Differentiating the multipoint Expected Improvement for optimal batch design

This work deals with parallel optimization of expensive objective functions which are modeled as sample realizations of Gaussian processes. The study is formalized as a Bayesian optimization problem, or continuous multi-armed bandit problem, where a batch of q > 0 arms is pulled in parallel at each iteration. Several algorithms have been developed for choosing batches by trading off exploitation and exploration. As of today, the maximum Expected Improvement (EI) and Upper Confidence Bound (UCB) selection rules appear as the most prominent approaches for batch selection. Here, we build upon recent work on the multipoint Expected Improvement criterion, for which an analytic expansion relying on Tallis' formula was recently established. The computational burden of this selection rule being still an issue in application, we derive a closed-form expression for the gradient of the multipoint Expected Improvement, which aims at facilitating its maximization using gradient-based ascent algorithms. Substantial computational savings are shown in application. In addition, our algorithms are tested numerically and compared to state-of-the-art UCB-based batch-sequential algorithms. Combining starting designs relying on UCB with gradient-based EI local optimization finally appears as a sound option for batch design in distributed Gaussian Process optimization

Quantifying uncertainties on excursion sets under a Gaussian random field prior

We focus on the problem of estimating and quantifying uncertainties on the excursion set of a function under a limited evaluation budget. We adopt a Bayesian approach where the objective function is assumed to be a realization of a Gaussian random field. In this setting, the posterior distribution on the objective function gives rise to a posterior distribution on excursion sets. Several approaches exist to summarize the distribution of such sets based on random closed set theory. While the recently proposed Vorob'ev approach exploits analytical formulae, further notions of variability require Monte Carlo estimators relying on Gaussian random field conditional simulations. In the present work we propose a method to choose Monte Carlo simulation points and obtain quasi-realizations of the conditional field at fine designs through affine predictors. The points are chosen optimally in the sense that they minimize the posterior expected distance in measure between the excursion set and its reconstruction. The proposed method reduces the computational costs due to Monte Carlo simulations and enables the computation of quasi-realizations on fine designs in large dimensions. We apply this reconstruction approach to obtain realizations of an excursion set on a fine grid which allow us to give a new measure of uncertainty based on the distance transform of the excursion set. Finally we present a safety engineering test case where the simulation method is employed to compute a Monte Carlo estimate of a contour line

Fast uncertainty reduction strategies relying on Gaussian process models

This work deals with sequential and batch-sequential evaluation strategies of real-valued functions under limited evaluation budget, using Gaussian process models. Optimal Stepwise Uncertainty Reduction (SUR) strategies are investigated for two diff erent problems, motivated by real test cases in nuclear safety. First we consider the problem of identifying the excursion set above a given threshold T of a real-valued function f. Then we study the question of finding the set of "safe controlled con gurations", i.e. the set of controlled inputs where the function remains below T, whatever the value of some others non-controlled inputs. New SUR strategies are presented, together with effi cient procedures and formulas to compute and use them in real-world applications. The use of fast formulas to recalculate quickly the posterior mean or covariance function of a Gaussian process (referred to as the "kriging update formulas") does not only provide substantial computational savings. It is also one of the key tools to derive closed-form formulas enabling a practical use of computationally-intensive sampling strategies. A contribution in batch-sequential optimization (with the multi-points Expected Improvement) is also presented.Cette thèse traite de stratégies d'évaluation séquentielle et batch-séquentielle de fonctions à valeurs réelles sous un budget d'évaluation limité, à l'aide de modèles à processus Gaussiens. Des stratégies optimales de réduction séquentielle d'incertitude (SUR) sont étudiées pour deux problèmes différents, motivés par des cas d'application en sûreté nucléaire. Tout d'abord, nous traitons le problème d'identification d'un ensemble d'excursion au dessus d'un seuil T d'une fonction f à valeurs réelles. Ensuite, nous étudions le problème d'identification de l'ensemble des configurations "robustes, contrôlées", c'est à dire l'ensemble des inputs contrôlés où la fonction demeure sous T quelle que soit la valeur des différents inputs non-contrôlés. De nouvelles stratégies SUR sont présentés. Nous donnons aussi des procédures efficientes et des formules permettant d'utiliser ces stratégies sur des applications concrètes. L'utilisation de formules rapides pour recalculer rapidement le posterior de la moyenne ou de la fonction de covariance d'un processus Gaussien (les "formules d'update de krigeage") ne fournit pas uniquement une économie computationnelle importante. Elles sont aussi l'un des ingrédient clé pour obtenir des formules fermées permettant l'utilisation en pratique de stratégies d'évaluation coûteuses en temps de calcul. Une contribution en optimisation batch-séquentielle utilisant le Multi-points Expected Improvement est également présentée

Plan d'expériences numériques adaptatifs pour les études mécaniques

La prise en compte des incertitudes fait aujourd’hui partie intégrante des analyses en mécanique des matériaux et des structures : variabilité des agencements microstructuraux, connaissance imprécise des propriétés matériaux, volumes élémentaires représentatifs, statistiques de défauts, écarts aux prescriptions géométriques des structures, évolutions temporelles non maîtrisables des chargements, etc. La propagation de ces connaissances incertaines dans les logiciels de calcul complexes requiert en général un nombre important de simulations numériques vite rédhibitoire en pratique. Afin de réduire ce coût de calcul, des approches statistiques basées sur la théorie des plans d’expériences peuvent être utilisées. Une stratégie classique de plan d’expérience consiste à assurer une bonne couverture de l’espace de variation des entrées. Cependant, l’uniformité d’une telle répartition n’est pas optimale quand on s’intéresse à des caractéristiques locales de la réponse des structures : fortes variations des comportements apparents en fonction des paramètres d’entrées (gradients), optimisation topologique ou matérielle, etc. Ces connaissances précises nécessitent de concentrer les simulations dans des régions spécifiques plutôt que d’explorer l’ensemble de l’espace de variation. Ce travail est donc dédié au développement de techniques de planification adaptatives pour raffiner localement l’échantillonnage autour d’une zone d’intérêt. Une nouvelle méthode, basée sur un couplage d’interpolation par Krigeage et d’optimisation d’une fonction coût (une variante du critère d’Expected Improvement) intégrant l’objectif visé, est proposée. La pertinence et l’efficacité de cette méthode ont été soulignées dans le cadre d’une étude de compacité maximale pour un empilement de sphères polydisperses. Pour une situation bi-disperse, le problème consiste en la recherche d’une ligne de crête en fonction de l’étalement granulométrique et de la fraction volumique de chaque classe. La méthodologie générale proposée, utilisée ici avec le logiciel LMGC90, permet de retrouver à moindre coût des résultats de la littérature obtenus par des plans d’expérience uniformes et intensifs

NaCl-induced high-temperature corrosion of β21S Ti alloy

Titanium alloys are very interesting for aeronautics applications because of their low density, high mechanical resistance and good resistance to corrosion in aggressive environments. However, recent developments impose the use of these materials at higher temperatures than those initially envisaged (above 400 °C), revealing some uncertainties of their behavior. Depending on the operating conditions, the material can be exposed to variable humidity levels and, in some cases, can be in contact with silica or marine salt. This study aims to evaluate the influence of NaCl solid deposit on the behavior of b21S Ti alloy at 560 °C under realistic ambient atmospheres. The tests were carried out in laboratory air and in water vapor-enriched air, on uncoated samples and on samples with solid NaCl deposit. The reaction-product evolution (up to 600 h) was characterized by thermogravimetric analysis, SEM observations (surface and cross section), XRD and microhardness profiling on cross sections. An aggravation of the corrosion phenomena in the presence of NaCl solid deposit was observed, that was related to the presence of gaseous metal chlorides, leading to the establishment of an active corrosion process

NaCl induced corrosion of Ti-6Al-4V alloy at high temperature

This paper presents a study on the Ti-6Al-4V behaviour in presence of NaCl deposit under dry and moistair environments at 560◦C. The results evidence a detrimental effect of the NaCl deposit with a synergisticeffect in presence of moist air environment. Treatments under dry and moist air with NaCl deposit for600 h, lead respectively to weight gains per unit area 5 and 15 times higher than observed under classicoxidation in dry air. Enhancement of the corrosion phenomenon is attributed to the presence of gaseousmetal chlorides, leading to the establishment of an active corrosion process

A search for small noncoding RNAs in Staphylococcus aureus reveals a conserved sequence motif for regulation

Bioinformatic analysis of the intergenic regions of Staphylococcus aureus predicted multiple regulatory regions. From this analysis, we characterized 11 novel noncoding RNAs (RsaA‐K) that are expressed in several S. aureus strains under different experimental conditions. Many of them accumulate in the late-exponential phase of growth. All ncRNAs are stable and their expression is Hfq-independent. The transcription of several of them is regulated by the alternative sigma B factor (RsaA, D and F) while the expression of RsaE is agrA-dependent. Six of these ncRNAs are specific to S. aureus, four are conserved in other Staphylococci, and RsaE is also present in Bacillaceae. Transcriptomic and proteomic analysis indicated that RsaE regulates the synthesis of proteins involved in various metabolic pathways. Phylogenetic analysis combined with RNA structure probing, searches for RsaE‐mRNA base pairing, and toeprinting assays indicate that a conserved and unpaired UCCC sequence motif of RsaE binds to target mRNAs and prevents the formation of the ribosomal initiation complex. This study unexpectedly shows that most of the novel ncRNAs carry the conserved C−rich motif, suggesting that they are members of a class of ncRNAs that target mRNAs by a shared mechanis

On the origins and the evolution of the fuel-cladding bonding phenomenon in PWR fuel rods

This study proposes a new and detailed description of the fuel-cladding bonding phenomenon occurring in PWR fuel rods. Very early and late bonding states were characterized on specimens of 35.3 GWd.tU−1 moderate burnup and of 64.5 GWd.tU−1 high burnup respectively. Results were then compared with those achieved on a re-created bonded situation obtained on a Zircaloy-4/hyper-stoichiometric UO2+x model materials diffusion couple. These results tend to indicate that a chemical adhesion is probably at the origin of the PWR fuel-cladding bonding. In addition, the progressive formation of ZrO2/UO2 interfacial circumvolutions observed with increasing burnup, which lead to the physical anchorage of ZrO2 and UO2, is likely to lead to their mechanical adhesion. Thus, the in-reactor ZrO2/UO2 bonding could be considered, since the occurrence of the first bonded situations, as an adhesion phenomenon owning two components: an initial chemical progressively strengthened by a second mechanical

Degradation mechanism of Ti-6Al-2Sn-4Zr-2Mo-Si alloy exposed to solid NaCl deposit at high temperature

This study focuses on the corrosion behaviour of Ti-6Al-2Sn-4Zr-2Mo-Si alloy in presence of NaCl deposit in air at 560 °C. The active oxidation mechanism at the origin of the corrosion phenomenon enhancement in presence of solid NaCl is thought to be connected to the formation of both external and internal thick oxidation areas. Thermodynamic calculations allowed showing the role played by the different alloying elements in the forma-tion of the external oxide and detailed TEM characterisations brought new insights regarding the nature and origin of the internal oxidation area