This repository is intended to share some of my recent findings in the understanding, understanding and applycation of PINN's. The framework used to develop the code was PyTorch.
- Approximate Function
- Simple ODE
- 1D PDE: 1D Poisson (Direchlet)
- 2D PDE: Diffusion Equation
I highly sugged that you run the notebook in Google Colab, in order to take advantage of the GPU capabilities.
Special tahnks to Juan Diego Toscano (@jdtoscano94) for sharing some of the code that I used to created this notebooks.
You can find his work here: https://github.com/jdtoscano94/Learning-PINNs-in-Pytorch-Physics-Informed-Machine-Learning
[1] Raissi, M., Perdikaris, P., & Karniadakis, G. E. (2017). Physics informed deep learning (part i): Data-driven solutions of nonlinear partial differential equations. arXiv preprint arXiv:1711.10561. http://arxiv.org/pdf/1711.10561v1
[2] Lu, L., Meng, X., Mao, Z., & Karniadakis, G. E. (1907). DeepXDE: A deep learning library for solving differential equations,(2019). URL http://arxiv. org/abs/1907.04502. https://arxiv.org/abs/1907.04502
[3] Rackauckas Chris, Introduction to Scientific Machine Learning through Physics-Informed Neural Networks. https://book.sciml.ai/notes/03/
[4] Repository: Physics-Informed-Neural-Networks (PINNs).https://github.com/omniscientoctopus/Physics-Informed-Neural-Networks/tree/main/PyTorch/Burgers'%20Equation