SymDer: Symbolic Derivative Network for Discovering Sparse Interpretable Dynamics from Partial Observations

Implementation of a machine learning method for identifying the governing equations of a nonlinear dynamical system using using only partial observations. Our machine learning framework combines an encoder for state reconstruction with a sparse symbolic model. In order to train our model by matching time derivatives, we implement an algorithmic trick (see symder/odeint_zero.py) for taking higher order derivatives of a variable that is implicitly defined by a differential equation (i.e. the symbolic model).

Please cite "Discovering sparse interpretable dynamics from partial observations" (https://doi.org/10.1038/s42005-022-00987-z) and see the paper for more details. This is the official repository for the paper.

Requirements

JAX >= 0.2.8, Haiku >= 0.0.4, scikit-learn, NumPy, SciPy

Usage

Data generation scripts are contained in data/. Encoder models and related tools are contained in encoder/. Symbolic models and the tools for taking higher order symbolic time derivatives are contained in symder/. The individual *_model.py files provide examples of how to use our method on a variety of ODE and PDE systems.