Computation of High-Order Sensitivities of Model Responses to Model Parameters—I: Underlying Motivation and Current Methods

The mathematical/computational model of a physical system comprises parameters and independent and dependent variables. Since the physical system is seldom known precisely and since the model’s parameters stem from experimental procedures that are also subject to uncertainties, the results predicted by a computational model are imperfect. Quantifying the reliability and accuracy of results produced by a model (called “model responses”) requires the availability of sensitivities (i.e., functional partial derivatives) of model responses with respect to model parameters. This work reviews the basic motivations for computing high-order sensitivities and illustrates their importance by means of an OECD/NEA reactor physics benchmark, which is representative of a “large-scale system” involving many (21,976) uncertain parameters. The computation of higher-order sensitivities by conventional methods (finite differences and/or statistical procedures) is subject to the “curse of dimensionality”. Furthermore, as will be illustrated in this work, the accuracy of high-order sensitivities computed using such conventional methods cannot be a priori guaranteed. High-order sensitivities can be computed accurately and efficiently solely by applying the high-order adjoint sensitivity analysis methodology. The principles underlying this adjoint methodology are also reviewed in preparation for introducing, in the accompanying Part II, the “High-Order Function/Feature Adjoint Sensitivity Analysis Methodology” (nth-FASAM), which aims at most efficiently computing exact expressions of high-order sensitivities of model responses to functions (“features”) of model parameters.