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This paper proposes "causal embedding," a method for reconstructing the dynamics of a driven system from pairs of observation points, and claims it offers better stability and learnability than Takens delay embedding and some reservoir computing approaches. The authors report gains over next-generation reservoir computing and SINDy-PI, but the evidence is limited to the abstract, so the claims need independent benchmarking. For ML readers, the key question is whether this framework generalizes beyond the tested systems.
Universal set of Observables for Forecasting Physical Systems through Causal Embedding
arXiv:2105.10759v4 Announce Type: replace-cross Abstract: We show how a pair of points can uniquely represent a left-infinite sequence obtained from observations of an underlying dynamical system through a phenomenon called \textit{causal embedding}. A driven dynamical system creates such pairs, and a function can be learnt on them that can reconstruct the underlying dynamics as in Takens delay embedding. The approach assures embedding stability unlike Takens delay embedding, and learnability which can be absent while stability can be present in the current reservoir computing framework. This accurately models underlying systems where recent methods like the next-generation reservoir computing fail. We demonstrate results and compare with the other methods including SINDY-PI.
Abstract:We show how a pair of points can uniquely represent a left-infinite sequence obtained from observations of an underlying dynamical system through a phenomenon called \textit{causal embedding}. A driven dynamical system creates such pairs, and a function can be learnt on them that can reconstruct the underlying dynamics as in Takens delay embedding. The approach assures embedding stability unlike Takens delay embedding, and learnability which can be absent while stability can be present in the current reservoir computing framework. This accurately models underlying systems where recent methods like the next-generation reservoir computing fail. We demonstrate results and compare with the other methods including SINDY-PI.
Dynamical Systems (math.DS); Machine Learning (cs.LG)
arXiv:2105.10759 [math.DS]
(or arXiv:2105.10759v4 [math.DS] for this version)
https://doi.org/10.48550/arXiv.2105.10759 Focus to learn more arXiv-issued DOI via DataCite
https://doi.org/10.1109/TNNLS.2025.3632965 Focus to learn more DOI(s) linking to related resources
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