Multiscale Neural Operators for Solving Time-Independent PDEs

Winfried Ripken, Lisa Coiffard, Felix Pieper, Sebastian Dziadzio
11/10/2023
cs.LG

Official code: merantix-momentum/multiscale-pde-operators (5 stars, MIT, last commit 2023-11-13).

Abstract

Time-independent Partial Differential Equations (PDEs) on large meshes pose significant challenges for data-driven neural PDE solvers. We introduce a novel graph rewiring technique to tackle some of these challenges, such as aggregating information across scales and on irregular meshes. Our proposed approach bridges distant nodes, enhancing the global interaction capabilities of GNNs. Our experiments on three datasets reveal that GNN-based methods set new performance standards for time-independent PDEs on irregular meshes. Finally, we show that our graph rewiring strategy boosts the performance of baseline methods, achieving state-of-the-art results in one of the tasks.

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Code Implementations(1)

merantix-momentum/multiscale-pde-operatorsOfficial
MIT

Source code for paper: "Multiscale Neural Operators for Solving Time-Independent PDEs"

52PythonOct 30, 20232 years agoMIT

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Cite this paper

@article{ripken2023multiscale,
  title  = {Multiscale Neural Operators for Solving Time-Independent PDEs},
  author = {Winfried Ripken and Lisa Coiffard and Felix Pieper and Sebastian Dziadzio},
  year   = {2023},
  eprint = {2311.05964},
  archivePrefix = {arXiv},
  url    = {http://arxiv.org/abs/2311.05964v1}
}

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