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datafold is a MIT-licensed Python package containing operator-theoretic, data-driven models to identify dynamical systems from time series data and to infer geometrical structures in point clouds.
The package includes:
- Implementations and variants of the Dynamic Mode Decomposition as data-driven methods to
identify and analyze dynamical systems from time series collection data. This incldues:
DMDFull
orDMDEco
as standard methods of DMDOnlineDMD
orStreamingDMD
modify the DMD to handle streaming dataDMDControl
augments the DMD to handle additional control inputEDMD
- The Extended-DMD, which allows setting up a highly flexible dictionary to decompose and embed time series data and thereby handle nonlinear dynamics within the Koopman operator framework.EDMD
wraps an arbitrary DMD variation for the decomposition. The key advantage of this is, that theEDMD
directly profits from the above functionalities.EDMD
can be used in control or streaming settings. Furthermore, the dictionary can also be learnt from the data, corresponding to the EDMD-DL.
- An efficient implementation of the
DiffusionMaps
model to infer geometric meaningful structures from (time series) data, such as the eigenfunctions of the Laplace-Beltrami operator. As a distinguishing factor to other implementations, the model can handle a sparse kernel matrix and allows setting an arbitrary kernel, including the standard Gaussian kernel, continuous k-nearest neighbor kernel, or dynamics-adapted cone kernel. - Cross-validation. The method
EDMDCV
allows model parameters to be optimized with cross-validation splittings that account for the temporal order in time series data. - Methods to perform Model Predictive Control (MPC) with Koopman operator-based methods (
mainly the
EDMD
). - Regression models for high-dimensional data, which are commonly used for out-of-sample extensions for the Diffusion Maps model. This includes the (auto-tuned) Laplacian Pyramids or Geometric Harmonics to interpolate general function values on a point cloud manifold.
- A data structure
TSCDataFrame
to handle time series collection (TSC) data. It simplifies model inputs/output and make it easier to describe various forms of time series data.
See also this introduction page. For a mathematical thorough introduction, we refer to the scientific literature.
Note
The project is under active development in a research-driven environment.
Code quality varies from "experimental/early stage" to "well-tested". Well tested code is listed in the software documentation and are directly accessible through the highest module level (e.g.
from datafold import ...
). Experimental code is only accessible via "deep imports" (e.g.from datafol.dynfold.outofsample import ...
) and may raise a warning when using it.The interfaces within datafold are not stable. The software is not intended for production. Nevertheless, if we break something it is intentional and we hope that such adaptations become less over time.
There is no deprecation cycle. The software uses semantic versioning policy [major].[minor].[patch], i.e.
- major - making incompatible changes in the (documented) API
- minor - adding functionality in a backwards-compatible manner
- patch - backwards-compatible bug fixes
We do not intend to indicate a feature complete milestone with version 1.0.
If you use datafold in your research, please cite this paper published in the Journal of Open Source Software (JOSS).
Lehmberg et al., (2020). datafold: data-driven models for point clouds and time series on manifolds. Journal of Open Source Software, 5(51), 2283, https://doi.org/10.21105/joss.02283
BibTeX:
@article{Lehmberg2020,
doi = {10.21105/joss.02283},
url = {https://doi.org/10.21105/joss.02283},
year = {2020},
publisher = {The Open Journal},
volume = {5},
number = {51},
pages = {2283},
author = {Daniel Lehmberg and Felix Dietrich and Gerta K{\"o}ster and Hans-Joachim Bungartz},
title = {datafold: data-driven models for point clouds and time series on manifolds},
journal = {Journal of Open Source Software}}
Installation requires Python>=3.9 with pip and setuptools installed (both packages ship with a standard Python installation). The package dependencies install automatically. The main dependencies and their usage in datafold are listed in the section "Dependencies" below.
There are two ways to install datafold:
This is the standard way for users. The package is hosted on the official Python package index (PyPI) and installs the core package (excluding tutorials and tests). The tutorial files can be downloaded separately here.
To install the package and its dependencies with pip
, run
python -m pip install datafold
Note
If you run Python in an Anaconda environment you can use pip from within conda
.
See also
official instructions.
conda activate venv
conda install pip
pip install datafold
This way is recommended if you want to access the latest (but potentially unstable) development state, run tests or wish to contribute (see section "Contributing" for details). Download or git-clone the source code repository.
Download the repository
Install the package from the downloaded repository
python -m pip install .
Any contribution (code/tutorials/documentation improvements), question or feedback is very welcome. Either use the issue tracker or Email us. Instructions to set up datafold for development can be found here.
The dependencies of the core package are managed in the file requirements.txt and install with datafold. The tests, tutorials, documentation and code analysis require additional dependencies which are managed in requirements-dev.txt.
datafold integrates with common packages from the Python scientific computing stack:
- NumPy
- NumPy is used throughout datafold and is the default package for numerical data and algorithms.
- scikit-learn
- All datafold algorithms that are part of the "machine learning pipeline" align
to the scikit-learn API.
This is done by deriving the models from
BaseEstimator.
and appropriate
MixIns
. datafold defines ownMixIns
that align with the API in a duck-typing fashion to allow identifying dynamical systems from temporal data inTSCDataFrame
.
- SciPy
- The package is used for elementary numerical algorithms and data structures in conjunction with NumPy. This includes (sparse) linear least square regression, (sparse) eigenpairs solver and sparse matrices as optional data structure for kernel matrices.
Note: This list covers only Python packages.
- scikit-learn
- provides algorithms and models along the entire machine learning pipeline, with a
strong focus on static data (i.e. without temporal context). datafold integrates
into scikit-learn' API and all data-driven models are subclasses of
BaseEstimator.
An important contribution of datafold is the
DiffusionMaps
model as popular framework for manifold learning, which is not contained in scikit-learn's set of algorithms. Furthermore, datafold includes dynamical systems as a new model class that is operable with scikit-learn - the attributes align to supervised learning tasks. The key differences are that a model processes data of typeTSCDataFrame
and instead of a one-to-one relation in the model's input/output, the model can return arbitrary many output samples (a time series) for a single input (an initial condition).
- PyDMD
- provides many variants of the Dynamic Mode Decomposition (DMD). datafold provides a wrapper
to make models of
PyDMD
accessible. However, a limitation ofPyDMD
is that it only processes single coherent time series, see PyDMD issue 86. The DMD models that are directly included in datafold utilize the functionality of the data structureTSCDataFrame
and can therefore process time series collections - in an extreme case only containing snapshot pairs.
- PySINDy
- specializes on a sparse system identification of nonlinear dynamical systems to infer governing equations.