Attaining entropy production and dissipation maps from Brownian movies via neural networks

Quantifying entropy production (EP) is essential to understand stochastic systems at mesoscopic scales, such as living organisms or biological assemblies. However, without tracking the relevant variables, it is challenging to figure out where and to what extent EP occurs from recorded time-series image data from experiments. Here, applying a convolutional neural network (CNN), a powerful tool for image processing, we develop an estimation method for EP through an unsupervised learning algorithm that calculates only from movies. Together with an attention map of the CNN's last layer, our method can not only quantify stochastic EP but also produce the spatiotemporal pattern of the EP (dissipation map). We show that our method accurately measures the EP and creates a dissipation map in two nonequilibrium systems, the bead-spring model and a network of elastic filaments. We further confirm high performance even with noisy, low spatial resolution data, and partially observed situations. Our method will provide a practical way to obtain dissipation maps and ultimately contribute to uncovering the nonequilibrium nature of complex systems.

Deep Reinforcement Learning for Feedback Control in a Collective Flashing Ratchet

A collective flashing ratchet transports Brownian particles using a spatially periodic, asymmetric, and time-dependent on-off switchable potential. The net current of the particles in this system can be substantially increased by feedback control based on the particle positions. Several feedback policies for maximizing the current have been proposed, but optimal policies have not been found for a moderate number of particles. Here, we use deep reinforcement learning (RL) to find optimal policies, with results showing that policies built with a suitable neural network architecture outperform the previous policies. Moreover, even in a time-delayed feedback situation where the on-off switching of the potential is delayed, we demonstrate that the policies provided by deep RL provide higher currents than the previous strategies.

Learning entropy production via neural networks

This Letter 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 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 non-Markovian systems.