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Python package to discover stochastic differential equations from time series data

# tee-lab/PyDaddy

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# PyDaddy

## Python Data Driven Dynamics

A Python package to discover stochastic differential equations from time series data.

PyDaddy is a comprehensive and easy to use python package to discover data-derived stochastic differential equations from time series data. PyDaddy takes the time series of state variable $x$, scalar or 2-dimensional vector, as input and discovers an SDE of the form: $$\frac{dx}{dt} = f(x) + g(x) \cdot \eta(t)$$

where $\eta(t)$ is uncorrelated white noise. The function $f$ is called the drift, and governs the deterministic part of the dynamics. $g^2$ is called the diffusion and governs the stochastic part of the dynamics.

PyDaddy offers rich functionality to visualize the time series data and discover the drift and diffusion components. PyDaddy can also discover symbolic equations (such as polynomials) to the drift and diffusion functions using sparse regression.

An example summary plot generated by PyDaddy, for a vector time series dataset.

PyDaddy also provides a range of functionality such as equation-learning for the drift and diffusion functions using sparse regresssion, a suite of diagnostic functions, etc.. For more details, check out the PyDaddy tutorials, example notebooks and documentation for more details on how to use the package.

## Installation

PyDaddy is available both on PyPI and anaconda cloud and requires an environment with python3 environment.

### Using pip

pip install pydaddy


or

pip install git+https://github.com/tee-lab/PyDaddy.git


### Using anaconda

conda install -c tee-lab pydaddy


### Manual installation

Alternatively, the package can also be installed by cloning/downloading the git repository and running setup.py file.

git clone https://github.com/tee-lab/PyDaddy.git
cd PyDaddy
python setup.py install


## Documentation

For more information about PyDaddy, check out the package documentation.

## Citation

If you are using this package in your research, please cite the repository and the associated paper as follows:

Nabeel, A., Karichannavar, A., Palathingal, S., Jhawar, J., Danny Raj, M., & Guttal, V. (2022). PyDaddy: A Python Package for Discovering SDEs from Time Series Data (Version 0.1.5) [Computer software]. https://github.com/tee-lab/PyDaddy

Nabeel, A., Karichannavar, A., Palathingal, S., Jhawar, J., Danny Raj, M., & Guttal, V. (2022). PyDaddy: A Python package for discovering stochastic dynamical equations from timeseries data. arXiv preprint arXiv:2205.02645.

## Licence

PyDaddy is distributed under the GNU General Public License v3.0.

## About

Python package to discover stochastic differential equations from time series data

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