Recurrent Neural Networks for Partially Observed Dynamical Systems

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.

• Publication year

  2021

• Venue

  Physical Review E

• Publication date

  2021-09-21

• Fields of study

  Mathematics, Physics, Computer Science, Medicine

• Identifiers
  DOI 10.1103/PhysRevE.105.044205arXiv 2109.11629PMID 35590539
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar, PubMed

• No claims are published for this paper.

• No concepts are published for this paper.

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