Learning force fields from stochastic trajectories

11 Oct
Widely Applied Mathematics Seminar
Dr. Anna Frishman
Thursday, October 11, 2018 -
3:00pm to 4:00pm
Pierce 209
Particles in biological and soft matter systems undergo Brownian dynamics: their deterministic motion, induced by forces, competes with random diffusion due to thermal noise. More broadly, Brownian dynamics is a generic and simple model for dynamical systems with noise. Provided only with the time-series of positions of such a system, i.e a trajectory in phase space, it could be challenging to infer what force field had produced it. At the same time, this is the key information about the dynamical system, which would allow to characterize it completely. I will show that there is an information-theoretic bound on the rate at which information about the force field can be extracted from a trajectory, quantified by a channel capacity. I will discuss the relation between this capacity and the entropy production rate, as defined in stochastic thermodynamics. I will then present a practical method, Stochastic Force Inference, that optimally uses the information contained in a trajectory to approximate force fields. 
This technique also permits the evaluation of out-of- equilibrium currents and entropy production. Beyond thermal systems, Stochastic Force Inference provides a powerful data analysis framework that could be used on a broad class of stochastic systems where inferring effective forces and currents from limited noisy data is of interest. 
Speaker Bio: 
Anna Frishman did her PhD at the Weizmann Institute of Science with Prof. Grisha Falkovich, working on Lagrangian aspects of turbulence. She is currently a postdoctoral fellow at the Princeton Center for Theoretical Science (PCTS). Her research interests include out-of-equilbrium statistical physics, fluid dynamics, and, at the interface, turbulence. The subjects of her recent projects include 2D turbulence, stochastic force inference for over-damped systems, and bubble breakup dynamics.  
D. Nelson
Vamsi Arza