Recurrent Neural Networks for Partially Observed Dynamical Systems

Autor:	Bhat, Uttam, Munch, Stephan B.
Rok vydání:	2021
Předmět:	Computer Science - Machine Learning Nonlinear Sciences - Chaotic Dynamics
Druh dokumentu:	Working Paper
DOI:	10.1103/PhysRevE.105.044205
Popis:	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 RNN and facilitates principled incorporation of structure and other constraints into these approaches. Comment: 11 pages, 5 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2109.11629 Zobrazit plný text záznamu View this record from Arxiv