Contribution to the method of Experimental design

Abstract

Recent advancements in modeling, combined with a significant increase in computing power, have enabled the development of simulators capable of replicating physical phenomena with unmatched precision. However, the complexity and time cost of these simulators often make their direct use impractical. To overcome these challenges, it is common to use computer experiment designs to create simpler surrogate functions using approximation or interpolation methods. This work focuses on the creation of computer experiment designs based on stochastic processes. Traditional methods, although extensively studied, have limitations in the context of computer simulations where the error primarily arises from the model. Therefore, suitable plans are needed to optimize the coverage of the experimental domain and detect potential irregularities. We propose new computer experiment designs using marked point processes and area-interaction point processes. These approaches incorporate geometric knowledge and prior information about the experimental points, allowing for a uniform distribution within the unit hypercube. Specifically, Strauss marked point processes with two marks and area-interaction point processes are used to generate these plans. For this purpose, we employ Monte Carlo Markov Chain (MCMC) techniques, including the Metropolis-Hastings algorithm.