README.md

SciML

Scientific Machine Learning exercises

To clone the repository files, run the following command from the command line

git clone https://github.com/apengsigkarup

The recommended way to install the necessary code to work with and run the exercises is to install the environment using conda

conda create -n SciML-env
conda activate SciML-env
conda install -r environment.yaml

In the Exercises/ directory there are some notebooks that contains selected problems for Physics-Informed Machine Learning / Scientific Machine Learning. In each exercise the task is to complete the code in all cells where '' is stated. The notebooks contains figures of results that was obtained in the complete solution and hence is the target to reproduce.

To open and use the notebooks, it is possible to use the free Google Colab.

Exercises (Google Colab)

The following notebooks can be opened and run directly in Google Colab (no local installation required):

• 00 – Getting Started [] (https://colab.research.google.com/github/apengsigkarup/SciML/blob/main/Exercises/00_Notebook_Getting_Started.ipynb)

• 01 – Function Approximation [] (https://colab.research.google.com/github/apengsigkarup/SciML/blob/main/Exercises/01_Notebook_FunctionApproximation.ipynb)

• 03 – PINN: Helmholtz Equation [] (https://colab.research.google.com/github/apengsigkarup/SciML/blob/main/Exercises/03_Notebook_PINN_Helmholtz.ipynb)

• 05b – UPINNs [] (https://colab.research.google.com/github/apengsigkarup/SciML/blob/main/Exercises/05b_Notebook_UPINNs.ipynb)

• 07 – Fourier Series (1D) [] (https://colab.research.google.com/github/apengsigkarup/SciML/blob/main/Exercises/07_Notebook_Fourier_Series_1D.ipynb)