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 Gaussian 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.

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 on how to use the package, check out the example notebooks and documentation.

Schematic illustration of PyDaddy functionality.

PyDaddy is available both on PyPI and Anaconda Cloud, and can be installed on any system with a Python 3 environment. If you don't have Python 3 installed on your system, we recommend using Anaconda or Miniconda. See the PyDaddy package documentation for detailed installation instructions.

To install the latest stable release version of PyDaddy, use:

pip install pydaddy

To install the latest development version of PyDaddy, use:

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

To install using conda, Anaconda or Miniconda need to be installed first. Once this is done, use the following command.

conda install -c tee-lab pydaddy

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

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.

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