Neural Network Framework Decodes Oocyte Development and Renewal in Fish

A new computational study published by researchers Louis Fostier, Manon Lesage, Violette Thermes, Frédérique Clément, and Romain Yvinec introduces a framework for functional and parametric inference in size-structured population models. Applied to early oogenesis in juvenile fish, the investigation focuses on the developmental window that establishes the ovarian reserve conditioning lifelong reproductive capacity. In juvenile fish ovaries, this critical biological process is regulated by local hormonal feedback mechanisms that predominantly involve Anti-Müllerian Hormone. To capture these dynamics mathematically, the investigators developed a mechanistic size-structured population model that accounts for an unstructured germ-cell compartment alongside a distinct population of growing oocytes, integrating Anti-Müllerian Hormone feedback directly into the net renewal of the precursor cells compartment.

Using repeated cross-sectional observations of oocyte size distributions gathered from fish ovaries, the researchers formulated and solved a nonlinear inverse problem utilizing Physics-Informed Neural Networks. This computational architecture was designed to infer three essential demographic functions governing the population: the size-dependent oocyte growth rate, the recruitment rate of new oocytes, and the net renewal rate of the precursor cells compartment under Anti-Müllerian Hormone regulation. Because the underlying population equations incorporate a nonlocal interaction term, the authors introduced an auxiliary Physics-Informed Neural Network formulation. This auxiliary component enables the system to handle the mathematical challenges of nonlocal interactions while jointly inferring demographic functions and unobserved state variables.

The overall inference strategy unites non-parametric Physics-Informed Neural Networks with a data-guided model-selection step. Under this two-stage methodology, the demographic functions are initially inferred without prescribing any functional forms in advance. The learned non-parametric profiles are subsequently evaluated to select parsimonious parametric laws that best reflect the observed dynamics. Following this structural selection, the parameters of those selected laws are estimated within a dedicated parametric Physics-Informed Neural Network. This progressive pipeline allows the researchers to transition systematically from unbiased functional discovery to calibrated parametric representations.

To ensure the mathematical validity and robustness of the methodology, the authors investigated identifiability at both functional and parametric levels. Their verification strategy combined theoretical structural identifiability analysis with synthetic-data experiments designed to assess the practical recovery of both unknown functions and their governing parameters. In addition, the complete inference procedure was embedded within an individual-level bootstrap framework. This bootstrap setup allowed the team to systematically evaluate the sensitivity of the estimations to stochastic training behaviors as well as the variability inherent in repeated-cross-sectional sampling.

When applied directly to juvenile fish oogenesis, the resulting framework successfully recovered interpretable growth and renewal dynamics, granted direct analytical access to previously unobserved biological quantities, and enabled conditional in silico investigation of ovarian processes. Beyond the study of fish reproductive systems, the authors emphasize that this computational approach establishes a broad and rigorous foundation for functional and parametric inference in size-structured population models that exhibit nonlocal interactions when calibrated against sparse cross-sectional data.

Subject of Research: Physics-informed neural network modeling of juvenile fish oogenesis

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

Article References: Fostier, L., Lesage, M., Thermes, V., Clément, F., & Yvinec, R. (2026). PINN-based functional inference in size-structured population models: Application to fish oogenesis. PLOS Computational Biology, 22(11), e1014933. https://doi.org/10.1371/journal.pcbi.1014933

Image Credits: AI Generated

DOI: 10.1371/journal.pcbi.1014933

Keywords: physics-informed neural networks, fish oogenesis, population models, anti-mullerian hormone, demographic functions, computational biology, inverse problems, oocyte growth, PINN-based, functional, inference, size-structured