Optimal ANOVA-based emulators of models with(out) derivatives

This paper proposes new ANOVA-based approximations of functions and emulators of high-dimensional models using either available derivatives or local stochastic evaluations of such models. Our approach makes use of sensitivity indices to design adequate structures of emulators. For high-dimensional models with available derivatives, our derivative-based emulators reach dimension-free mean squared errors (MSEs) and parametric rate of convergence (i.e., $\mathsf{O}(N^{-1})$). This approach is extended to cope with every model (without available derivatives) by deriving global emulators that account for the local properties of models or simulators. Such generic emulators enjoy dimension-free biases, parametric rates of convergence and MSEs that depend on the dimensionality. Dimension-free MSEs are obtained for high-dimensional models with particular inputs' distributions. Our emulators are also competitive in dealing with different distributions of the input variables and for selecting inputs and interactions. Simulations show the efficiency of our approach.