Despite the supreme importance of fluid flow models, the well-posedness of three-dimensional viscous and inviscid flow equations remains unsolved. Promising efforts have recently evolved around the concept of statistical solutions. In this talk, we present stochastic lattice Boltzmann methods for efficiently approximating statistical solutions to the incompressible Navier–Stokes equations in three spatial dimensions. Space-time adaptive kinetic relaxation frequencies are used to find stable and consistent numerical solutions along the inviscid limit toward the Euler equations. With single level Monte Carlo and stochastic Galerkin methods, we approximate responses, e.g., from initial random perturbations of the flow field. The novel combinations of schemes are implemented in the parallel C++ data structure OpenLB and executed on heterogeneous high-performance computing machinery. Based on exploratory computations, we search for scaling of the energy spectra and structure functions in terms of Kolmogorov’s K41 theory. For the first time, we numerically approximate the limit of statistical solutions of the incompressible Navier–Stokes solutions toward weak-strong unique statistical solutions of the incompressible Euler equations in three dimensions. Applications to wall-bounded turbulence and the potential to provide training data for generative artificial intelligence algorithms are discussed.