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Discovering Differential Equations with Neural ODEs

This repository demonstrates how to use the Universal Differential Equation [1] method to discover terms in a differential equation using neural networks, neural ODEs, and sparse symbolic regression [2].

MathWorks® Products

Requires MATLAB® release R2023b or newer.

License

The license is available in the license.txt file in this GitHub repository.

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Copyright 2024 The MathWorks, Inc.

References

  1. Christopher Rackauckas, Yingbo Ma, Julius Martensen, Collin Warner, Kirill Zubov, Rohit Superkar, Dominic Skinner, Ali Ramadhan, and Alan Edelman. "Universal Differential Equations for Scientific Machine Learning". Preprint, submitted January 13, 2020. https://arxiv.org/abs/2001.04385
  2. Steven L. Brunton, Joshua L. Proctor, and J. Nathan Kutz. "Discovering governing equations from data by sparse identification of nonlinear dynamical systems". Proceedings of the National Academy of Sciences, 113 (15) 3932-3937, March 28, 2016.