Keywords
Cellular automata
Surrogate modelling
Explainable AI
How to Cite
Abstract
A recurring intuition is that chaotic boundary forcing mixes a medium more thoroughly than regular or random forcing. We test this in a boundary-driven probabilistic cellular automaton, quantifying mixing via Shannon entropy and Moran's~I, and find the intuition fails. Experiments demonstrate that neither coupling strength nor forcing character (chaotic Lorenz, white-noise, periodic, or static) significantly affects the final entropy. Instead, a gradient-boosted surrogate (R2 =0.81) and SHAP attribution identify the internal diffusive update weight as the dominant mixing driver. Exact spectral analysis confirms this mechanism: boundary drives perturb bulk functionals only at order 1/N, whereas the diffusion weight heavily controls modal damping. While steering this diffusion weight recovers ninety-five per cent of mixing performance, an advective benchmark shows true chaotic velocity fields mix six times faster. This localizes our null result to additive boundary forcing rather than chaotic transport itself. Ultimately, bulk mixing in this system is governed by internal diffusive transport rather than the boundary drive.
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