Numerical Solution of an Inverse Problem in Size-Structured Population Dynamics

TL;DR

This paper introduces a new regularization method for solving inverse problems in size-structured population dynamics, specifically estimating cell division rates from size distribution data, validated through numerical simulations.

Contribution

It proposes a novel filtering-based regularization technique for inverse problems in size-structured models, with proven convergence and comparative analysis.

Findings

The filtering method accurately estimates division rates from simulated data.

The method outperforms the quasi-reversibility approach in certain scenarios.

Numerical simulations confirm the theoretical convergence results.

Abstract

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].