Data-driven PINN inference of oocyte dynamics in fish ovaries

Early oogenesis in juvenile fish establishes the ovarian reserve and thus 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 the dynamics of precursor germ cells and growing oocytes in ovary, incorporating an AMH feedback exerted on the precursor germ cells renewal. 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 the size-dependent oocyte growth rate, the AMH-regulated renewal rate of precursor cells, and the recruitment rate of new oocytes. The proposed framework enables flexible, data-driven identification of biological rates under minimal prior assumptions. Once calibrated, the model provides in silico access to key unobservable quantities, including cell transit times, the impact of AMH perturbations such as invalidation conditions, and the mechanisms underlying inter-individual variability in the establishment of the pool of small oocytes. This work presents a novel application of PINNs to inverse problems for size-structured partial differential equation models with nonlocal interaction terms, and establishes a quantitative framework for studying early oogenesis in juvenile fish.