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The mean exit time escaping basin of attraction in the presence of whitenoise is of practical importance in various scientific fields. In this work, wepropose a strategy to control mean exit time of general stochastic dynamicalsystems to achieve a desired value based on the quasipotential concept andmachine learning. Specifically, we develop a neural network architecture tocompute the global quasipotential function. Then we design a systematiciterated numerical algorithm to calculate the controller for a given mean exittime. Moreover, we identify the most probable path between metastableattractors with help of the effective Hamilton-Jacobi scheme and the trainedneural network. Numerical experiments demonstrate that our control strategy iseffective and sufficiently accurate.

Controlling mean exit time of stochastic dynamical systems based on quasipotential and machine learning