有限数据下生物模式形成的贝叶斯建模方法
A Bayesian Approach to Modelling Biological Pattern Formation with Limited Data
摘要：
生物组织中的模式形成在生物体的发育中起着重要作用。自从阿兰·图灵的经典工作以来，一种杰出的建模方法就是通过反应扩散机制。最近，已经提出了替代模型，将扩散分子信号的动力学与组织力学联系起来。为了区分不同的模型，应该将它们与实验观察进行比较。然而，在许多实验情况下，只有有限的，稳定的模式形成过程的制度是可观察的，没有知识的瞬态行为或初态。所有替代模型中的基本动态的不稳定性质使模型和参数识别严重复杂化，因为初始条件的微小变化会导致不同的平稳模式。为了克服这个问题，可以将模型的初态随机化。在后一种情况下，模型参数的固定值对应于模式族而不是固定的静态解，并且标准方法直接将模式数据与模型输出进行比较，例如，在最小二乘意义上，是不合适的。相反，应该比较模式的统计特性，这在实际应用中通常有限的可用数据量的情况下是困难的。为了解决这个问题，我们扩展了最近开发的统计方法，使用模式数据，所谓的相关积分Likestive（CIL）方法的参数识别。我们建议修改，允许增加识别过程的准确性，而不需要重新配置数据集。所提出的方法进行了测试，使用不同类别的图案形成模型。对于所有考虑的方程，并行GPU为基础的实现的数值求解器与有效的时间步进计划。
英文摘要：
Pattern formation in biological tissues plays an important role in the development of living organisms. Since the classical work of Alan Turing, a pre-eminent way of modelling has been through reaction-diffusion mechanisms. More recently, alternative models have been proposed, that link dynamics of diffusing molecular signals with tissue mechanics. In order to distinguish among different models, they should be compared to experimental observations. However, in many experimental situations only the limiting, stationary regime of the pattern formation process is observable, without knowledge of the transient behaviour or the initial state. The unstable nature of the underlying dynamics in all alternative models seriously complicates model and parameter identification, since small changes in the initial condition lead to distinct stationary patterns. To overcome this problem the initial state of the model can be randomised. In the latter case, fixed values of the model parameters correspond to a family of patterns rather than a fixed stationary solution, and standard approaches to compare pattern data directly with model outputs, e.g., in the least squares sense, are not suitable. Instead, statistical characteristics of the patterns should be compared, which is difficult given the typically limited amount of available data in practical applications. To deal with this problem, we extend a recently developed statistical approach for parameter identification using pattern data, the so-called Correlation Integral Likelihood (CIL) method. We suggest modifications that allow increasing the accuracy of the identification process without resizing the data set. The proposed approach is tested using different classes of pattern formation models. For all considered equations, parallel GPU-based implementations of the numerical solvers with efficient time stepping schemes are provided.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
