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The transition between ergodic and many-body localized phases is expected tooccur via an avalanche mechanism, in which \emph{ergodic bubbles} that arisedue to local fluctuations in system properties thermalize their surroundingsleading to delocalization of the system, unless the disorder is sufficientlystrong to stop this process. We propose an algorithm based on neural networksthat allows to detect the ergodic bubbles using experimentally measurabletwo-site correlation functions. Investigating time evolution of the system, weobserve a logarithmic in time growth of the ergodic bubbles in the MBL regime.The distribution of the size of ergodic bubbles converges during time evolutionto an exponentially decaying distribution in the MBL regime, and a power-lawdistribution with a thermal peak in the critical regime, supporting thus thescenario of delocalization through the avalanche mechanism. Our algorithmpermits to pin-point quantitative differences in time evolution of systems withrandom and quasiperiodic potentials, as well as to identify rare (Griffiths)events. Our results open new pathways in studies of the mechanisms ofthermalization of disordered many-body systems and beyond.

Detecting ergodic bubbles at the crossover to many-body localization using neural networks