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Variational sampling and optimal design of rare nonequilibrium molecular dynamics


Nonequilibrium driving can independently tune the structure and dynamics of molecular and colloidal systems, resulting in novel assembly and transport phenomena that are not found in equilibrium. Exploring nonequilibrium dynamics through numerical simulations is crucial towards understanding the working mechanisms of functional inorganic or biological materials. However, behavior of dynamical observables in such systems at experimental timescales is often dominated by statistically rare fluctuations that are poorly sampled in simulated trajectories. Rare event sampling algorithms that assume a Boltzmann distribution of configurations and detailed balance for dynamics cannot be applied out of thermal equilibrium, thus limiting available techniques that can efficiently sample nonequilibrium rare events.

In this thesis we have developed novel variational algorithms for the sampling and design of rare nonequilibrium molecular dynamics trajectories by application of an optimized driving force. This approach relies on the equivalence of a trajectory ensemble conditioned on a rare event to occur to an ensemble driven with the optimal force where the rare event occurs typically. For systems with many interacting degrees of freedom, we numerically learn the optimal force within arbitrary basis sets by statistically estimating explicit gradients of trajectory probability. This method allows us to efficiently compute large deviation functions of dynamical observables in nonequilibrium steady-states, and to automate the inverse design of self-assembling colloids and molecular machines for desired structure and dynamics. We have finally augmented our approach with reinforcement learning techniques, resulting in a new paradigm to efficiently compute nonequilibrium reaction rates, Variational Path Sampling. Our approach of using optimized forces to improve sampling of nonequilibrium trajectories is versatile and can give access to rare reactive fluctuations and dynamical phases that cannot be sampled otherwise.

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