Status  Confirmed 
Seminar Series  LPTMS 
Subjects  physics 
Date  Tuesday 9 October 2018 
Time  11:00 
Institute  LPTMS 
Seminar Room  LPTMS, salle 201, 2ème étage, Bât 100, Campus d'Orsay 
Speaker's Last Name  Ronceray 
Speaker's First Name  Pierre 
Speaker's Email Address  
Speaker's Institution  Princeton Center for Theoretical Science 
Title  Learning force fields from stochastic trajectories 
Abstract  From nanometerscale proteins to micronscale colloidal particles, particles in biological and soft matter systems undergo Brownian dynamics: their deterministic motion due to external forces and interactions competes with the random diffusion due to thermal noise. In the absence of forces, all trajectories look alike: the key information characterizing the system’s dynamics thus lies in its force field. However, reconstructing the force field by inspecting microscopy observations of the system’s trajectory is a hard problem, for two reasons. First, there needs to be enough information about the force available in the trajectory: the effect of the force field becomes apparent only after a long enough observation time. Second, one needs a practical method to extract that information and reconstruct the force field, which is challenging for force fields with a spatial structure, in particular in the presence of measurement noise. Here we address these two problems for steadystate Brownian trajectories. We first give a quantitative meaning to the information contained in a trajectory, and show how it limits force inference. We then propose a practical procedure to optimally use this information to reconstruct the force field by decomposing it into moments. Using simple model stochastic processes, we demonstrate that our method permits a quantitative evaluation of phase space forces and currents, circulation, and entropy production with a minimal amount of data. 
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