Despite the fact that mathematical simulations are now common place in science, decision making, forward planning, policy, regulation, and litigation, the fundamental connections between a mathematical simulation and the empirical quantities of the world it targets remain vague and wishy-washy. The focus of this meeting is not so much how science and policy draw insights from the general behaviour of complicated simulation modelling, but rather on the mathematical foundation and empirical justification for quantitative interpretation of simulations for use in the real world, the design of computational experiments and model inter-comparisons, the quantitative comparison of simulation and observations under controlled lab conditions, and the end-to-end communication of information between all those involved. The final attendance list will determine the precise selection of topics in the small (~20) intense program, however we expect to include (a) clarifying the relationship between temperature measured by a thermometer or inferred from a satellite, and the variable of the same name in the numerical solution of a set of partial differential equations (on a finite grid), (b) the extent to which ensembles of simulations (whether over sets of initial conditions, parameter values, mathematical model structures, …) can be deployed/interpreted rationally as a probability distribution for the future quantitative measurements, (c) the improvement (specialization) of experimental design for “grand” ensemble experiments and model inter-comparison projects, and how that design might best differ depending on the target of the exercise, and (d) the quantitative contrast of simulation with observations of laboratory experiments under carefully controlled conditions.