Séminaire du LPTMS: Pierre Ronceray


11:00 - 12:00

LPTMS, salle 201, 2ème étage, Bât 100, Campus d'Orsay
15 Rue Georges Clemenceau, Orsay, 91405

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Learning force fields from stochastic trajectories

Pierre Ronceray (Princeton Center for Theoretical Science, USA)

From nanometer-scale proteins to micron-scale 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 steady-state 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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