Solving PDEs with Physics-Informed Neural Networks

The following repository contains examples using Physics-Informed Neural Networks (PINN) to solve PDEs. We use the package NeuralPDE.jl to solve. This work is part of my senior capstone for Lawrence University in Appleton, WI. I have documented the techniques used here along with appropriate background information in this paper.

List of examples

Find a list of the example problems we have solved or are working on below

• Integral-PDE
• PDAE
• Linear, homogeneous PDE
• Einstein field equations to find Schwarzschild metric. This problem has been solved in its most simple case. Continued work is needed in extending the problem. Find more information in the README in src/solve_einstein.

Running the Code

Several required packages are included in the Project.toml to allow one to run this code out of the box. You can use the environment in this repo to quickly load the correct versions of the packages by running

julia> using Pkg
julia> Pkg.instantiate()

Then, to run the code either activate the environment and run from the REPL, or run the scripts with

julia --project <file_name>.jl

from terminal. Note that Julia needs to be in your path for this to work.

Contribution

Pull requests are encouraged!