Definition of Term: Best Input

No matter how careful a particular model of a real system has been formulated, there will always be a discrepancy between reality, represented by the system value \(y\), and the simulator output \(f(x)\) for any valid input \(\strut{x}\). Perhaps, the simplest way of incorporating this model discrepancy into our analysis is to postulate a best input \(x^+\), representing the best fitting values of the input parameters in some sense, such that the difference \(d=y-f(x^+)\) is independent or uncorrelated with \(f\), \(f(x^+)\) and \(x^+\).

While there are subtleties in the precise interpretation of \(x^+\), especially when certain inputs do not correspond to clearly defined features of the system, the notion of a best input is vital for procedures such as calibration, history matching and prediction for the real system.