Learning entropy production via neural networks

This paper presents a neural estimator for entropy production, or NEEP, that estimates entropy production (EP) from trajectories without any prior knowledge of the system. For steady state, we rigorously prove that the estimator, which can be built up from different choices of deep neural networks, provides EP by optimizing the objective function proposed here. We verify the NEEP with stochastic processes such as those found in the bead-spring system and discrete flashing ratchet model. We also demonstrate that our method is applicable to high-dimensional data and non-Markovian systems.