PRESS: Physics-Regularized Parameter Estimation from Steady-State Turing Patterns

Zi-Yan Shi, Jaron Yeh, Chien Yu Hung

Keywords: Turing pattern, Reaction-Diffusion System, Inverse problem, Physics-Informed Neural Networks, Machine Learning

TL;DR: We propose PRESS, a physics-regularized framework for estimating the reaction-diffusion parameters from static steady-state Turing patterns.

Abstract: The Turing mechanism explains how biological systems leverage spontaneous symmetry breaking within reaction-diffusion processes to generate complex spatial patterns. Despite the widespread recognition of this mechanism, accurately recovering the underlying control parameters solely from these static patterns remains a major bottleneck in inverse problem research. This study challenges this limitation by proposing $\textbf{PRESS}$ (Physics-Regularized Estimation from Steady-State Turing Patterns), an efficient parameter discovery framework that integrates a novel steady-state physics-informed residual loss to constrain neural network architectures. Unlike traditional approaches that rely on temporal derivatives, our key contribution is a regularization strategy that leverages the equilibrium condition of reaction-diffusion systems, enabling robust inference directly from single snapshots. We systematically evaluate the impact of this physical constraint on both CNNs and Multilayer Perceptrons (MLPs) for the simultaneous inference of four governing parameters. Experimental results demonstrate that integrating the steady-state physics loss significantly enhances model performance. Crucially, PRESS is capable of accurately extracting parameters directly from raw pattern images, substantially outperforming unconstrained baseline models. Our findings confirm that steady-state physical laws serve as a potent regularization tool, providing an efficient, end-to-end, and physically consistent solution for quantifying Turing systems.

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Submission Number: 119