cemac / LIFD_Physics_Informed_Neural_Networks

Leeds Institute for Fluid Dynamics Machine Learning For Earth Sciences

Physics Informed Neural Networks

These set of notebooks explore Physics Informed Neural Networks to explore Partial Differential Equations

This tutorial has been split into 3 tutorials.

Recommended Background Reading

If you are unfamiliar with some of the concepts covered in this tutorial it's recommended to read through the background reading below either as you go through the notebook or beforehand. These links are also contained within the notebooks

• Introduction to Neural Networks
• Physics Guided Neural Networks
• Physics-Informed Neural Networks: A Deep LearningFramework for Solving Forward and Inverse ProblemsInvolving Nonlinear Partial Differential Equations

Quick look

If you want a quick look at the contents inside the notebook before deciding to run it please view the pdfs generated (note some HTML code not fully rendered)

• PINNs 1D Heat Equation Example nonML
• PINNs 1D Heat Equation Example
• PINNs Navier Stokes example
• PINNs Navier Stokes Hidden Fluid Mechanics

Quick start

If you're already familiar with git, anaconda and virtual environments the environment you need to create is found in PINN.yml and the code below to install activate and launch the notebook. The .yml file has been tested on the latest linux, macOS and windows operating systems.

git clone  --recurse-submodules -j8 [e-mail]:cemac/LIFD_Physics_Informed_Neural_Networks.git
cd LIFD_Physics_Informed_Neural_Networks
conda env create -f PINN.yml
conda activate PINN
jupyter-notebook

Installation and Requirements

This notebook is designed to run on a laptop with no special hardware required therefore recommended to do a local installation as outlined in the repository howtorun and jupyter_notebooks sections.

These notebooks require some additional data from the PINNs repository

If you have not already then in your gitbash or terminal please run the following code in the LIFD_ENV_ML_NOTEBOOKS directory via the terminal(Mac or Linux) or git bash (windows)

git submodule init
git submodule update --init --recursive

If this does not work please clone the PINNs repository into your Physics_Informed_Neural_Networks folder on your computer

Licence information

LIFD_ENV_ML_NOTEBOOKS by cemac is licensed under a Creative Commons Attribution 4.0 International License.

Acknowledgements

Thanks to Matthew Gaddes for the basis of this tutotial. This tutorial is part of the LIFD ENV ML NOTEBOOKS please refer to for full acknowledgements.