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Quantifying entropy production (EP) is essential to understand stochasticsystems at mesoscopic scales, such as living organisms or biologicalassemblies. However, without tracking the relevant variables, it is challengingto figure out where and to what extent EP occurs from recorded time-seriesimage data from experiments. Here, applying a convolutional neural network(CNN), a powerful tool for image processing, we develop an estimation methodfor EP through an unsupervised learning algorithm that calculates only frommovies. Together with an attention map of the CNN's last layer, our method cannot only quantify stochastic EP but also produce the spatiotemporal pattern ofthe EP (dissipation map). We show that our method accurately measures the EPand creates a dissipation map in two nonequilibrium systems, the bead-springmodel and a network of elastic filaments. We further confirm high performanceeven with noisy, low spatial resolution data, and partially observedsituations. Our method will provide a practical way to obtain dissipation mapsand ultimately contribute to uncovering the nonequilibrium nature of complexsystems.

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