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Abstract |
Generalized Langevin equations with non-linear forces and memory kernels are
commonly used to describe the effective dynamics of coarse-grained variables in
molecular dynamics. Such reduced dynamics play an essential role in the study of
a broad class of processes, ranging from chemical reactions in solution to
conformational changes in biomolecules or phase transitions in condensed matter
systems. I will first discuss the derivation of the generalized Langevin
equations, emphasizing the need for memory in the effective dynamics due to the
lack of a proper separation of time scales. Then, I will turn on the inference
of such generalized Langevin equations from observed trajectories, using a
maximum likelihood approach. This data-driven approach provides a reduced
dynamical model for collective variables, enabling the accurate sampling of
their long-time dynamical properties at a computational cost drastically reduced
with respect to all-atom numerical simulations. I will illustrate the potential
of this method on several model systems, both in and out of equilibrium. |
