Physics-informed neural networks (PINNs)

Nick McGreivy and Phil Travis are working on solving some problems in Plasma Physics with Physics-Informed Neural Networks (PINNs). This work is no longer in progress, but was presented at APS-DPP 2019.

Resources

This project is an application of Maziar Rassi's "physics informed neural networks" to plasma physics problems. The original paper by Rassi can be found on arXiv:1711.10561. Rassi also has a blog post explaining the concept here.

The poster given at APS DPP 2019 is in the root directory as APS-Poster-McGreivy-2019.pdf.

Requirements

Code requires:

• Python 3.x
• TensorFlow 1.14 (not 2.0 or above, unsure about the lower bound--Google Colab should work fine)
• ... and other common libraries

Code examples

vlasovFreeStream.py: solving the free-streaming Vlasov equation

using physics informed neural networks. This is the most commented / documented code file. This model converges to a solution nicely.

boundaryLayer.py: solving a boundary layer problem

for small epsilon. In this case, it is solved for $$\epsilon = 0.01$$ and $$0.005$$. This NN also converges.

vlasovEfield.py: Attempting to solve the Vlasov equation

now with an electric field term whose solution is given by Gauss's law. The solution did not converge within a reasonable amount of time and model capacity.

Here the solution f is being represented by a neural network whose inputs are x, v, and t. The electric field is represented by a different neural network whose inputs are x and t.

fluidOscillations.py:: Here we solve a set of cold-plasma fluid equations, which are continuity and momentum equations with an electric field term. These equations are