Inverse-Dirichlet Weighting Enables Reliable Training of Physics Informed Neural Networks

@article{Maddu2021InverseDirichletWE,
  title={Inverse-Dirichlet Weighting Enables Reliable Training of Physics Informed Neural Networks},
  author={Suryanarayana Maddu and Dominik Sturm and Christian L. M{\"u}ller and Ivo F. Sbalzarini},
  journal={ArXiv},
  year={2021},
  volume={abs/2107.00940}
}
We characterize and remedy a failure mode that may arise from multi-scale dynamics with scale imbalances during training of deep neural networks, such as Physics Informed Neural Networks (PINNs). PINNs are popular machine-learning templates that allow for seamless integration of physical equation models with data. Their training amounts to solving an optimization problem over a weighted sum of data-fidelity and equation-fidelity objectives. Conflicts between objectives can arise from scale… Expand

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