Building on the well-understood mathematical theory of controlled differential equations, we demonstrate how to construct models that:

• Act directly on irregularly-sampled partially-observed multivariate time series.
• May be trained with memory-efficient adjoint backpropagation - even across observations.
• Demonstrate state-of-the-art performance.

They are straightforward to implement and evaluate using existing tools, in particular PyTorch and the torchdiffeq library.

Code for reproducing experiments is provided, as well as a convenience library controldiffeq to make computing Neural CDEs easy.

The library is in the controldiffeq folder, which may be imported as a Python module: import controldiffeq. Check the folder for details on how to use it.

An example can be found here, which demonstrates how to train a Neural CDE to detect the chirality (clockwise/anticlockwise) of a spiral.

Everything to reproduce the experiments of the paper can be found in the experiments folder. Check the folder for details.

As an example (taken from the paper - have a look there for similar results on other datasets):

@article{kidger2020neuralcde,
    author={Kidger, Patrick and Morrill, James and Foster, James and Lyons, Terry},
    title={{Neural Controlled Differential Equations for Irregular Time Series}},
    year={2020},
    journal={arXiv:2005.08926}
}