A Non-Nested Infilling Strategy for Multi-Fidelity based Efficient Global Optimization
| Autor: | M. Durand, Corentin Lothodé, Frédéric Hauville, O. P. Le Maître, Matthieu Sacher, Régis Duvigneau |
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| Přispěvatelé: | Institut de Recherche de l'Ecole Navale (IRENAV), Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE)-Arts et Métiers Sciences et Technologies, HESAM Université (HESAM)-HESAM Université (HESAM), Institut de Recherche Dupuy de Lôme (IRDL), Université de Bretagne Sud (UBS)-Université de Brest (UBO)-École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne)-Centre National de la Recherche Scientifique (CNRS), Uncertainty Quantification in Scientific Computing and Engineering (PLATON), Centre de Mathématiques Appliquées - Ecole Polytechnique (CMAP), École polytechnique (X)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-Centre National de la Recherche Scientifique (CNRS)-Inria Saclay - Ile de France, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Analysis and Control of Unsteady Models for Engineering Sciences (ACUMES), Inria Sophia Antipolis - Méditerranée (CRISAM), Sirli Innovations [Pornichet], Laboratoire de Mathématiques Raphaël Salem (LMRS), Université de Rouen Normandie (UNIROUEN), Normandie Université (NU)-Normandie Université (NU)-Centre National de la Recherche Scientifique (CNRS), HESAM Université - Communauté d'universités et d'établissements Hautes écoles Sorbonne Arts et métiers université (HESAM)-HESAM Université - Communauté d'universités et d'établissements Hautes écoles Sorbonne Arts et métiers université (HESAM), École Nationale d'Ingénieurs de Brest (ENIB)-Université de Bretagne Sud (UBS)-Université de Brest (UBO)-École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne)-Centre National de la Recherche Scientifique (CNRS) |
| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: |
Statistics and Probability
Mathematical optimization Control and Optimization Discretization Computer science media_common.quotation_subject Stochastic Preconditioner Fidelity Context (language use) Parallel Computation [SPI.MECA.MEFL]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Fluids mechanics [physics.class-ph] Surrogate model Discrete Mathematics and Combinatorics [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP] Point (geometry) Global optimization Domain Decomposition media_common Preconditioned Conjugate Gradient Method Domain decomposition methods Optimisation et contrôle [Mathématique] [INFO.INFO-NA]Computer Science [cs]/Numerical Analysis [cs.NA] Nonlinear system global optimization Gaussian process model multifidelity non-nested datasets Modeling and Simulation [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC] Sampling Method |
| Zdroj: | International Journal for Uncertainty Quantification International Journal for Uncertainty Quantification, Begell House Publishers, 2021, 11 (1), pp.1-30 International Journal for Uncertainty Quantification, 2021, 11 (1), pp.1-30. ⟨10.1615/Int.J.UncertaintyQuantification.2020032982⟩ |
| ISSN: | 2152-5080 2152-5099 |
| DOI: | 10.1615/Int.J.UncertaintyQuantification.2020032982⟩ |
| Popis: | International audience; Efficient Global Optimization (EGO) has become a standard approach for the global optimization of complex systems with high computational costs. EGO uses a training set of objective function values computed at selected input points to construct a statistical surrogate model, with low evaluation cost, on which the optimization procedure is applied. The training set is sequentially enriched, selecting new points, according to a prescribed infilling strategy, in order to converge to the optimum of the original costly model. Multi-fidelity approaches combining evaluations of the quantity of interest at different fidelity levels have been recently introduced to reduce the computational cost of building a global surrogate model. However, the use of multi-fidelity approaches in the context of EGO is still a research topic. In this work, we propose a new effective infilling strategy for multi-fidelity EGO. Our infilling strategy has the particularity of relying on non-nested training sets, a characteristic that comes with several computational benefits. For the enrichment of the multi-fidelity training set, the strategy selects the next input point together with the fidelity level of the objective function evaluation. This characteristic is in contrast with previous nested approaches, which require estimation all lower fidelity levels and are more demanding to update the surrogate. The resulting EGO procedure achieves a significantly reduced computational cost, avoiding computations at useless fidelity levels whenever possible, but it is also more robust to low correlations between levels and noisy estimations. Analytical problems are used to test and illustrate the efficiency of the method. It is finally applied to the optimization of a fully nonlinear fluid-structure interaction system to demonstrate its feasibility on real large-scale problems, with fidelity levels mixing physical approximations in the constitutive models and discretization refinements. |
| Databáze: | OpenAIRE |
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