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.

翻译：本文提出了一种新的基于方差分析（ANOVA）的函数逼近方法，以及利用可用导数或模型局部随机评估构建高维模型仿真器的方法。我们的方法利用灵敏度指数来设计合适的仿真器结构。对于具有可用导数的高维模型，我们基于导数的仿真器实现了维度无关的均方误差（MSE）和参数化收敛速率（即 $\mathsf{O}(N^{-1})$）。该方法通过构建考虑模型或仿真器局部特性的全局仿真器，进一步扩展至适用于所有（无可用导数的）模型。此类通用仿真器具有维度无关的偏差、参数化收敛速率，以及依赖于维度的均方误差。对于具有特定输入分布的高维模型，我们获得了维度无关的均方误差。我们的仿真器在处理不同输入变量分布及选择输入变量与交互作用方面也表现出竞争力。仿真实验验证了该方法的有效性。