pdefinder 0.1.7

A package for discovering PDEs using data-driven techniques

Below is a description of our package

pdefinder is a Python package for discovering partial differential equations (PDEs) from data using data-driven techniques. The package implements methods inspired by PDE-FIND and includes utilities for building candidate libraries, computing numerical derivatives, performing sparse regression, and optimizing candidate coefficients.

Features

• Candidate Library Construction: Build a library of candidate PDE terms using polynomial functions and numerical differentiation.
• Numerical Differentiation: Compute derivatives using finite differences, polynomial interpolation, or Tikhonov regularization.
• Sparse Regression Methods: Available techniques include STRidge, Lasso, ElasticNet, and FoBa.
• Data Subsampling: Easily subsample data along spatial and temporal dimensions.
• LLM Integration: Interface with language models (via the OpenAI API) for initial coefficient estimation and verification.
• Optimization: Utilize CUDA-enabled PyTorch for efficient optimization of PDE coefficients.

Installation

Clone the repository and install the package locally:

git clone https://github.com/Amartya-Roy/pdefinder.git
cd pdefinder
pip install .

Alternatively, build the package distribution and install:

python setup.py sdist bdist_wheel
pip install dist/pdefinder-0.1.0-py3-none-any.whl

Usage

Command-Line Interface

You can run the PDE discovery pipeline from the command line. For example:

pdefinder --dataset KS --data_dir /path/to/data --P 5 --D 5 --epochs 1000

Python API

Import and run the main function in your own script:

from pdefinder import run_pde_finder

# Run the PDE discovery pipeline with custom parameters.
w_final, pde_expression = run_pde_finder(
    dataset='KS',
    P=5,
    D=5,
    num_epochs=1000,
    data_dir='/path/to/data',      
    llm_initial='my_llm',         # Identifier for the initial LLM
    llm_verification='my_llm'     # Identifier for the verification LLM
)

print("Optimized Coefficients:", w_final)
print("Discovered PDE:", pde_expression)

Parameters

• dataset: The dataset to use.(.mat or .npy format)
• P: Maximum polynomial power to include in the candidate library (default pipeline).
• D: Maximum derivative order to include (default pipeline).
• num_epochs: Number of epochs for the PyTorch optimization step (default pipeline).
• data_dir: Directory where the dataset files are located.
• llm_initial: Identifier for the language model used to generate initial coefficient guesses.
• llm_verification: Identifier for the language model used for verification.

Dependencies

The package requires:

• Python 3.6 or higher
• numpy
• scipy
• torch
• openai

Install the dependencies using pip:

pip install numpy scipy torch openai

License

This project is licensed under the MIT License.

Contributing

Contributions are welcome! Please open an issue or submit a pull request on GitHub for any bug reports, feature requests, or improvements.

Acknowledgments

This package is inspired by recent advances in data-driven PDE discovery methods. Special thanks to Soumya Mallick who helped me thinking about this idea.

Repository

For more information, visit the GitHub repository:
https://github.com/Amartya-Roy/pdefinder