| Abstract: |
| Many processes in nature such as conformal changes in biomolecules and clusters of interacting particles are modeled using stochastic differential equations with small noise. The study of rare transitions between metastable states in such systems is of great interest and importance. The direct simulation of rare transitions is difficult due to long waiting times and high dimensionality. Transition Path Theory (E and Vanden-Eijnden, 2006) is a mathematical framework for describing transition processes. The key component of its implementation is the numerical solution of the committor problem, a certain boundary value problem for the stationary Backward Kolmogorov equation. In this talk, I will discuss how one can learn coarse-grained models, solve the committor problem accurately in moderately high dimensions, and use optimal stochastic control to quantify transition processes between the metastable states. |
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