PINN-based functional inference in size-structured population models: Application to fish oogenesis.

PINN-based inversion of repeated cross-sectional oocyte size distributions in juvenile fish infers three AMH-linked demographic functions, including an AMH-regulated precursor renewal rate.

• Why it matters: Early oogenesis sets the ovarian reserve and lifelong reproductive capacity, but local hormonal feedback—especially AMH effects—remains hard to quantify from sparse size snapshots.
• What they did: The authors build a mechanistic size-structured model with an unstructured germ-cell precursor compartment and growing oocytes, then solve a nonlinear inverse problem using PINNs with an auxiliary formulation for a nonlocal interaction term.
• The result: They infer unobserved state variables and size-dependent growth, renewal, and recruitment profiles without fixed functional forms, then use learned profiles for data-guided selection of parsimonious parametric laws and bootstrap-based sensitivity assessment.

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