In this work, we take the first steps in making use of this connection.

As discussed in Sec. 3 of the main text, the computational complexity of Koopman training is We assume that both standard training and Koopman training use simple matrix computation methods. We note that none of these factors are relevant for Koopman training. The finite section method, Eq. 4, implies the run time complexity would be The authors contributed equally 34th Conference on Neural Information Processing Systems (NeurIPS 2020), V ancouver, Canada. Koopman operator(s) and evolve each partition separately from the others. In Sec. 3, we discussed when we think this "patching" approach should give small errors.

Koopman operator theory, a powerful framework for discovering the underlying dynamics of nonlinear dynamical systems, was recently shown to be intimately connected with neural network training. In this work, we take the first steps in making use of this connection.