Under-resolved computer simulations are typically unavoidable in many practical turbulent flow applications exhibiting extreme geometrical complexity and broad ranges of length and time scales. In such applications, coarse-grained simulation (CGS) becomes the effective simulation strategy, mostly by necessity rather than by choice. In CGS strategies, resolved/unresolved scale separation is assumed possible, large energy-containing structures are mostly resolved, smaller structures are spatially filtered out and unresolved subgrid effects are modeled; this includes classical large-eddy simulation (LES) strategies with the explicit use of closure subgrid scale models and implicit LES, relying on subgrid modeling implicitly provided by physics-capturing numerical algorithms. Predictability issues in CGS of under-resolved mixing of material scalars driven by under-resolved velocity fields and initial conditions are addressed in this paper, and shock-driven turbulent mixing is a particular focus.