From fascinating Idea of PINN (ft. Maziar Raissi), this one is baby step to explore and understand PINNs.
Idea is to make PINN for approximating (Exactly) simple 1-D equations and understand the implementation.
- Polynomial - f(x) = y = x^2 in range (-20,20)
- Trigonometric - f(x) = y = x + sin(4 pi x) in range (0,1)
- 1st_order_ode - df(x)/dx = 1/x in range(0.5,10) with f(1)=0
https://maziarraissi.github.io/PINNs/
@article{raissi2019physics,
title={Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations},
author={Raissi, Maziar and Perdikaris, Paris and Karniadakis, George E},
journal={Journal of Computational Physics},
volume={378},
pages={686--707},
year={2019},
publisher={Elsevier}
}
@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}
}