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LeMON: Learning to Learn Multi-Operator Networks

Data Generation: See detailed instruction in gen_data.sh

bash scripts/gen_data.sh

Data output Structure

Default Output

By default, the generated data is saved in the Dir/type_name/ directory with the following structure:

Component File Path Pattern
Symbols Dir/type_name/(type_name)_(IC_per_params).prefix
Data Dir/type_name/(type_name)_(IC_per_params)_data.h5

Custom Output

To generate specific datasets, modify the file_name variable in gen_data.sh. Examples are provided within the script.

When using a custom file_name, the output structure becomes:

Component File Path Pattern
Symbols Dir/type_name/(type_name)_(IC_per_params)_(file_name).prefix
Data Dir/type_name/(type_name)_(IC_per_params)_(file_name)_data.h5

Run the code

Data

Just specify your data.train_types and data.eval_types and if some specific_name needed, add data.eval_data=specific_name and data.train_data=specific_name

Num of training and Num of evaluation:

data.train_size is the num of training sample in total, and we subsample data.train_size_get for real training. Same for data.eval_size and data.eval_size_get

We use skip = data.train_size (~line 54 of evaluator.py) to avoid sampling the same data for training and evaluation. However, if you want to save space/ your evaluation dataset and training dataset are different, you can comment that out.

Experiments

Single Operator Comparison:

bash scripts/deeponet.sh
bash scripts/fno.sh
bash scripts/prose_onlyqc.sh

LeMON experiments:

LeMON code is based on learn2learn library.

bash scripts/learnable_lr.sh

Citation

If you find our paper and code useful, please consider citing:

@article{sun2024lemon,
  title={Lemon: Learning to learn multi-operator networks},
  author={Sun, Jingmin and Zhang, Zecheng and Schaeffer, Hayden},
  journal={arXiv preprint arXiv:2408.16168},
  year={2024}
}

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