This repository implements PINN in PyTorch environment to solve 1D Burgers' equation. Automatic differentiation, which is a generalization of back-propagation, is utilized to leverage the convenctional (fully-connected / dense) neural network architecture's representation power and to satisfy govering equations, initial, and boundary conditions.
Please note this repository is not intended to reproduce the results of PINN_TF2.
Burgers equation solution inferred by PINN (found in ./00_burgers/):
The above result is consistent with Raissi+2019.
[1] Raissi, M., Perdikaris, P., Karniadakis, G.E.: Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations, Journal of Computational Physics, Vol. 378, pp. 686-707, 2019. (paper)
[2] Baydin, A.G., Pearlmutter, B.A., Radul, A.A., Siskind, J.M.: Automatic Differentiation in Machine Learning: A Survey, Journal of Machine Learning Research, Vol. 18, No. 1, pp. 5595–5637, 2018. (paper)
[3] Rumelhart, D., Hinton, G., Williams, R.: Learning representations by back-propagating errors, Nature, Vol. 323, pp. 533–536, 1986. (paper)