An Inverse Chance-Constrained Approach to the Calibration of Robust Models.

This paper proposes a strategy to calibrate computational models according to uncertain input-output data. To this end, uncertainty in the data is first characterized using adversarial data sets. Samples drawn from such sets are then mapped from the input-output space to the parameter space using an inverse mapping. This mapping minimizes the collective output spread of an ensemble of point predictions while satisfying a set of individual data-matching requirements. The distribution of the resulting parameter points, which often exhibits strong parameter dependencies, is then modeled using Sliced Normal distributions. The chance-constrained formulation used to learn this distribution enables the analyst to trade-off a greater likelihood for most of the data against a lower likelihood for some of the data, thereby relaxing the conservatism of the calibrated model. This formulation neglects the worst-performing quantiles of each adversarial distribution and eliminates the detrimental effects that outliers have on the resulting model. This calibration approach not only has a considerably lower computational cost than the standard forward approach but it also allows for the identification of suitable distribution classes, which in turn yield better calibrated models.