Achieving Good Nonlinear Models: Keep It Simple, Vary the Embedding, and Get the Dynamics Right

TL;DRAbstract

This chapter presents an overview of three fundamental notions in modeling nonlinear dynamical systems from time series. They are the use of the minimum description length (MDL) principle in model selection; the use of variable embedding and cylindrical basis models to build models that better capture the dynamics; and the use of ΨΦ-models to eliminate systematic error when making long-term prediction. Their purposes are to separate what can be modeled (“determinism”) from what cannot (“noise”); to capture varying time-scales and different geometric features in embedding space; and to make models that have good long-term dynamical behavior as well as short-term predictive ability.

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