Hishinuma Hidekazu, Takigawa-Imamura Hisako, Miura Takashi
Department of Anatomy and Cell Biology, Graduate School of Medical Sciences, Kyushu University, Fukuoka, Fukuoka, Japan.
PLoS Comput Biol. 2025 Jan 23;21(1):e1012689. doi: 10.1371/journal.pcbi.1012689. eCollection 2025 Jan.
Mathematical modeling has been utilized to explain biological pattern formation, but the selections of models and parameters have been made empirically. In the present study, we propose a data-driven approach to validate the applicability of mathematical models. Specifically, we developed methods to automatically select the appropriate mathematical models based on the patterns of interest and to estimate the model parameters. For model selection, we employed Contrastive Language-Image Pre-training (CLIP) for zero-shot feature extraction, mapping the given pattern images to latent space and specifying the appropriate model. For parameter estimation, we developed a novel technique that rapidly performs approximate Bayesian inference based on Natural Gradient Boosting (NGBoost). This method allows for parameter estimation under minimal constraints; i.e., it does not require time-series data or initial conditions and is applicable to various types of mathematical models. We tested the method with Turing patterns and demonstrated its high accuracy and correspondence to analytical features. Our strategy enables efficient validation of mathematical models using spatial patterns.
数学建模已被用于解释生物模式形成，但模型和参数的选择一直是凭经验进行的。在本研究中，我们提出了一种数据驱动的方法来验证数学模型的适用性。具体而言，我们开发了基于感兴趣的模式自动选择合适的数学模型并估计模型参数的方法。对于模型选择，我们采用对比语言-图像预训练（CLIP）进行零样本特征提取，将给定的模式图像映射到潜在空间并指定合适的模型。对于参数估计，我们开发了一种基于自然梯度提升（NGBoost）快速执行近似贝叶斯推理的新技术。该方法允许在最小约束下进行参数估计；即，它不需要时间序列数据或初始条件，并且适用于各种类型的数学模型。我们用图灵模式测试了该方法，并证明了其高精度和与分析特征的一致性。我们的策略能够使用空间模式对数学模型进行有效验证。
