Provenance data for Physics-informed neural networks: the case of the eikonal equation

• Lyncoln S. de Oliveira Federal University of Rio de Janeiro http://orcid.org/0000-0002-0015-0709
• Rômulo M. Silva Federal University of Rio de Janeiro
• Liliane Kunstmann Federal University of Rio de Janeiro
• Débora Pina Federal University of Rio de Janeiro
• Daniel de Oliveira Fluminense Federal University
• Alvaro L. G. A. Coutinho Federal University of Rio de Janeiro
• Marta Mattoso Federal University of Rio de Janeiro

DOI: https://doi.org/10.5753/sbbd.2022.225367

Abstract

Physics Informed Neural Networks (PINNs) have been showing a great impact on numerical methods applications. Despite the complexity of configuration and model generation, once trained, it presents a significant improvement in calculation time compared to numerical methods. The Physics constraining in training takes place through the modeling of new components added to the neural network's loss function. Such components augment the hyperparameter settings. In this work, we show how collecting provenance data can help the scientist to evaluate hyperparameters in the training of PINNs. We present experiments of PINNs with the partial differential equation given by the Eikonal equation.

Keywords: provenance, deep learning, data science, steering, human-in-the-loop

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