BiLO: Bilevel Local Operator Learning for PDE Inverse Problems

This repository contains the code for the paper "BiLO: Bilevel Local Operator Learning for PDE Inverse Problems"

Tutorial

See the tutorial for example of solving inverse problem using BiLO.

Citing

If you use BiLO, please cite the following paper:

@misc{zhang2024bilo,
      title={BiLO: Bilevel Local Operator Learning for PDE inverse problems}, 
      author={Ray Zirui Zhang and Xiaohui Xie and John Lowengrub},
      year={2024},
      eprint={2404.17789},
      archivePrefix={arXiv},
      primaryClass={cs.LG}
}

Experiments

To run the experiments in the paper, use the following command:

python ExpRunner.py test [--dryrun]

Set test to be fk for Fisher-KPP equation example, varpoi for variable Poisson equation example, heat for Heat equation example, ode for nonlinear ODE example. fkop for Fisher-KPP equation example with DeepONet. darcy for Darcy flow equation, varpoiop for Variable Poisson equation example with DeepONet.

To see the commands that will be run, use the --dryrun flag.

The experiments are managed by mlflow. Set the path in config.py.

Dataset

The pretrain datasets, which are numerical solutions generated by Matlab, can be found here.