Algorithmically designed artificial neural networks (ADANNs)

This repository contains the code for the paper "Algorithmically Designed Artificial Neural Networks (ADANNs): Higher order deep operator learning for parametric partial differential equations". The paper is available on arXiv.

Running the code

All the numerical results in the paper can be reproduced by running the script execute_notebooks.sh in the 2_ADANNs directory. The following commands (run in the 2_ADANNs directory) can be used to reproduce the results of specific sections of the paper:

Section 4.2.2

papermill ADANN_semilinear_heat.ipynb Z_output_ADANN_semilinear_heat_1d.ipynb -p dim 1 -p test_run False

Section 4.2.3

papermill ADANN_semilinear_heat.ipynb Z_output_ADANN_semilinear_heat_2d.ipynb -p dim 2 -p test_run False

Section 4.3.2

papermill ADANN_Burgers.ipynb Z_output_ADANN_Burgers.ipynb -p test_run False

Section 4.4.2

papermill ADANN_Reaction_Diffusion.ipynb Z_output_ADANN_Reaction_Diffusion.ipynb -p test_run False

Section A.1

papermill ADANN_learning_rate_experiments.ipynb Z_output_ADANN_learning_rate_experiments.ipynb -p test_run False

Requirements

To run the scripts and reproduce the numerical results the following python packages are needed:

• pytorch
• matplotlib
• pandas
• importlib
• openpyxl
• scipy
• seaborn
• neuraloperator
• wandb
• ruamel.yaml
• configmypy
• tensorly
• tensorly-torch
• torch-harmonics
• opt-einsum
• h5py
• zarr
• scikit-optimize
• papermill