  This Letter presents a neural estimator for entropy production, or NEEP, that
estimates entropy production (EP) from trajectories of relevant variables
without detailed information on the system dynamics. For steady state, we
rigorously prove that the estimator, which can be built up from different
choices of deep neural networks, provides stochastic EP by optimizing the
objective function proposed here. We verify the NEEP with the stochastic
processes of the bead-spring and discrete flashing ratchet models, and also
demonstrate that our method is applicable to high-dimensional data and can
provide coarse-grained EP for Markov systems with unobservable states.
