基于 PINN 的尺寸结构种群模型功能推断：应用于鱼类卵子发生
PINN-based functional inference in size-structured population models: Application to fish oogenesis
研究团队提出一种基于物理信息神经网络（PINN）的推断框架，从稀疏的横截面观测数据中反演鱼类卵子发生的尺寸结构种群模型功能。模型将生殖细胞区室与生长中的卵母细胞种群分开描述，并纳入 AMH 对前体细胞区室更新的反馈调控，通过非线性反问题推断卵母细胞尺寸依赖生长率、AMH 调控的净更新率和卵母细胞招募率三个功能。作者引入辅助 PINN 处理非局部相互作用项，并联合推断未观测状态变量与功能函数；推断策略先以非参数 PINN 不预设函数形式地学习功能曲线，再据此选择简约参数律并在参数化 PINN 中估计参数。
来源：PLOS Computational Biology · journals.plos.org
by Louis Fostier, Manon Lesage, Violette Thermes, Frédérique Clément, Romain Yvinec
Early oogenesis in juvenile fish establishes the ovarian reserve, which conditions lifelong reproductive capacity. This process is regulated by local hormonal feedback mechanisms, mainly involving Anti-Müllerian Hormone (AMH). In this work, we develop a mechanistic size-structured population model describing an unstructured germ-cell compartment and a population of growing oocytes, with AMH feedback on the renewal of the precursor cells compartment. Using repeated cross-sectional observations of oocyte size distributions in fish ovaries, we formulate and solve a nonlinear inverse problem with Physics-Informed Neural Networks (PINNs) to infer three demographic functions: the size-dependent oocyte growth rate, the AMH-regulated net renewal rate of the precursor cells compartment, and the recruitment rate of new oocytes. We introduce an auxiliary PINN formulation to handle the nonlocal interaction term and jointly infer unobserved state variables and demographic functions. Our inference strategy combines non-parametric PINNs with a data-guided model-selection step: demographic functions are first inferred without prescribing their functional forms, and the learned profiles are then used to select parsimonious parametric laws, whose parameters are subsequently estimated within a parametric PINN. We investigate identifiability at both the functional and parametric levels, combining structural identifiability analysis with synthetic-data experiments assessing the practical recovery of functions and parameters. The inference procedure is embedded within an individual-level bootstrap framework to assess sensitivity to repeated-cross-sectional sampling and stochastic training. Applied to juvenile fish oogenesis, the framework recovers interpretable growth and renewal dynamics, provides access to unobserved quantities, and enables conditional in silico investigation. More broadly, this work provides a framework for functional and parametric inference in size-structured population models with nonlocal interactions from sparse cross-sectional data.