Turbulent and multiscale flows often make single-trajectory prediction a fragile object: small perturbations may destroy pointwise predictability, while ensemble-level quantities remain meaningful. This talk discusses statistical solutions as a framework for describing such dynamics through probability laws on velocity fields and their associated correlation marginals. I will explain how this viewpoint connects classical weak formulations, energy/structure constraints, and weak-strong stability, and why it provides a natural language for uncertainty in fluid dynamics. I will then outline how modern neural surrogates can be interpreted as approximations of these evolving laws, rather than as deterministic replacements for the underlying PDE dynamics.