Many biological systems are naturally modeled as structured populations, in which each individual is characterized by one or more physiological variables (e.g., size, age, or developmental stage). The evolution of the corresponding population distribution can be described by transport-reaction partial differential equations (PDEs).
Such models arise in numerous biological applications, including cell populations, developmental biology, tissue remodeling, and microbiology.
Although these mechanistic models provide a quantitative description of the underlying biological processes, estimating unknown parameters, or even unknown biological functions, from experimental observations remains a challenging inverse problem. In practice, measurements are often sparse, noisy, and available only at a limited number of time points, making classical optimization or Bayesian inference approaches computationally demanding.
Recent advances in Scientific Machine Learning, particularly Physics-Informed Neural Networks (PINNs), provide a promising framework for solving such inverse problems by combining mechanistic models with experimental data. In particular, a recent work in the team demonstrates the potential of PINNs for inverse problems in size-structured population models using repeated cross-sectional biological observations.
The objective of this internship is to develop and validate a PINN-based framework for parameter inference in time-dependent structured PDE models.
The work will initially focus on simplified ("toy") models that represent structured population dynamics, enabling methodological development under controlled conditions before their application to experimental data.

Applicants should have a strong background in applied mathematics, scientific computing, machine learning, or computational biology. Experience with differential equations, numerical methods, optimization, and Python programming is expected. Knowledge of deep learning frameworks (e.g., PyTorch, TensorFlow, or JAX) is appreciated but not mandatory

• Niveaux d’étude
• Stage Bac+5