Hi, I’m Juan Diego Toscano. Thanks for stopping by.
This repository will help you get involved in the physics-informed machine learning world. In particular, it is a step-by-step guide that covers some of the basic concepts required to run a Physics-informed Neural Network(PINN) in Pytorch (from approximating functions, solving PDEs, forward and Inverse problems). You will also find some tutorials on Deeponets.
I solved some of the problems on this repository on my Youtube channel, so please review them if you have time. Youtube Channel: https://www.youtube.com/channel/UC6ryWzulr-Xom2Bym7O_CvQ
Right now, I am a bit busy. However, in the future, I will upload more examples on DeepOnets, and other types of PINNs.
If you have any questions or if I can help you in some way, please feel free to reach me at: juan_toscano@brown.edu.
Note: Most of the examples in this repository were taken from:
DeepXDE library: https://deepxde.readthedocs.io/en/latest/
PINNs Repository 1: https://github.com/omniscientoctopus/Physics-Informed-Neural-Networks/tree/main/PyTorch/Burgers'%20Equation
PINNs Repository 2: https://github.com/alexpapados/Physics-Informed-Deep-Learning-Solid-and-Fluid-Mechanics.
DeepOnets Respository 1: https://github.com/PredictiveIntelligenceLab/Physics-informed-DeepONets
[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
[5] Raissi, M., Perdikaris, P., & Karniadakis, G. E. (2017). Physics Informed Deep Learning (part ii): Data-driven Discovery of Nonlinear Partial Differential Equations. arXiv preprint arXiv:1711.10566. https://arxiv.org/abs/1711.10566
[6] Repository: PPhysics-Informed Deep Learning and its Application in Computational Solid and Fluid Mechanics.https://github.com/alexpapados/Physics-Informed-Deep-Learning-Solid-and-Fluid-Mechanics.
[7] Lu, L., Jin, P., & Karniadakis, G. E. (2019). Deeponet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators. arXiv preprint arXiv:1910.03193.
[8] Wang, S., Wang, H., & Perdikaris, P. (2021). Learning the solution operator of parametric partial differential equations with physics-informed DeepONets. Science advances, 7(40), eabi8605.