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Introduction

This module can be used to train a Physics-Informed Neural Network (PINN) to solve the following nonlinear ordinary differential equation (ODE),

$$\overset{\textstyle\cdot\cdot}{u} \: + \: u - \: 3 \: \frac{u^2}{2} = 0 ,$$

which describes the orbit of photons in a Schwarzschild spacetime about a spherically symmetric body, where

$$u = \frac{r_s }{ r},$$

and $r_s$ is the Schwarzschild radius.

Installation

The notebooks can run within Colab and as well as locally using the following commands:

conda update conda
conda create -n slicer python=3.11
conda activate slicer
conda install jupyterlab notebook
conda install pytorch
conda install matplotlib
conda install pandas

Then clone the repository in the activated environment, here called slicer,

git clone https://github.com/soot-bit/pinnslicer.git
cd pinnslicer

then install the project in editable mode (installs dependencies too) using,

pip install -e .