CONFIDE: Contextual Finite Differences Modelling of PDEs

This repository is an implementation of the CONFIDE paper, which is part of the proceedings of KDD 2024.

Example results for signal prediction using (from left to right): (1) Ground truth, (2) CONFIDE, (3) FNO, and (4) UNET (other baselines are worse).

Data creation

To create the datasets used in the paper run:

• Constant coefficient PDE: python create_data/create_data.py --config-file create_data/configs/const_pde_default.yaml
• Burgers' PDE: python create_data/create_data.py --config-file create_data/configs/burgers_default.yaml
• FitzHugh-Nagumo PDE: python create_data/create_data.py --config-file create_data/configs/fn2d_default.yaml

The data would be created using default arguments. To view / modify them check the file create_data/configs/create_data_defaults.py file, and the corresponding modifications in the YAML files.

Training

To train the CONFIDE model run: python src/train_confide_model.py --config-file CONFIG_PATH where CONFIG_PATH should be changed to the specific required experiment. For example, use src/configs/burgers_pde/confide.yaml for the Burgers' equation.

To train baselines:

• CONFIDE-0: python src/train_confide_0_model.py --config-file CONFIG_PATH.
• FNO: python train_fno.py --config-file CONFIG_PATH.
• UNET: python train_unet.py --config-file CONFIG_PATH.
• Latent-ODE (Neural ODE): python train_latent_ode_model.py --config-file CONFIG_PATH.

Requirements:

Described in the requirementes.txt file. Joblib is used for data creation and neuralop is used speficially for FNO.

Citing:

Please cite this project when using it:

@inproceedings{linial2024confide,
  title={CONFIDE: Contextual Finite Difference Modelling of PDEs},
  author={Linial, Ori and Avner, Orly and Di Castro, Dotan},
  booktitle={Proceedings of the 30th ACM SIGKDD Conference on Knowledge Discovery and Data Mining},
  pages={1839--1850},
  year={2024}
}