1. Multi-fidelity modeling with different input domain definitions using Deep Gaussian Processes
- Author
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Nouredine Melab, El-Ghazali Talbi, Ali Hebbal, Mathieu Balesdent, Loïc Brevault, DTIS, ONERA, Université Paris Saclay [Palaiseau], ONERA-Université Paris-Saclay, Optimisation de grande taille et calcul large échelle (BONUS), Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189 (CRIStAL), Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS), and The work of Ali Hebbal is a funded by ONERA - The French Aerospace Lab and the University of Lille through a PhD thesis. This work is also part of two projects (HERACLES and MUFIN) funded by ONERA. The Experiments presented in this paper were carried out using the Grid’5000 testbed, supported by a scientific interest group hosted by Inria and including CNRS, RENATER and several Universities as well as other organizations (see https://www.grid5000.fr).
- Subjects
FOS: Computer and information sciences ,Domain of a function ,Computer Science - Machine Learning ,Control and Optimization ,Computer science ,media_common.quotation_subject ,0211 other engineering and technologies ,Fidelity ,Machine Learning (stat.ML) ,02 engineering and technology ,Machine Learning (cs.LG) ,Domain (software engineering) ,symbols.namesake ,0203 mechanical engineering ,[STAT.ML]Statistics [stat]/Machine Learning [stat.ML] ,Statistics - Machine Learning ,multifidélité ,modélisation bayésienne ,Gaussian process ,021106 design practice & management ,media_common ,business.industry ,Quantum Physics ,Computer Graphics and Computer-Aided Design ,Computer Science Applications ,020303 mechanical engineering & transports ,Test case ,Control and Systems Engineering ,espace entree dimension variée ,symbols ,Global Positioning System ,Engineering design process ,business ,Parametrization ,Algorithm ,Software ,processus gaussien - Abstract
International audience; Multi-fidelity approaches combine different models built on a scarce but accurate data-set (high-fidelity data-set), and a large but approximate one (low-fidelity data-set) in order to improve the prediction accuracy. Gaussian Processes (GPs) are one of the popular approaches to exhibit the correlations between these different fidelity levels. Deep Gaussian Processes (DGPs) that are functional compositions of GPs have also been adapted to multi-fidelity using the Multi-Fidelity Deep Gaussian process model (MF-DGP). This model increases the expressive power compared to GPs by considering non-linear correlations between fidelities within a Bayesian framework. However, these multi-fidelity methods consider only the case where the inputs of the different fidelity models are defined over the same domain of definition (e.g., same variables, same dimensions). However, due to simplification in the modeling of the low-fidelity, some variables may be omitted or a different parametrization may be used compared to the high-fidelity model. In this paper, Deep Gaussian Processes for multi-fidelity (MF-DGP) are extended to the case where a different parametrization is used for each fidelity. The performance of the proposed multifidelity modeling technique is assessed on analytical test cases and on structural and aerodynamic real physical problems.
- Published
- 2020