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Article overview
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Predictability Exponent of Stochastic Dynamical Systems | | Tao Xu
; Jianping He
; Yushan Li
; | | Date: |
12 May 2022 | | Abstract: | Predicting the trajectory of stochastic dynamical systems (SDSs) is an
intriguing problem in numerous fields, where characterizing the predictability
of SDSs is of fundamental importance. Prior works have tackled this issue by
indirectly investigating the uncertainty of distribution in each prediction.
How accurately the trajectory of SDSs can be directly predicted still remains
open. This paper proposes a new metric, namely predictability exponent, to
characterize the decaying rate of probability that the prediction error never
exceeds arbitrary $epsilon$. To evaluate predictability exponent, we begin
with providing a complete framework for model-known cases. Then, we bring to
light the explicit relationship between predictability exponent and entropy by
discrete approximation techniques. The definition and evaluation on
predictability exponent are further extended to model-unknown cases by
optimizing over model spaces, which build a bridge between the accuracy of
trajectory predictions and popular entropy-based uncertainty measures. Examples
of unpredictable trajectory design are presented to elaborate the applicability
of the proposed predictability metric. Simulations are conducted to illustrate
the efficiency of the obtained results. | | Source: | arXiv, 2205.06006 | | Services: | Forum | Review | PDF | Favorites | |
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