Learning-PIML-in-Python-PINNs-DeepONets-RBA

Hi, I’m Juan Diego Toscano. Thanks for stopping by.

This repository will help you to get involved in the physics-informed machine learning world. Inside the Tutorials folders, you will find several step-by-step guides on the basic concepts required to run and understand Physics-informed Machine Learning models (from approximating functions, solving and discovering ODE/PDEs with PINNs, to solving parametric PDEs with DeepONets).

Also, for advanced users, you can find our latest research in PINNs to achieve state-of-the-art performance using residual-based attention (RBA).

I reviewed some of these problems on my YouTube channel, so please watch them if you have time.

PINNs Youtube Tutorial:https://youtu.be/AXXnSzmpyoI

Inverse PINNs Youtube Tutorial: https://youtu.be/77jChHTcbv0

PI-DeepONets Youtube Tutorial:https://youtu.be/YpNYVD9B_Js

Also, if you are interested and PINNs and Machine Learning, please consider subscribing to the Crunch Group (Brown University) Youtube channel. They upload weekly seminars on Scientific Machine Learning.

https://www.youtube.com/channel/UC2ZZB80udkRvWQ4N3a8DOKQ

Note: The tutorials 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 Repository 1: https://github.com/PredictiveIntelligenceLab/Physics-informed-DeepONets

Also here is our official implementation of RBA weights in PyTorch:

RBA Repository: https://github.com/soanagno/rba-pinns

References

[1] Anagnostopoulos, S. J., Toscano, J. D., Stergiopulos, N., & Karniadakis, G. E. (2024). Residual-based attention in physics-informed neural networks. Computer Methods in Applied Mechanics and Engineering, 421, 116805.

[2] 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

[3] 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

[4] Rackauckas Chris, Introduction to Scientific Machine Learning through Physics-Informed Neural Networks. https://book.sciml.ai/notes/03/

[5] Repository: Physics-Informed-Neural-Networks (PINNs).https://github.com/omniscientoctopus/Physics-Informed-Neural-Networks/tree/main/PyTorch/Burgers'%20Equation

[6] 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

[7] Repository: Physics-Informed Deep Learning and its Application in Computational Solid and Fluid Mechanics.https://github.com/alexpapados/Physics-Informed-Deep-Learning-Solid-and-Fluid-Mechanics.

[8] 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.

[9] 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.