How to learn a stochastic partial differential equation from a video?
Team: Pierre Ronceray (CPT)
October 2021 - present | CENTURI PhD student
2017 - 2019 | Master 2 of Statistical Physics : "Physics of complex system", Sorbonne University
2015 - 2017 | BSc in Physics and Master 1, Ecole Normale Supérieure de Paris-Saclay/Sorbonne University
About his PhD project
Understanding the organization and dynamics of biological matter, from the protein to the tissue scale, is a major challenge from a physicist point of view. Thanks to new microscopy techniques, more and more videos of biological matter (membranes, ciliated epithelia, etc.) are being made at scales where the dynamics is dominated by thermal noise. Current data analysis methods take little account of this thermal and active noise. They therefore only partially exploit the information. The goal of my thesis will be to model the dynamics of some biological materials by stochastic partial differential equations (SPDE) and to develop new techniques to infer these equations from experimental videos. A first approach will be to apply a Fourier transform to the video (which will represent the field supposed to follow an EDPS). This approach should allow us to measure the parameters of linear EDPS, for example that of a system modeled by a Gaussian free field. But in the case of non-linear models, it will be necessary to find how to adapt this method or to design other means to infer the parameters of the model. The final objective of this thesis is the realization and application of a method applicable to real data. We hope to be able to discover which forces are predominant for the dynamics, and this for different biological systems.