Operator Learning on Free-Form Geometries - Laboratoire d'Informatique de Paris 6
Conference Papers Year : 2023

Operator Learning on Free-Form Geometries

Abstract

Operator Learning models usually rely on a fixed sampling scheme for training which might limit their ability to generalize to new situations. We present CORAL, a new method which leverages Coordinate-Based Networks for OpeRAtor Learning without any constraints on the training mesh or input sampling. CORAL is able to solve complex Initial Value Problems such as 2D Navier-Stokes or 3Dspherical Shallow-Water and can perform zero-shot super-resolution to recover a dense grid, even when the training grid is irregular and sparse. It can also be applied to the task of geometric design with structured or point-cloud data, to infer the steady physical state of a system given the characteristics of the domain.
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Dates and versions

hal-04702425 , version 1 (19-09-2024)

Identifiers

  • HAL Id : hal-04702425 , version 1

Cite

Louis Serrano, Jean-Noël Vittaut, Patrick Gallinari. Operator Learning on Free-Form Geometries. ICLR 2023 Workshop on Physics for Machine Learning, May 2023, Kigali, Rwanda. ⟨hal-04702425⟩
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