标题： 从图灵模式中学习系统参数 显示英文标题

标题： Learning System Parameters from Turing Patterns

摘要： 图灵机制描述了由于反应扩散过程中的自发对称性破缺而出现的空间模式，并构成了许多发育过程的基础。 在生物系统中识别图灵机制是一个具有挑战性的问题。 本文介绍了一种从观察到的图灵图案中预测图灵参数值的方法。 这些参数值对应于生成图灵图案作为稳态的参数化反应扩散方程系统。 选择具有四个参数的Gierer-Meinhardt模型作为案例研究。 采用了一种基于电阻距离直方图的新颖不变模式表示方法，并结合Wasserstein核，以应对依赖于初始条件的局部模式结构的高度可变排列，这些初始条件被认为是未知的。 这使得可以计算模式之间的物理上合理的距离，计算模式聚类，并且最重要的是进行模型参数预测：对于小规模的训练集，包括算子值核在内的经典最先进方法优于应用于原始模式数据的神经网络，而对于大规模的训练集，后者更准确。 对于单个参数值，获得了出色的预测结果，而对于同时预测所有参数值，则得到了合理准确的结果。 显示英文摘要

摘要： The Turing mechanism describes the emergence of spatial patterns due to spontaneous symmetry breaking in reaction-diffusion processes and underlies many developmental processes. Identifying Turing mechanisms in biological systems defines a challenging problem. This paper introduces an approach to the prediction of Turing parameter values from observed Turing patterns. The parameter values correspond to a parametrized system of reaction-diffusion equations that generate Turing patterns as steady state. The Gierer-Meinhardt model with four parameters is chosen as a case study. A novel invariant pattern representation based on resistance distance histograms is employed, along with Wasserstein kernels, in order to cope with the highly variable arrangement of local pattern structure that depends on the initial conditions which are assumed to be unknown. This enables to compute physically plausible distances between patterns, to compute clusters of patterns and, above all, model parameter prediction: for small training sets, classical state-of-the-art methods including operator-valued kernels outperform neural networks that are applied to raw pattern data, whereas for large training sets the latter are more accurate. Excellent predictions are obtained for single parameter values and reasonably accurate results for jointly predicting all parameter values.