In the context of my Master Thesis I am testing the PINNs algorithm to infer hidden parameters in PDEs using neural networks.
The data is generated with finite differences on
following https://github.com/barbagroup/CFDPython.
The size of the mesh and T can be inferred from parameters in the options-dictionary
.
The amount of points is taken so that we can compare the results with those of https://github.com/Slowpuncher24/mlhiphy_v2 and https://github.com/Slowpuncher24/pde-net-in-tf.
The PDEs are:
- An advection-diffusion equation:
We provide the PINNs algorithm with the following form of the PDE, in which the coefficients have to be learned:
- A diffusion equation with nonlinear source:
Here we provide the PINNs algorithm with the following form of the PDE:
- The Burgers equation:
Here we provide the PINNs algorithm with the following form of the PDE:
The PINNs algorithm was developed by Maziar Raissi, Paris Perdikaris, and George Em Karniadakis. It is described in (https://maziarraissi.github.io/PINNs/) and their paper 'Physics Informed Deep Learning (Part II): Data-driven Discovery of Nonlinear Partial Differential Equations' (https://arxiv.org/pdf/1711.10566.pdf).