Numerical Solution of an Inverse Problem in Size-Structured Population Dynamics
For researchers in mathematical biology and inverse problems, this provides a novel regularization method for a known bottleneck (ill-posedness), though numerical validation uses classical techniques and comparisons are limited.
The paper tackles the inverse problem of determining the division rate from stable size distribution in size-structured cell population models, proposing a new filtering-based regularization technique with proven convergence and numerical validation.
We consider a size-structured model for cell division and address the question of determining the division (birth) rate from the measured stable size distribution of the population. We propose a new regularization technique based on a filtering approach. We prove convergence of the algorithm and validate the theoretical results by implementing numerical simulations, based on classical techniques. We compare the results for direct and inverse problems, for the filtering method and for the quasi-reversibility method proposed in [Perthame-Zubelli].