Information Criteria Fail for Dynamical Systems: Sampling Rate and Dimension Dependence
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Abstract
Information criteria such as Akaike's (AIC) and Bayes' (BIC) are widely used for model selection in physics and beyond, quantifying the tradeoff between model complexity and goodness-of-fit to enforce parsimony. However, their derivation assumes uncorrelated samples, an assumption systematically violated by dynamical systems data. Here, through analysis of simple but representative dynamical models -- exponential decay, harmonic oscillation, and chaos -- we demonstrate that model selection depends sensitively on sampling rate and system dimensionality. We derive explicit formulas predicting when standard information criteria fail that should be adaptable to many real-world scenarios, enabling experimentalists to design sampling protocols that avoid pathological regimes.Keywords
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