Sobolev Training for Physics Informed Neural Networks

Understand

Physics Informed Neural Networks (PINNs) is a promising application of deep learning.

• The smooth architecture of a fully connected neural network is appropriate for finding the solutions of PDEs; the corresponding loss function can also be intuitively designed and guarantees the convergence for various kinds of PDEs.
• However, the rate of convergence has been considered as a weakness of this approach.
• This paper proposes Sobolev-PINNs, a novel loss function for the training of PINNs, making the training substantially efficient.