README.md

PINN-PE

Numerical component of Hu, R., Lin, Q., Raydan, A. et al. Higher-order error estimates for physics-informed neural networks approximating the primitive equations. Partial Differ. Equ. Appl. 4, 34 (2023). https://doi.org/10.1007/s42985-023-00254-y

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You will need to install PyTorch and DeepXDE. If you are using a conda environment you can install both with the following commands:

conda install pytorch
conda install -c conda-forge deepxde

After both are installed, you will need to set DeepXDE's backend to pytorch in order for it to know that it should use PyTorch for it's neural networks. Consult the DeepXDE documentation for how to do this.

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Program Entry Point

You can run the program in main.py by passing the equation number of the benchmark equation from section 5 that you wish to train as a command line argument. For example,

python3 main.py 5.2

will train the PINN on the initial and boundary data given from equation 5.2.

The program will attempt to execute two runs in parallel; one trained using the $L^2$ residuals and the other using the $H^1$ residuals.