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The Turing mechanism describes the emergence of spatial patterns due tospontaneous symmetry breaking in reaction-diffusion processes and underliesmany developmental processes. Identifying Turing mechanisms in biologicalsystems defines a challenging problem. This paper introduces an approach to theprediction of Turing parameter values from observed Turing patterns. Theparameter values correspond to a parametrized system of reaction-diffusionequations that generate Turing patterns as steady state. The Gierer-Meinhardtmodel with four parameters is chosen as a case study. A novel invariant patternrepresentation based on resistance distance histograms is employed, along withWasserstein kernels, in order to cope with the highly variable arrangement oflocal pattern structure that depends on the initial conditions which areassumed to be unknown. This enables to compute physically plausible distancesbetween patterns, to compute clusters of patterns and, above all, modelparameter prediction: for small training sets, classical state-of-the-artmethods including operator-valued kernels outperform neural networks that areapplied to raw pattern data, whereas for large training sets the latter aremore accurate. Excellent predictions are obtained for single parameter valuesand reasonably accurate results for jointly predicting all parameter values.

Learning System Parameters from Turing Patterns