PINN-based functional inference in size-structured population models: Application to fish oogenesis
- 1PRC, INRAE, CNRS, Université de Tours, Nouzilly, France
- 2Université Paris-Saclay, Inria, Centre Inria de Saclay, Palaiseau, France
- 3INRAE, Fish Physiology and Genomics Institute, UR1037, LPGP, Rennes, France
Abstract
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. Author summary: The earliest stages of female germ cell development play a key role in shaping the future reproductive capacity of fish. In juvenile ovaries, precursor cells proliferate and differentiate into growing oocytes, a process regulated by Anti-Müllerian Hormone (AMH), whose precise role remains difficult to quantify experimentally. In this work, we combine repeated observations of oocyte size distributions with a mechanistic population model and Physics-Informed Neural Networks (PINNs) to reconstruct biological processes that cannot be directly observed. We develop a methodology that first learns oocyte growth and unstructured-compartment net-renewal functions without assuming their mathematical forms, and then uses these profiles to select simpler mathematical expressions. We also study whether these functions and their parameters can be reliably recovered from the available observations, and use a bootstrap approach to assess sensitivity to sampling and training variability. Applied to juvenile oogenesis, our approach provides a quantitative description of oocyte growth, recruitment, and hormonal feedback. Beyond this application, our work illustrates how mechanistic models and machine learning can be combined to infer hidden biological processes from sparse population-level observations.
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BibTeX
@article{fostier2026pinnbased,
title = {{PINN-based functional inference in size-structured population models: Application to fish oogenesis}},
author = {Louis Fostier and Manon Lesage and Violette Thermes and Frédérique Clément and Romain Yvinec},
journal = {PLOS Computational Biology},
year = {2026},
month = nov,
doi = {10.1371/journal.pcbi.1014933},
url = {https://journals.plos.org/ploscompbiol/article?id=10.1371/journal.pcbi.1014933},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - PINN-based functional inference in size-structured population models: Application to fish oogenesis
AU - Louis Fostier
AU - Manon Lesage
AU - Violette Thermes
AU - Frédérique Clément
AU - Romain Yvinec
PY - 2026
DA - 2026/11/06
JO - PLOS Computational Biology
DO - 10.1371/journal.pcbi.1014933
UR - https://journals.plos.org/ploscompbiol/article?id=10.1371/journal.pcbi.1014933
AB - 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. Author summary: The earliest stages of female germ cell development play a key role in shaping the future reproductive capacity of fish. In juvenile ovaries, precursor cells proliferate and differentiate into growing oocytes, a process regulated by Anti-Müllerian Hormone (AMH), whose precise role remains difficult to quantify experimentally. In this work, we combine repeated observations of oocyte size distributions with a mechanistic population model and Physics-Informed Neural Networks (PINNs) to reconstruct biological processes that cannot be directly observed. We develop a methodology that first learns oocyte growth and unstructured-compartment net-renewal functions without assuming their mathematical forms, and then uses these profiles to select simpler mathematical expressions. We also study whether these functions and their parameters can be reliably recovered from the available observations, and use a bootstrap approach to assess sensitivity to sampling and training variability. Applied to juvenile oogenesis, our approach provides a quantitative description of oocyte growth, recruitment, and hormonal feedback. Beyond this application, our work illustrates how mechanistic models and machine learning can be combined to infer hidden biological processes from sparse population-level observations.
SN - 1553-7358
ER -