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The diffusion-driven Turing instability is a potential mechanism for spatialpattern formation in numerous biological and chemical systems. However,engineering these patterns and demonstrating that they are produced by thismechanism is challenging. To address this, we aim to solve the inverse problemin artificial and experimental Turing patterns. This task is challenging sincehigh levels of noise corrupt the patterns and slight changes in initialconditions can lead to different patterns. We used both least squares toexplore the problem and physics-informed neural networks to build anoise-robust method. We elucidate the functionality of our network in scenariosmimicking biological noise levels and showcase its application through aprototype involving an experimentally obtained chemical pattern. The findingsreveal the significant promise of machine learning in steering the creation ofsynthetic patterns in bioengineering, thereby advancing our grasp ofmorphological intricacies within biological systems while acknowledgingexisting limitations.

Unraveling biochemical spatial patterns: machine learning approaches to the inverse problem of Turing patterns