Résumé:
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.
