effective formulation represents the variations over the entirety of the domain of applicability, not just at a limited number of tested settings. (b) Model predictions must be robust to the new evidence. New experimental measurements must further validate the model, not invalidate the model. Inspired by the novelty index introduced by Sornette et al. [3], we introduce a unique point of view to robustness. We define robustness in terms of lack of sensitivity of model discrepancy to new experimental measurements. It is plausible to assume the predictions of a model would be dominated by different assumptions at different regimes in the domain of applicability. Each new experiment conducted to explore these regimes may validate the underlying assumptions of the model if discrepancy stays stable; or invalidate the underlying assumptions of the model if the discrepancy is increased. 3.2 Possible Trends of Discrepancy Bias The discrepancy bias, introduced in the previous section, constitutes a key component in defining the predictive maturity of a numerical model. Depending on this predictive maturity, the discrepancy bias, when plotted against the number of available experiments, can take one of three forms: Case A į(x) § zero everywhere in the domain; The discrepancy bias is considered insignificant if it is equal to or lower than the experimental uncertainty over the range of controlled parameters {xmin, xmax}. The calibrated model predictions fit the experimental measurements well throughout the domain of applicability, eliminating the need for biascorrection. Such model can be used for forecasting purposes. Case B į(x) § constant acceptably low value everywhere in the domain; There is a systematic, close to constant, acceptably low bias between model predictions and the experiments that cannot be further reduced by calibrating the parameters. The model predictions across the domain of applicability must be corrected by į(x) to adjust for this systematic bias before forecasting. Case C į(x) § unacceptably high or non-constant; 436
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