  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. In
this article, we survey the model validation literature and propose to
formulate validation as an iterative construction process that mimics the
process occurring implicitly in the minds of scientists. We thus offer a formal
representation of the progressive build-up of trust in the model, and thereby
replace incapacitating claims on the impossibility of validating a given model
by an adaptive 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, an anomalous diffusion model for
solar radiation transport in the cloudy atmosphere, and a computational fluid
dynamics code for the Richtmyer-Meshkov instability. This article is an
augmented version of Sornette et al. [2007] that appeared in Proceedings of the
National Academy of Sciences in 2007 (doi: 10.1073/pnas.0611677104), with an
electronic supplement at URL
http://www.pnas.org/cgi/content/full/0611677104/DC1. Sornette et al. [2007] is
also available in preprint form at physics/0511219.
