  Predicting the future behaviour 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,
quantifying how the system forgets its initial state 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.
