The effect of time discretization on the solution of parabolic PDEs with ANNs

@article{Calabr2022TheEO,
  title={The effect of time discretization on the solution of parabolic PDEs with ANNs},
  author={Francesco Calabr{\`o} and Salvatore Cuomo and Daniela di Serafino and Giuseppe Izzo and Eleonora Messina},
  journal={ArXiv},
  year={2022},
  volume={abs/2206.00452}
}
We investigate the resolution of parabolic PDEs via Extreme Learning Machine (ELMs) Neural Networks, which have a single hidden layer and can be trained at a modest computational cost as compared with Deep Learning Neural Networks. Our approach addresses the time evolution by applying classical ODEs techniques and uses ELM-based collocation for solving the resulting stationary elliptic problems. In this framework, the θ-method and Backward Difference Formulae (BDF) techniques are investigated… 
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