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Multi-scale Physical Representations for Approximating PDE Solutions with Graph Neural Operators. (arXiv:2206.14687v1 [cs.LG])
June 30, 2022, 1:12 a.m. | Léon Migus, Yuan Yin, Jocelyn Ahmed Mazari, Patrick Gallinari
cs.CV updates on arXiv.org arxiv.org
Representing physical signals at different scales is among the most
challenging problems in engineering. Several multi-scale modeling tools have
been developed to describe physical systems governed by \emph{Partial
Differential Equations} (PDEs). These tools are at the crossroad of principled
physical models and numerical schema. Recently, data-driven models have been
introduced to speed-up the approximation of PDE solutions compared to numerical
solvers. Among these recent data-driven methods, neural integral operators are
a class that learn a mapping between function spaces. These …
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