NeuralGraphPDE.jl

Neural ODE + Method of Lines + Graph Neural Networks = NeuralGraphPDE
Author YichengDWu
Popularity
11 Stars
Updated Last
6 Months Ago
Started In
June 2022

NeuralGraphPDE

Stable Dev Build Status Coverage SciML Code Style

This package is based on GraphNeuralNetwork.jl and Lux.jl.

The goal is to extend Neural (Graph) ODE to Neural Graph PDE (experimental).

Technically, it has become a general framework for graph neural networks.

References

  1. Iakovlev V, Heinonen M, Lähdesmäki H. Learning continuous-time PDEs from sparse data with graph neural networks[J]. arXiv preprint arXiv:2006.08956, 2020.
  2. Poli M, Massaroli S, Rabideau C M, et al. Continuous-depth neural models for dynamic graph prediction[J]. arXiv preprint arXiv:2106.11581, 2021.
  3. Chamberlain B, Rowbottom J, Gorinova M I, et al. Grand: Graph neural diffusion[C]. International Conference on Machine Learning. PMLR, 2021: 1407-1418.
  4. Brandstetter J, Worrall D, Welling M. Message passing neural PDE solvers[J]. arXiv preprint arXiv:2202.03376, 2022.
  5. Li Z, Kovachki N, Azizzadenesheli K, et al. Neural operator: Graph kernel network for partial differential equations[J]. arXiv preprint arXiv:2003.03485, 2020.
  6. Toshev, Artur, et al. "On the Relationships between Graph Neural Networks for the Simulation of Physical Systems and Classical Numerical Methods." ICML 2022 2nd AI for Science Workshop. 2022.