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

Gated networks: an inventory

Gated networks are networks that contain gating connections, in which the outputs of at least two neurons are multiplied. Initially, gated networks were used to learn relationships between two input sources, such as pixels from two images. More recently, they have been applied to learning activity recognition or multi-modal representations. The aims of this paper are threefold: 1) to explain the basic computations in gated networks to the non-expert, while adopting a standpoint that insists on their symmetric nature. 2) to serve as a quick reference guide to the recent literature, by providing an inventory of applications of these networks, as well as recent extensions to the basic architecture. 3) to suggest future research directions and applications.Comment: Unpublished manuscript, 17 page

Real-Time Distributed Aircraft Simulation through HLA

This paper presents some ongoing researches carried out in the context of the PRISE (Research Platform for Embedded Systems Engineering) Project. This platform has been designed to evaluate and validate new embedded system concepts and techniques through a special hardware and software environment. Since many actual embedded equipments are not available, their corresponding behavior is simulated using the HLA architecture, an IEEE standard for distributed simulation, and a Run-time infrastructure called CERTI and developed at ONERA. HLA is currently largely used in many simulation applications, but the limited performances of the RTIs raises doubts over the feasibility of HLA federations with real-time requirements. This paper addresses the problem of achieving real-time performances with HLA. Several experiments are discussed using well-known aircraft simulators such as the Microsoft Flight Simulator, FlightGear, and X-plane connected with the CERTI Run-time Infrastructure. The added value of these activities is to demonstrate that according to a set of innovative solutions, HLA is well suited to achieve hard real time constraints

Momentum-space atom correlations in a Mott insulator

We report on the investigation of the three-dimensional single-atom-resolved distributions of bosonic Mott insulators in momentum-space. Firstly, we measure the two-body and three-body correlations deep in the Mott regime, finding a perfectly contrasted bunching whose periodicity reproduces the reciprocal lattice. In addition, we show that the two-body correlation length is inversely proportional to the in-trap size of the Mott state with a pre-factor in agreement with the prediction for an incoherent state occupying a uniformly filled lattice. Our findings indicate that the momentum-space correlations of a Mott insulator at small tunnelling is that of a many-body ground-state with Gaussian statistics. Secondly, in the Mott insulating regime with increasing tunnelling, we extract the spectral weight of the quasi-particles from the momentum density profiles. On approaching the transition towards a superfluid, the momentum spread of the spectral weight is found to decrease as a result of the increased mobility of the quasi-particles in the lattice. While the shapes of the observed spectral weight agree with the ones predicted by perturbative many-body calculations, the fitted mobilities are larger than the theoretical ones. This discrepancy is similar to that previously reported on the time-of-flight visibility.Comment: 13 pages, 10 figure

The European Central Bank and the German Constitutional Court: Police Patrols and Fire Alarms

In May 2020, a ruling of the German Federal Constitutional Court (FCC) questioned the legality of the Bundesbank’s participation in the European Central Bank’s (ECB’s) Public Sector Purchase Programme. Applying elements of a principal-agent analysis, this article analyses how the FCC ruling presents us with a new understanding of the relationship between the ECB, other EU institutions and Eurozone member states. Existing principal-agent analyses of the ECB focus upon its relations with other EU-level institutions and point to the limited ex ante control mechanisms and efforts to reinforce ex post control mechanisms—notably European Parliament oversight. The FCC ruling and the ECB’s reaction demonstrate the relative importance of national level controls over the ECB agent. This article understands the role of private plaintiffs in Germany as a form of ‘fire alarm’ on ECB policymaking against the background of weak ex post controls at the EU-level

A gravity current model with capillary trapping for oil migration in multilayer geological basins

We propose a reduced model accounting capillary trapping to simulate oil migration in geological basins made of several rock types. Our model is derived from Darcy type models thanks to Dupuit approximation and a vertical integration in each geological layer. We propose a time-implicit finite volume scheme which is shown to be unconditionally stable and to admit discrete solutions. Numerical outcomes are then provided in order to illustrate the behavior of our reduced model