Sequential sampling for functional estimation via Sieve

Sequential sampling methods are often used to estimate functions describing models subjected to time-intensive simulations or expensive experiments. These methods provide guidelines for point selection in the domain to capture maximum information about the function. However, in most sequential sampling methods, determining a new point is a time-consuming process. In this paper, we propose a new method, named Sieve, to sequentially select points of an initially unknown function based on the definition of proper intervals. In contrast with existing methods, Sieve does not involve function estimation at each iteration. Therefore, it presents a greater computational efficiency for achieving a given accuracy in estimation. Sieve brings in tools from computational geometry to subdivide regions of the domain efficiently. Further, we validate our proposed method through numerical simulations and two case studies on the calibration of internal combustion engines and the optimal exploration of an unknown environment by a mobile robot.