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Physics-informed neural networks for data-driven simulation: advantages, limitations, and opportunities

Fernández, Félix and Gijón, Alfonso and Molina-Solana, Miguel and Gómez-Romero, Juan
Physica A: Statistical Mechanics and its Applications (under review) (SUBMITTED)

Abstract:

The last decade has seen a rise in the number and variety of techniques available for data-driven simulation of physical phenomena. One of the most promising approaches is Physics-Informed Neural Networks (PINNs). This method allows system identification and analysis by combining both data obtained from sensors and physics knowledge expressed as partial differential equations. In this work, we investigated the suitability of PINNs to substitute current available numerical methods in physics simulations. A selection of typical heat transfer and fluid dynamics problems was proposed, and multiple PINNs were comprehensibly trained and tested to solve them. Despite the promising capabilities of PINNs, the outcome of the experiments was not entirely satisfactory, as not enough accuracy was achieved even though optimal configurations and long training times were used. The main cause for this limitation was found to be the lack of adequate activation functions, since they proved to have a notable impact on the final accuracy of each model.

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Bibtex:

@article{FernandezMata2022,
  author = {Fernández, Félix and Gijón, Alfonso and Molina-Solana, Miguel and Gómez-Romero, Juan},
  title = {Physics-informed neural networks for data-driven simulation: advantages, limitations, and opportunities},
  journal = {Physica A: Statistical Mechanics and its Applications},
  year = {SUBMITTED},
  volume = {(under review)},
  doi = {},
  comment = {},
  timestamp = {37}
}