Preliminary Analysis on Dynamics Equation Discovery with Locally Structured Unitary Network

This work analyses effectiveness of Locally Structured Unitary Networks (LSUN) for dynamics modeling. LSUN is expected to be used for data-driven modeling of physical phenomena because its features of locality, overlap, and shift variability enable dimensionality reduction that effectively captures complex physical phenomena varying in space and time. In this study, LSUN is trained on simulated data of dynamical models governed by partial differential equations, and the relationship between its impulse responses and the original governing equations is discussed. It is confirmed the LSUN’s ability to capture local structure for data generated from bivariate wave equations and transport equations.