  Validation is often defined as the process of determining the degree to which
a model is an accurate representation of the real world from the perspective of
its intended uses. Validation is crucial as industries and governments depend
increasingly on predictions by computer models to justify their decisions. We
propose to formulate the validation of a given model as an iterative
construction process that mimics the often implicit process occurring in the
minds of scientists. We offer a formal representation of the progressive
build-up of trust in the model. We thus replace static claims on the
impossibility of validating a given model by a dynamic process of constructive
approximation. This approach is better adapted to the fuzzy, coarse-grained
nature of validation. Our procedure factors in the degree of redundancy versus
novelty of the experiments used for validation as well as the degree to which
the model predicts the observations. We illustrate the new methodology first
with the maturation of Quantum Mechanics as the arguably best established
physics theory and then with several concrete examples drawn from some of our
primary scientific interests: a cellular automaton model for earthquakes, a
multifractal random walk model for financial time series, an anomalous
diffusion model for solar radiation transport in the cloudy atmosphere, and a
computational fluid dynamics code for the Richtmyer-Meshkov instability.
