural networks hybrid methodology modeling networks neural networks non-parametric numerical parametric physics.class-ph systems type work

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