Inverse Problems, Resampling Monte Carlo Techniques and Applications to Biophysical Systems

Abstract: In this talk we shall survey recent research on inverse problems, developed by our group at IMPA's Laboratory for Analysis and Mathematical Modelling.
On the methodological side, we have developed non-intrusive resampling tools [1] as well as optimization techniques [2,3,4,5]. Such tools have proven very effective to tackle a number of relevant problems in Mathematical Physics, Finance, and Biology and are naturally extensible to other fields. We shall then illustrate the method with an application to biophysical systems, with a case study of the uncertain quantification of the success probability of invading populations of Aedes aegypti mosquitoes (responsible for the Dengue and Zika epidemics) by infection with Wolbachia bacteria [6]. Time allowing we shall discuss other applications of Monte Carlo techniques for the solution of Hamilton-Jacobi-Bellman equations.

References:
[1] Gobet, Liu, Zubelli. A nonintrusive stratified resampler for regression Monte Carlo. SIAM J. Numer. Anal. 56 (2018)
[2] Zubelli, Marabini, Sorzano, Herman. Three-dimensional reconstruction by Chahine’s method from electron microscopic projections corrupted by instrumental aberrations. Inverse problems 19 (2003)
[3] Doumic, Perthame, Zubelli. Numerical solution of an inverse problem in size-structured population dynamics. Inverse Problems 25 (2009)
[4] Perthame, Zubelli. On the inverse problem for a size-structured population model. Inverse Problems 23 (2007)
[5] Singer, Grunbaum, Image reconstruction of the interior of bodies that diffuse radiation, SCIENCE 248 (1992)
[6] Strugarek, Vauchelet, Zubelli, Quantifying the survival uncertainty of Wolbachia-infected mosquitoes in a spatial model. Mathematical Biosciences & Engineering 15 (2018)