We propose implementing the algorithm "Sparse Identification for Nonlinear Dynamics," or SINDy (https://www.pnas.org/doi/full/10.1073/pnas.1517384113) to learn the ordinary differential equations which govern a chaotic double pendulum. We will use this data set: https://developer.ibm.com/exchanges/data/all/double-pendulum-chaotic/, which is gathered from filming an example double pendulum and samples the positions of the two ends of the pedulum hundreds of times per second. Without any prior knowledge of the governing ODEs, we will attempt to learn the governing dynamics. We will break our data set into chunks of 1-2 seconds, and reserve some of these chunks of data as the test set. Because the dynamics of the double pendulum are chaotic, the only hope of predicting correct behaviors for the test set will be by learning the governing ODEs.
There are substantial opportunities for using algorithms of this type in industry. Examples include identifying low-dimensional representation of complex systems, such as power grids, economic models, etc.