Publications

2023

• CMA-ES and Advanced Adaptation Mechanisms
  
  • Akimoto Youhei
  • Hansen Nikolaus
  , 2023, pp.1157-1182. (10.1145/3583133.3595054)
  DOI : 10.1145/3583133.3595054
• An Introduction to Scientific Experimentation and Benchmarking
  
  • Auger Anne
  • Hansen Nikolaus
  , 2023, pp.854-877. (10.1145/3583133.3595064)
  DOI : 10.1145/3583133.3595064
• GECCO 2023 Tutorial on Benchmarking Multiobjective Optimizers 2.0
  
  • Brockhoff Dimo
  • Tusar Tea
  , 2023, pp.1183-1212. Benchmarking is an important part of algorithm design, selection and recommendation---both in single- and multiobjective optimization. Benchmarking multiobjective solvers seems at first sight more complicated than benchmarking single-objective ones as there exists no natural total order on the objective space. In the past, comparisons of multiobjective solvers have therefore been done either entirely visually (at first) or via quality indicators and the attainment function. Only very recently did we realize that the quality indicator approach transforms a multiobjective problem into a single-objective (set-based) problem and thus all recent progress from the rapidly evolving single-objective benchmarking field can be transferred to the multiobjective case as well. Moreover, many multiobjective test functions have been proposed in the past but not much has changed in the last 15 or so years in terms of addressing the disadvantages of those problems (like Pareto sets on constraint boundaries, usage of distance variables, etc.). In this tutorial, we will discuss the past and future of benchmarking multiobjective optimizers. In particular, we will discuss the new view on benchmarking multiobjective algorithms by falling back on single-objective comparisons and thus being able to use all methodologies and tools from the single-objective domain such as empirical distributions of runtimes. We will also discuss the advantages and drawbacks of some widely used multiobjective test suites that we have all become familiar with over the years and explain how we can do better: by going back to the roots of what a multi-objective problem is in practice, namely the simultaneous optimization of multiple objective functions. Finally, we discuss recent advances in the visualization of (multiobjective) problem landscapes and compare the previous and newly proposed benchmark problems in the context of those landscape visualizations. (10.1145/2598394.2605339)
  DOI : 10.1145/2598394.2605339
• Comparing Boundary Handling Techniques of CMA-ES on the bbob and sbox-cost Test Suites
  
  • Brockhoff Dimo
  , 2023, pp.2318-2325. Bound constraints on the variables are the most basic constraints in an optimization problem formulation and, thus, among the most common. It is therefore essential to understand the impact of different boundary handling techniques on algorithm performance. Equally, it is important to understand the practical impact of using bound constraint handling in an algorithm on principally unbounded problems but where the user has a good indication of the domain of the (sought) optimum. Both questions will be investigated in this paper on the newly introduced box-constrained version sbox-cost of the well-known, unconstrained test suite bbob and for the example of the two boundary handling techniques, implemented in the CMA-ES python module pycma. The numerical experiments performed with the COCO platform show that there is (i) only a minor difference in performance between the two test suites and (ii) a slight performance reduction for the (default) BoundTransform boundary handling compared to the BoundPenalty version of CMA-ES. (10.1145/3583133.3596413)
  DOI : 10.1145/3583133.3596413
• Weak approximations and VIX option price expansions in forward variance curve models
  
  • Bourgey F.
  • Gobet Emmanuel
  • de Marco S.
  Quantitative Finance, Taylor & Francis (Routledge), 2023, 23 (9), pp.1259-1283. (10.1080/14697688.2023.2227230)
  DOI : 10.1080/14697688.2023.2227230
• Bayesian calibration of a finite-rate nitridation model from molecular beam and plasma wind tunnel experiments
  
  • Capriati Michele
  • del Val Anabel
  • Schwartzentruber Thomas E
  • Minton Timothy K
  • Congedo Pietro Marco
  • Magin Thierry E
  , 2023. The accurate modeling of gas-surface interaction phenomena is crucial for predicting the heat flux and the mass loss experienced by atmospheric entry bodies. Gas-surface interactions refer to the phenomena occurring between the reacting gas and the material. An important part of the modeling is the description of the surface chemical reactions. We propose to stochastically calibrate the rates of the elementary reactions between a nitrogen gas and a carbon surface by using molecular beam data. The parameters' joint posterior is then propagated through a CFD model to reproduce plasma wind tunnel experiments. The predictive quantities exhibit good agreement with the experimental counterparts. (10.13009/EUCASS2023-897)
  DOI : 10.13009/EUCASS2023-897
• An Adaptive Multi-Level Max-Plus Method for Deterministic Optimal Control Problems
  
  • Akian Marianne
  • Gaubert Stéphane
  • Liu Shanqing
  , 2023. We introduce a new numerical method to approximate the solution of a finite horizon deterministic optimal control problem. We exploit two Hamilton-Jacobi-Bellman PDE, arising by considering the dynamics in forward and backward time. This allows us to compute a neighborhood of the set of optimal trajectories, in order to reduce the search space. The solutions of both PDE are successively approximated by max-plus linear combinations of appropriate basis functions, using a hierarchy of finer and finer grids. We show that the sequence of approximate value functions obtained in this way does converge to the viscosity solution of the HJB equation in a neighborhood of optimal trajectories. Then, under certain regularity assumptions, we show that the number of arithmetic operations needed to compute an approximate optimal solution of a $d$-dimensional problem, up to a precision $\varepsilon$, is bounded by $O(C^d (1/\varepsilon) )$, for some constant $C>1$, whereas ordinary grid-based methods have a complexity in$O(1/\varepsilon^{ad}$) for some constant $a>0$.
• Structures arborescentes aléatoires
  
  • Bellin Etienne
  , 2023. Cette thèse se concentre sur certaines structures arborescentes aléatoires et leurs applications. Quatre modèles sont étudiés. Le premier est celui des factorisations minimales du cycle de taille n. Une telle factorisation est la donnée de n-1 transpositions dont la composition égale la permutation cyclique (1...n). En exploitant une bijection avec les arbres étiquetés et en explicitant certaines fonctions génératrices sur ces arbres, nous déduisons la loi jointe du nombre de fois que 1 et 2 apparaissent dans une factorisation minimale de taille n choisie uniformément au hasard. Le deuxième problème est celui des tuples de stationnement (parking functions). Nous étudions la distance entre les k premières coordonnées d'un n-uplet de stationnement choisi uniformément au hasard et k variables i.i.d uniformes. Nous montrons que la distance en variation totale tend vers 0 lorsque k est petit devant racine carrée de n et que la distance de Kolmogorov tend vers 0 lorsque k = o(n). Nous donnons aussi des estimations sur la vitesse de convergence. Cette étude est possible, encore une fois, grâce à une bijection avec les arbres étiquetés qui permet de se ramener à l'étude d'arbres aléatoires puis de marches aléatoires conditionnées. Le troisième problème consiste à étudier le nombre d'indépendance d'arbres aléatoires. Le nombre d'indépendance d'un graphe est le plus grand cardinal d'un sous-ensemble de sommets du graphe tel qu’aucune paire de sommets de cet ensemble ne sont reliés par une arête. Nous obtenons des théorèmes limites pour les arbres simplement générés par des méthodes robustes de convergence locale, et généralisons des résultats précédemment obtenus de manière calculatoire. Enfin le dernier problème est celui des factorisations monotones qui sont des factorisations minimales satisfaisant une certaine condition supplémentaire de monotonie. Nous décrivons une bijection entre ces objets et les arbres plans. Pour tout k < n nous représentons les k premières transpositions d'une factorisation monotone de taille n comme une lamination du disque, i.e comme une union de cordes disjointes du cercle unité. Nous étudions ensuite la convergence du processus (0<k<n) de lamination en exploitant la bijection avec les arbres plans.
• Ambitropical geometry, hyperconvexity and zero-sum games
  
  • Akian Marianne
  • Gaubert Stéphane
  • Vannucci Sara
  , 2023. Shapley operators of undiscounted zero-sum two-player games are order-preserving maps that commute with the addition of a constant. We characterize the fixed point sets of Shapley operators, in finite dimension (i.e., for games with a finite state space). Some of these characterizations are of a lattice theoretical nature, whereas some other rely on metric or tropical geometry. More precisely, we show that fixed point sets of Shapley operators are special instances of hyperconvex spaces: they are sup-norm non-expansive retracts, and also lattices in the induced partial order. Moreover, they retain properties of convex sets, with a notion of convex hull defined only up to isomorphism. For deterministic games with finite action spaces, these fixed point sets are supports of polyhedral complexes, with a cell decomposition attached to stationary strategies of the players, in which each cell is an alcoved polyhedron of $A_n$ type. We finally provide an explicit local representation of the latter fixed point sets, as polyhedral fans canonically associated to lattices included in the Boolean hypercube.
• Wasserstein medians: robustness, PDE characterization and numerics
  
  • Carlier Guillaume
  • Chenchene Enis
  • Eichinger Katharina
  , 2023. We investigate the notion of Wasserstein median as an alternative to the Wasserstein barycenter, which has become popular but may be sensitive to outliers. In terms of robustness to corrupted data, we indeed show that Wasserstein medians have a breakdown point of approximately 1 2. We give explicit constructions of Wasserstein medians in dimension one which enable us to obtain L p estimates (which do not hold in higher dimensions). We also address dual and multimarginal reformulations. In convex subsets of R d , we connect Wasserstein medians to a minimal (multi) flow problem à la Beckmann and a system of PDEs of Monge-Kantorovich-type, for which we propose a p-Laplacian approximation. Our analysis eventually leads to a new numerical method to compute Wasserstein medians, which is based on a Douglas-Rachford scheme applied to the minimal flow formulation of the problem.
• Connections between reference prior theory and global sensitivity analysis, an illustration with $f$-divergences
  
  • Van Biesbroeck Antoine
  • Gauchy Clément
  • Garnier Josselin
  • Feau Cyril
  , 2023. The reference prior theory constructs a framework which helps the resolution of the prior choice issue in Bayesian analysis, relying on the introduction of some information criteria called objective. Within the idea of a more global definition of such criteria, we discuss a connection between their definition and some sensitivity analysis tools, which opens the way to numerous measures for the reference prior choice. In our framework, we demonstrate the robustness of the Jeffreys prior as the optimum of our new objective information metrics. Those are rigorously introduced and accompanied with a proof of the optimal characteristic of the Jeffreys prior under appropriate assumptions.
• Entropic Fictitious Play for Mean Field Optimization Problem
  
  • Chen Fan
  • Ren Zhenjie
  • Wang Songbo
  Journal of Machine Learning Research, Microtome Publishing, 2023, 24, pp.no. 211. We study two-layer neural networks in the mean field limit, where the number of neurons tends to infinity. In this regime, the optimization over the neuron parameters becomes the optimization over the probability measures, and by adding an entropic regularizer, the minimizer of the problem is identified as a fixed point. We propose a novel training algorithm named entropic fictitious play, inspired by the classical fictitious play in game theory for learning Nash equilibriums, to recover this fixed point, and the algorithm exhibits a two-loop iteration structure. Exponential convergence is proved in this paper and we also verify our theoretical results by simple numerical examples.
• Optimal monetary policy in an estimated SIR model
  
  • Benmir Ghassane
  • Jaccard Ivan
  • Vermandel Gauthier
  European Economic Review, Elsevier, 2023, 156, pp.104502. This paper studies the design of Ramsey optimal monetary policy in a Health New Keynesian (HeNK) model with Susceptible, Infected and Recovered (SIR) agents. The nonlinear model is estimated with maximum likelihood techniques on Euro Area data. Our objective is to deconstruct the mechanism by which contagion risk affects the conduct of monetary policy. If monetary policy is the only game in town, we find that optimal policy features significant deviations from price stability to mitigate the effect of the pandemic. The best outcome is obtained when the optimal Ramsey policy is combined with a lockdown strategy of medium intensity. In this case, monetary policy can concentrate on its price stabilization objective. (10.1016/j.euroecorev.2023.104502)
  DOI : 10.1016/j.euroecorev.2023.104502
• Accessibility constraints in structural optimization via distance functions
  
  • Allaire Grégoire
  • Bihr Martin
  • Bogosel Beniamin
  • Godoy Matías
  Journal of Computational Physics, Elsevier, 2023, 484, pp.112083. This paper is concerned with a geometric constraint, the so-called accessibility constraint, for shape and topology optimization of structures built by additive manufacturing. The motivation comes from the use of sacrificial supports to maintain a structure, submitted to intense thermal residual stresses during its building process. Once the building stage is finished, the supports are of no more use and should be removed. However, such a removal can be very difficult or even impossible if the supports are hidden deep inside the complex geometry of the structure. A rule of thumb for evaluating the ease of support removal is to ask that the contact zone between the structure and its supports can be accessed from the exterior by a straight line which does not cross another part of the structure. It mimicks the possibility to cut the head of the supports attached to the structure with some cutting tool. The present work gives a new mathematical way to evaluate such an accessibility constraint, which is based on distance functions, solutions of eikonal equations. The main advantage is the possibility of computing shape derivatives of such a criterion with respect to both the structure and the support. We numerically demonstrate in 2D and 3D that, in the context of the level-set method for topology optimization, such an approach allows us to optimize simultaneously the mechanical performance of a structure and the accessibility of its building supports, guaranteeing its additive manufacturing. (10.1016/j.jcp.2023.112083)
  DOI : 10.1016/j.jcp.2023.112083
• Results on the Spectral Stability of Standing Wave Solutions of the Soler Model in 1-D
  
  • Aldunate Danko
  • Ricaud Julien
  • Stockmeyer Edgardo
  • van den Bosch Hanne
  Communications in Mathematical Physics, Springer Verlag, 2023, 401 (1), pp.227--273. We study the spectral stability of the nonlinear Dirac operator in dimension 1+1, restricting our attention to nonlinearities of the form $f(\langle\psi,\beta \psi\rangle_{\mathbb{C}^2}) \beta$. We obtain bounds on eigenvalues for the linearized operator around standing wave solutions of the form $e^{-i\omega t} \phi_0$. For the case of power nonlinearities $f(s)= s |s|^{p-1}$, $p>0$, we obtain a range of frequencies $\omega$ such that the linearized operator has no unstable eigenvalues on the axes of the complex plane. As a crucial part of the proofs, we obtain a detailed description of the spectra of the self-adjoint blocks in the linearized operator. In particular, we show that the condition $\langle\phi_0,\beta \phi_0\rangle_{\mathbb{C}^2} > 0$ characterizes groundstates analogously to the Schrödinger case. (10.1007/s00220-023-04646-4)
  DOI : 10.1007/s00220-023-04646-4
• Wind power predictions from nowcasts to 4-hour forecasts: a learning approach with variable selection
  
  • Bouche Dimitri
  • Flamary Rémi
  • D’alché-Buc Florence
  • Plougonven Riwal
  • Clausel Marianne
  • Badosa Jordi
  • Drobinski Philippe
  Renewable Energy, Elsevier, 2023, 211, pp.938-947. We study short-term prediction of wind speed and wind power (every 10 minutes up to 4 hours ahead). Accurate forecasts for these quantities are crucial to mitigate the negative effects of wind farms' intermittent production on energy systems and markets. We use machine learning to combine outputs from numerical weather prediction models with local observations. The former provide valuable information on higher scales dynamics while the latter gives the model fresher and location-specific data. So as to make the results usable for practitioners, we focus on well-known methods which can handle a high volume of data. We study first variable selection using both a linear technique and a nonlinear one. Then we exploit these results to forecast wind speed and wind power still with an emphasis on linear models versus nonlinear ones. For the wind power prediction, we also compare the indirect approach (wind speed predictions passed through a power curve) and the indirect one (directly predict wind power). (10.1016/j.renene.2023.05.005)
  DOI : 10.1016/j.renene.2023.05.005
• Error estimates of a theta-scheme for second-order mean field games
  
  • Bonnans Joseph Frédéric
  • Liu Kang
  • Pfeiffer Laurent
  ESAIM: Mathematical Modelling and Numerical Analysis, Société de Mathématiques Appliquées et Industrielles (SMAI) / EDP, 2023, 57 (4), pp.2493-2528. We introduce and analyze a new finite-difference scheme, relying on the theta-method, for solving monotone second-order mean field games. These games consist of a coupled system of the Fokker–Planck and the Hamilton–Jacobi–Bellman equation. The theta-method is used for discretizing the diffusion terms: we approximate them with a convex combination of an implicit and an explicit term. On contrast, we use an explicit centered scheme for the first-order terms. Assuming that the running cost is strongly convex and regular, we first prove the monotonicity and the stability of our thetascheme, under a CFL condition. Taking advantage of the regularity of the solution of the continuous problem, we estimate the consistency error of the theta-scheme. Our main result is a convergence rate of order O(hr) for the theta-scheme, where ℎ is the step length of the space variable and r ∈ (0, 1) is related to the Hölder continuity of the solution of the continuous problem and some of its derivatives. (10.1051/m2an/2023059)
  DOI : 10.1051/m2an/2023059
• A second-order accurate numerical scheme for a time-fractional Fokker–Planck equation
  
  • Mustapha Kassem
  • Knio Omar
  • Le Maître Olivier
  IMA Journal of Numerical Analysis, Oxford University Press (OUP), 2023. Abstract A second-order accurate time-stepping scheme for solving a time-fractional Fokker–Planck equation of order $\alpha \in (0, 1)$, with a general driving force, is investigated. A stability bound for the semidiscrete solution is obtained for $\alpha \in (1/2,1)$ via a novel and concise approach. Our stability estimate is $\alpha $-robust in the sense that it remains valid in the limiting case where $\alpha $ approaches $1$ (when the model reduces to the classical Fokker–Planck equation), a limit that presents practical importance. Concerning the error analysis, we obtain an optimal second-order accurate estimate for $\alpha \in (1/2,1)$. A time-graded mesh is used to compensate for the singular behavior of the continuous solution near the origin. The time-stepping scheme scheme is associated with a standard spatial Galerkin finite element discretization to numerically support our theoretical contributions. We employ the resulting fully discrete computable numerical scheme to perform some numerical tests. These tests suggest that the imposed time-graded meshes assumption could be further relaxed, and we observe second-order accuracy even for the case $\alpha \in (0,1/2]$, that is, outside the range covered by the theory. (10.1093/imanum/drac031)
  DOI : 10.1093/imanum/drac031
• Analysis of Stochastic Algorithms for Sampling and Riemannian Approximation
  
  • Jiménez Pablo
  , 2023. This thesis deals with the analysis of two stochastic algorithms: stochastic approximation on Riemannian manifolds and a Markov chain Monte Carlo method. For both algorithms, we extend the existing theory for a better understanding of the efficiency of these methods. In a first part, we focus on two frameworks for stochastic approximation on Riemannian manifolds. On the one hand, we examine the rate of convergence, by proving non-asymptotic bounds with weaker assumptions than before, as well as with a more flexible set of assumptions for the the noise. On the other hand, we take a close look at the the constant step-size case, in which we are interested in the convergence of the the stationary law of the Markov chain defined by the stochastic scheme. We perform an asymptotic decomposition with a bias-variance equilibrium, and a central limit theorem. We provide applications of our results on classical examples of Riemannian stochastic approximation. In a second part, we focus on the high dimensional behavior of a Markov chain Monte Carlo method which approximates the target distribution smoothly, in order to use its gradient to accelerate convergence. In the classical context of optimal scaling, we find behaviors similar to the existing theory for smooth distributions but new ones for distributions with a discontinuity in their derivative. We illustrate these results with simulations.
• Large population limit for a multilayer SIR model including households and workplaces
  
  • Kubasch Madeleine
  , 2023.
• Generalizing a causal effect from a trial to a target population : methodological and theoretical contributions
  
  • Colnet Bénédicte
  , 2023. Modern evidence-based medicine places Randomized Controlled Trials (RCTs) at the forefront of clinical evidence. Randomization enables the estimation of the average treatment effect (ATE) by eliminating the confounding effects of spurious or unwanted associated factors.More recently, concerns have been raised on the limited scope of RCTs: stringent eligibility criteria, unrealistic real-world compliance, short timeframe, limited sample size, etc. All these possible limitations threaten the external validity of RCT studies to other situations or populations.The usage of complementary non-randomized data, referred to as observational or from the real world, brings promises as additional sources of evidence.Today, there is a growing incentive to rely on these new data, which is also endorsed by health authorities such as the Food and Drug Administration (FDA) in the U.S. and the Haute Autorité de la Santé (HAS) in France.Combining both data types -- randomized and observational -- is a new venue that could make the most of both worlds.First, this thesis proposes a review of all the existing methods combining several data types to build clinical evidence. Then, the thesis is focused on improving the external validity of RCTs.In other words, how can we use representative sample of the target population of interest to re-weigh} or to generalize the trial's findings?Such methods are quite recent and have been proposed in the early 2010's.This thesis investigates theoretical properties of these methods, such as finite and large sample properties (bias and variance) of the estimation, which helps to provide practical guidelines about covariates selection and the impact of both samples' sizes. This thesis also proposes a sensitivity analysis when covariates are either partially or totally unobserved.Most -- if not all -- current statistical works concern the generalization of the effect on the scale of the absolute difference, while our clinicians collaborators pointed to us the need to encompass several causal measures (e.g. ratio, odds ratio, number needed to treat).Therefore, this thesis also opens the door to the generalization of all causal measures of interest. Doing so, we link generalization with a rather old concerns of causality, namely collapsibility of a measure. We also propose a new framing to apprehend heterogeneity of a treatment effect. Finally, it turns out that assumptions required for generalization depends on the nature of the outcome and the causal measure of interest.All our research questions are motivated by clinical applications, and in particular by the Traumabase consortium.
• Some application of machine learning in quantitative finance : model calibration, volatility formation mechanism and news screening
  
  • Zhang Jianfei
  , 2023. We begin this thesis in Chapter I by introducing our deep learning-based methodologies for efficient calibration of the quadratic rough Heston model, which is non-Markovian and non-semimartingale. A multi-factor approximation of the model is first proposed. Two deep neural networks are then trained on simulated data to learn the resulting pricing functions of SPX and VIX options respectively. Given SPX/VIX smiles, joint calibration results can be instantaneously obtained. Empirical tests show that the calibrated model can reproduce both SPX and VIX implied volatility surfaces very well. Through the application of automatic adjoint differentiation, the neural networks can be used to compute efficiently related hedging quantities.Under quadratic rough Heston, we then formulate an optimal market making problem on a basket composed of multiple derivatives of SPX, such as SPX and VIX futures, SPX and VIX options. The market maker maximizes its profit from spread capturing and penalizes the portfolio's inventory risk, which can be mostly explained by the variation of SPX. We tackle the high dimensionality of the problem with several relevant approximations. Closed-form asymptotic solutions can then be obtained.Motivated by the widely established fact that volatility is rough across many asset classes and the promising results of the quadratic rough Heston model thanks to the incorporation of the Zumbach effect, we are interested in the universality of the endogenous volatility formation mechanism in Chapter III. We take first a quasi-nonparametric approach. An LSTM network trained on a pooled dataset covering hundreds of liquid stocks shows superior volatility forecasting performance than other asset-specific or sector-specific devices, suggesting the existence of the universality in question. We propose then a parsimonious parametric forecasting method combining the main features of the rough fractional stochastic volatility and quadratic rough Heston models. With fixed parameters, this approach presents the same level of performance as the universal LSTM, confirming again the universality from a parametric perspective.Finally, we focus on the link between informative news releases and switches of intraday liquidity conditions. Particularly, by detecting significant jumps of volatility and trading volumes inside daily trading sessions, we propose a systematic approach to distinguish impactful news releases from the massively presented neutral ones. A news sentiment predictor fitted on the identified impactful data is shown to be much more effective than the one calibrated on the raw dataset in terms of short-term price movement prediction for the associated assets.
• Unbalanced CO-Optimal Transport
  
  • Tran Quang Huy
  • Janati Hicham
  • Courty Nicolas
  • Flamary Rémi
  • Redko Ievgen
  • Demetci Pinar
  • Singh Ritambhara
  Proceedings of the AAAI Conference on Artificial Intelligence, Association for the Advancement of Artificial Intelligence, 2023, 37 (8), pp.10006-10016. Optimal transport (OT) compares probability distributions by computing a meaningful alignment between their samples. COoptimal transport (COOT) takes this comparison further by inferring an alignment between features as well. While this approach leads to better alignments and generalizes both OT and Gromov-Wasserstein distances, we provide a theoretical result showing that it is sensitive to outliers that are omnipresent in real-world data. This prompts us to propose unbalanced COOT for which we provably show its robustness to noise in the compared datasets. To the best of our knowledge, this is the first such result for OT methods in incomparable spaces. With this result in hand, we provide empirical evidence of this robustness for the challenging tasks of heterogeneous domain adaptation with and without varying proportions of classes and simultaneous alignment of samples and features across single-cell measurements. (10.1609/aaai.v37i8.26193)
  DOI : 10.1609/aaai.v37i8.26193
• Estimation of extreme quantiles from heavy-tailed distributions with neural networks
  
  • Allouche Michaël
  • Girard Stéphane
  • Gobet Emmanuel
  , 2023. New parametrizations for neural networks are proposed in order to estimate extreme quantiles in both non-conditional and conditional heavy-tailed settings. All proposed neural network estimators feature a bias correction based on an extension of the usual second-order condition to an arbitrary order. The convergence rate of the uniform error between extreme log-quantiles and their neural network approximation is established. The finite sample performances of the non-conditional neural network estimator are compared to other bias-reduced extreme-value competitors on simulated data. It is shown that our method outperforms them in difficult heavy-tailed situations where other estimators almost all fail. The source code is available at github. Finally, conditional neural network estimators are implemented to investigate the behaviour of extreme rainfalls as functions of their geographical location in the southern part of France.
• Novel Framework for the Robust Optimization of the Heat Flux Distribution for an Electro-Thermal Ice Protection System and Airfoil Performance Analysis
  
  • Gallia Mariachiara
  • Guardone Alberto
  • Congedo Pietro Marco
  , 2023. <div><div>We present a framework for the robust optimization of the heat flux distribution for an anti-ice electro-thermal ice protection system (AI-ETIPS) and iced airfoil performance analysis under uncertain conditions. The considered uncertainty regards a lack of knowledge concerning the characteristics of the cloud i.e. the liquid water content and the median volume diameter of water droplets, and the accuracy of measuring devices i.e., the static temperature probe, uncertain parameters are modeled as uniform random variables. A forward uncertainty propagation analysis is carried out using a Monte Carlo approach. The optimization framework relies on a gradient-free algorithm (Mesh Adaptive Direct Search) and three different problem formulations are considered in this work. Two bi-objective deterministic optimizations aim to minimize power consumption and either minimize ice formations or the iced airfoil drag coefficient. A robust optimization formulation was also considered aiming to maximize the statistical frequency of the fully evaporative operating regime for fixed power consumption. The framework is applied to a reference test case, revealing the potential to improve the evaporation efficiency of the baseline design, increasing flight safety even at non-nominal conditions. We also conducted a preliminary examination of the impact of run-back ice formations on airfoil performance during a brief ice encounter in uncertain cloud conditions to understand how the rate of ice accretion relates to an airfoil performance metric, such as the drag coefficient. The analysis found that reducing the rate of ice build-up may not necessarily diminish the detrimental effects on aerodynamic performance, except when the rate is very low. Further studies are ongoing to explore airfoil performance degradation in more detail and to reduce the optimization framework computational cost.</div></div> (10.4271/2023-01-1392)
  DOI : 10.4271/2023-01-1392