Abstract
In analogy to the use of normalizing flows to augment the expressivity of base probability distributions, I propose to augment the expressivity of bases of Hilbert spaces via composition with normalizing flows. I show that the redsulting sequences are also bases of the Hilbert space under sufficient and necessary conditions on the flow. This lays a foundation for a theory of spectral learning, a nonlinear extension of spectral methods for solving differential equations. As an application I solve the vibrational molecular Schrödinger equation. The proposed numerical scheme results in several orders of magnitude increased accuracy over the use of standard spectral methods.
Talk in the series “Train Your Engineering Network”.
