In this talk, I will consider the problem of predicting future averages of an unknown quantum observable, given a dataset of noisy past values. The observable, the initial state of the physical system and even the nature of the latter are unknown. There is, however, a promise on the energy distribution of the state: with very high probability, it is constrained to be smaller than a threshold. In this mostly unexplored framework, one can find very funny objects, like self-testing datasets, which can only be generated with specific Hamiltonians, states and measurement operators; or “aha!” datasets, where predictability considerably increases when we add datapoints from an unrelated measurement. More weirdly, some simple datasets lead to what we call a “fog bank”: complete unpredictability at some extrapolation time \tau, and exact predictability for time \tau’>\tau. At the end of the talk, I will present some general no-go results on extrapolation and provide a hierarchy of efficient SDP relaxations of the set of feasible datapoints, with bounds on the speed of convergence.