This is an early access version, the complete PDF, HTML, and XML versions will be available soon.
Open AccessArticle
New Computer Experiment Designs with Area-Interaction Point Processes
by
Ahmed Ait Ameur
Ahmed Ait Ameur *,†
,
Hichem Elmossaoui
Hichem Elmossaoui †
and
Nadia Oukid
Nadia Oukid
LAMDA-RO Laboratory, Department of Mathematics, Faculty of Sciences, University Saad Dahlab Blida1, Soumâa BP 270, Blida, Algeria
*
Author to whom correspondence should be addressed.
†
These authors contributed equally to this work.
Mathematics 2024, 12(15), 2397; https://doi.org/10.3390/math12152397 (registering DOI)
Submission received: 15 June 2024
/
Revised: 14 July 2024
/
Accepted: 29 July 2024
/
Published: 31 July 2024
Abstract
This article presents a novel method for constructing computer experiment designs based on the theory of area-interaction point processes. This method is essential for capturing the interactions between different elements within a modeled system, offering a more flexible and adaptable approach compared with traditional mathematical modeling. Unlike conventional rough models that rely on simplified equations, our method employs the Markov Chain Monte Carlo (MCMC) method and the Metropolis–Hastings algorithm combined with Voronoi tessellations. It uses a new dynamic called homogeneous birth and death dynamics of a set of points to generate the designs. This approach does not require the development of specific mathematical models for each system under study, making it universally applicable while achieving comparable results. Furthermore, we provide an in-depth analysis of the convergence properties of the Markov Chain to ensure the reliability of the generated designs. An expanded literature review situates our work within the context of existing research, highlighting its unique contributions and advancements. A comparison between our approach and other existing computer experiment designs has been performed.
Share and Cite
MDPI and ACS Style
Ait Ameur, A.; Elmossaoui, H.; Oukid , N.
New Computer Experiment Designs with Area-Interaction Point Processes. Mathematics 2024, 12, 2397.
https://doi.org/10.3390/math12152397
AMA Style
Ait Ameur A, Elmossaoui H, Oukid N.
New Computer Experiment Designs with Area-Interaction Point Processes. Mathematics. 2024; 12(15):2397.
https://doi.org/10.3390/math12152397
Chicago/Turabian Style
Ait Ameur, Ahmed, Hichem Elmossaoui, and Nadia Oukid .
2024. "New Computer Experiment Designs with Area-Interaction Point Processes" Mathematics 12, no. 15: 2397.
https://doi.org/10.3390/math12152397
Note that from the first issue of 2016, this journal uses article numbers instead of page numbers. See further details
here.
Article Metrics
Article Access Statistics
For more information on the journal statistics, click
here.
Multiple requests from the same IP address are counted as one view.