LeMON-PROSE: Learning to Learn Multi-Operator Networks - Predictiong Operators and Symbolic Expressions

This work is based on previous works from our group:

• 🔭 PROSE: Predicting Multiple Operators and Symbolic Expressions

• 🔭 PROSE-PDE: Towards a Foundation Model for Partial Differential Equations: Multi-Operator Learning and Extrapolation.

Data Generation

The data generator is partially based on PDEBench, fplanck and Pseudo-spectral KdV solver.

See detailed instruction in script/gen_data.sh

bash scripts/gen_data.sh

The data is by default saving to your_directory/type_name/(type_name)_(IC_per_params).prefix for symbol part and your_directory/type_name/(type_name)_(IC_per_params)_data.h5 for data part

If some specific data need to be generated, change "file_name=specific_name", samples are given in script/gen_data.sh and data will be stored in your_directory/type_name/(type_name)_(IC_per_params)_(file_name).prefix and your_directory/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

LoRA fine-tuning vs Regular fine-tuning:

LoRA code is based on this_tutorial.

bash scripts/loraexperiments.sh

PAML experiments:

PAML code is based on learn2learn library.

bash scripts/PAML.sh