Eigenvalue initialisation and regularisation for koopman autoencoders and beyond

Abstract: Recent efforts have been made to learn the Koopman operator with predictive autoencoders. However, little attention has been payed to the initialisation of these networks. Noting the importance of eigenvalues to the action of a linear operator, one may ask whether it would be useful to employ them in the initialisation and regularisation of these autoencoders? To answer this, we devise a spectral eigenvalue initialisation and eigenvalue penalty scheme. Having done so, we discover that eigenvalues do in fact have great utility for this purpose. We demonstrate that in learning a Koopman operator for a damped driven pendulum, appropriate initialisation and regularisation can improve initial performance by an order of magnitude. We also show with this system that as the dissipative element of a dynamical system decreases, the utility of unit circle initialisation schemes increase and the utility of different regularisation schemes change. Additionally, we show that the benefits of eigenvalue initialisation and regularisation generalise to real-world cyclone wind data, sea surface temperature prediction and flow over a cylinder.

computational biologycomputational engineering, finance, and sciencenumerical analysiscomputational physics

Audience: researchers in the topic

ANU Mathematics and Computational Sciences Seminar