Pytorch Implementation of Physics-informed Neural Networks (PINN)

In this repo, the both of discrete-time and continuous-time Burgers equation for inference and parameters identification are implemented.

Attribute

Original Work: Maziar Raissi, Paris Perdikaris, and George Em Karniadakis

Github Repo : https://github.com/maziarraissi/PINNs

@article{raissi2017physicsI, title={Physics Informed Deep Learning (Part I): Data-driven Solutions of Nonlinear Partial Differential Equations}, author={Raissi, Maziar and Perdikaris, Paris and Karniadakis, George Em}, journal={arXiv preprint arXiv:1711.10561}, year={2017} }

@article{raissi2017physicsII, title={Physics Informed Deep Learning (Part II): Data-driven Discovery of Nonlinear Partial Differential Equations}, author={Raissi, Maziar and Perdikaris, Paris and Karniadakis, George Em}, journal={arXiv preprint arXiv:1711.10566}, year={2017} }

Also, this repo is a good reference.

Some confusion points

For discrete-time case, what you need is a Jocobian matrix. However, torch.autograd.grad returns vector-Jacobian product. You need one more step to recover the jocobian matrix. I added some notes in my code.