Year: 2022
Type: article
Abstract: Complex nonlinear dynamics are ubiquitous in many fields. Moreover, we rarely have access to all of the relevant state variables governing the dynamics. Delay embedding allows us, in principle, to account for unobserved state variables. Here we provide an algebraic approach to delay embedding that permits explicit approximation of error. We also provide the asymptotic dependence of the first-order approximation error on the system size. More importantly, this formulation of delay embedding can be directly implemented using a recurrent neural network (RNN). This observation expands the interpretability of both delay embedding and the RNN and facilitates principled incorporation of structure and other constraints into these approaches.
Source: Physical review. E
Authors: Uttam Bhat, Stephan B. Munch
Institution: University of California, Santa Cruz
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W3202358270