Estimating predictability of depinning dynamics by machine learning

Predicting the future behavior of complex systems exhibiting critical-like dynamics is often considered to be an intrinsically hard task. Here, we study the predictability of the depinning dynamics of elastic interfaces in random media driven by a slowly increasing external force, a paradigmatic complex system exhibiting critical avalanche dynamics linked to a continuous non-equilibrium depinning phase transition. To this end, we train a variety of machine learning models to infer the mapping from features of the initial relaxed line shape and the random pinning landscape to predict the sample-dependent staircase-like force-displacement curve that emerges from the depinning process. Even if for a given realization of the quenched random medium the dynamics are in principle deterministic, we find that there is an exponential decay of the predictability with the displacement of the line as it nears the depinning transition from below. Our analysis on how the related displacement scale depends on the system size and the dimensionality of the input descriptor reveals that the onset of the depinning phase transition gives rise to fundamental limits to predictability.