settings. Forecasting unavoidably brings up unknown forecasting errors. However, these unknown forecasting errors can be reduced by improving the fidelity of the simulation model through parameter calibration (known unknowns) and bias-correction (unknown unknowns). Naturally, as the number of experimental measurements available for model calibration is consistently increased, the forecasting errors would be consistently reduced. Once a sufficient number of experiments are obtained, and the forecasting errors are reduced to predetermined acceptable levels, allocating resources to further experimentation would have diminishing returns; and therefore allocation of resources to new experiments would not be justified. In Section 4, we hold out some of the available experiments to estimate the forecasting errors of a given simulation model for a given experimental campaign. Estimating forecasting errors is of particular importance in science and engineering, especially when such forecasts are used to determine the expected performance level of an engineering system under worst-case scenarios. Such applications are common in the context of certification. In this manuscript, we illustrate estimating forecasting errors for a given set of experimental measurements using a selected set of hold-out experiments. In Sections 5, we illustrate the merit of this procedure using a material model of plasticity representing a data-rich and situation. Compelling as this approach is, a set of premises must be satisfied for the proposed approach to be applicable. In Section 7, we discuss the underlying premises and limitations of our conceptual framework. 2 ESTIMATION OF MODEL DISCREPANCY The central philosophy of model calibration is to improve the accuracy of model predictions by exploiting a collection of available experimental measurements. Thus, model calibration invariably requires the comparison of large numbers of simulation runs against experimental measurements. Over the past two decades, model calibration has evolved into two strategies, which differ in the methods through which they improve model accuracy. The first type is the parameter calibration approach that captures the inaccuracy of the model parameters. The second type is the bias correction approach that captures the inadequacy of the physics model. These two fundamental concepts are combined together in the landmark study of Kennedy and O’Hagan [1]. Kennedy and O’Hagan’s [1] approach simultaneously calibrates model parameters and corrects for discrepancy bias. The parameter calibration approach has two distinct paradigms used for defining the improved parameter values. In the first approach, calibration is considered as an optimization problem. The 433
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