VALIDATION OF COMPUTER MODELS

We deal with validation of costly computer models y = y t ?(x) seen as deterministic black box models depending on both a control variable x and an unknown constant parameter t ? . The validation activities refer to the study of the predictive capability of the numerical model y with a special attention on how to take in account all sources of uncertainty. We illustrate well-known issues on toy examples, then we focus on two industral cases motivating our study. 1. Description of a physical system with a computer model A physical systemr :x2 R n ! R with 2 R m : ‐x is a controllable variable, ‐ is the physical parameter, ‐ physical experimentsd z = fz i =r (x i ) + i g i , ‐ i is an error term. A computer modely t :x2 R n ! R with t2T R d ; d 6m: ‐t is a parameter ofy, ‐ computer experimentsd y = fy t j (x i )g i,j . The true valuet ? : ‐P : R m !T the projection operator onT, ‐t ? :=P( ), ‐y t ?(x) is the best representation forr (x). Links betweeny t ? andr : i.y is perfect andt ? = (m =d) =)r (x) =y t ?(x), ii. an error (bias)e exists : t ? = (m =d) andr (x) =y (x) +e(x), iii. is not perfectly identified byy : t ? 6 (d < m) andr (x) =y t ?(x) +e(x).