Publications

2022

• The epidemic footprint of contact structures with several levels of mixing
  
  • Kubasch Madeleine
  • Bansaye Vincent
  • Deslandes François
  • Vergu Elisabeta
  , 2022.
• Dealing with multi-currency inventory risk in FX cash markets
  
  • Barzykin Alexander
  • Bergault Philippe
  • Guéant Olivier
  , 2022. In FX cash markets, market makers provide liquidity to clients for a wide variety of currency pairs. Because of flow uncertainty and market volatility, they face inventory risk. To mitigate this risk, they typically skew their prices to attract or divert the flow and trade with their peers on the dealer-to-dealer segment of the market for hedging purposes. This paper offers a mathematical framework to FX dealers willing to maximize their expected profit while controlling their inventory risk. Approximation techniques are proposed which make the framework scalable to any number of currency pairs.
• Algorithmic market making in dealer markets with hedging and market impact
  
  • Barzykin Alexander
  • Bergault Philippe
  • Guéant Olivier
  , 2022. In dealer markets, dealers provide prices at which they agree to buy and sell the assets and securities they have in their scope. With ever increasing trading volume, this quoting task has to be done algorithmically in most markets such as foreign exchange markets or corporate bond markets. Over the last ten years, many mathematical models have been designed that can be the basis of quoting algorithms in dealer markets. Nevertheless, in most (if not all) models, the dealer is a pure internalizer, setting quotes and waiting for clients. However, on many dealer markets, dealers also have access to an inter-dealer market or even public trading venues where they can hedge part of their inventory. In this paper, we propose a model taking this possibility into account, therefore allowing dealers to externalize part of their risk. The model displays an important feature well known to practitioners that within a certain inventory range the dealer internalizes the flow by appropriately adjusting the quotes and starts externalizing outside of that range. The larger the franchise, the wider is the inventory range suitable for pure internalization. The model is illustrated numerically with realistic parameters for USDCNH spot market.
• Phase retrieval and phaseless inverse scattering with background information
  
  • Hohage Thorsten
  • Novikov Roman
  • Sivkin Vladimir
  , 2022. We consider the problem of finding a compactly supported potential in the multidimensional Schrödinger equation from its differential scattering cross section (squared modulus of the scattering amplitude) at fixed energy. In the Born approximation this problem simplifies to the phase retrieval problem of reconstructing the potential from the absolute value of its Fourier transform on a ball. To compensate for the missing phase information we use the method of a priori known background scatterers. In particular, we propose an iterative scheme for finding the potential from measurements of a single differential scattering cross section corresponding to the sum of the unknown potential and a known background potential, which is sufficiently disjoint. If this condition is relaxed, then we give similar results for finding the potential from additional monochromatic measurements of the differential scattering cross section of the unknown potential without the background potential. The performance of the proposed algorithms is demonstrated in numerical examples.
• Market making by an FX dealer: tiers, pricing ladders and hedging rates for optimal risk control
  
  • Barzykin Alexander
  • Bergault Philippe
  • Guéant Olivier
  , 2022. Dealers make money by providing liquidity to clients but face flow uncertainty and thus price risk. They can efficiently skew their prices and wait for clients to mitigate risk (internalization), or trade with other dealers in the open market to hedge their position and reduce their inventory (externalization). Of course, the better control associated with externalization comes with transaction costs and market impact. The internalization vs. externalization dilemma has been a topic of recent active discussion within the foreign exchange (FX) community. This paper offers an optimal control framework for market making tackling both pricing and hedging, thus answering a question well known to dealers: `to hedge, or not to hedge?
• Stationary martingale solution for the 2D stochastic Gross-Pitaevskii equation
  
  • de Bouard Anne
  • Debussche Arnaud
  • Fukuizumi Reika
  , 2022. In this short report we give a proof of the existence of a stationary solution to the Gross-Pitaevskii equation in $2d$ driven by a space-time white noise.
• Uncertainty quantification methodology for seismic fragility curves of mechanical structures : Application to a piping system of a nuclear power plant
  
  • Gauchy Clément
  , 2022. Nuclear power plants are complex engineering systems for which reliability has to be guaranteed during its operational lifetime due to the hugely negative consequences provoked by nuclear accidents to human health or to the environment. The effects of natural hazards such as earthquakes on these facilities are included in the risk analysis but are difficult to estimate because of their randomness. Since the 1980s, a probabilistic seismic risk assessment framework has been developed to evaluate the reliability of structures, systems and components (SSC) of nuclear facilities against seismic risk. This framework is relying on a specific quantity of interest: the seismic fragility curve. At the scale of these facilities, these curves represent the conditional probabilities of failure of the SSCs given a scalar value derived from a seismic loading indicating its "strength" and which is called seismic intensity measure. The management of the various sources of uncertainty inherent to the problem to be addressed is often divided into two categories: (i) the so-called random uncertainties that arise from the natural variability of physical phenomena that are difficult to measure or control, and (ii) the so-called epistemic uncertainties that are associated with the lack of knowledge of the system under study and that can be reduced, in the short term, by means of experimental campaigns for example. In seismic probabilistic risk assessment studies for the nuclear industry, the main source of random uncertainty is the seismic loading and the sources of epistemic uncertainties are attributed to the mechanical parameters of the structure considered. In this framework, this thesis aims at understanding the effect of epistemic uncertainties on a seismic fragility curve by using an uncertainty quantification methodology. However, as numerical mechanical models are often computationally expensive, a metamodeling step, based on Gaussian process regression, is proposed. In practice, the sources of epistemic uncertainties are first modeled using a probabilistic framework. After establishing a Gaussian process metamodel of the numerical mechanical model, they are then propagated through the surrogate model. The propagation of epistemic uncertainties as well as the sensitivity analysis are then carried out on the seismic fragility curve via the metamodel, using a reduced number of calls to the mechanical computer code. This methodology thus allows both propagating and ranking the most influential epistemic sources of uncertainty on the fragility curve itself, at a reduced numerical cost. In addition, several procedures for planning numerical experiments are proposed to lighten the computational load, while ensuring the best possible estimation accuracy on the seismic fragility curve. The methodologies presented in this thesis are finally tested and evaluated on an industrial test case from the nuclear industry, namely a section of piping equipping French pressurized water reactors.
• Internal Energy Relaxation Processes and Bulk Viscosities in Fluids
  
  • Bruno Domenico
  • Giovangigli Vincent
  , 2022. We revisit internal energy relaxation processes and related bulk viscosity coefficients in fluid models derived from the kinetic theory. We discuss the apparition of bulk viscosity coefficients in relaxation regimes and the links with equilibrium one-temperature bulk viscosity coefficients. Multiple temperature models of single species fluids are investigated as well as state-to-state models for mixtures of gases. Monte Carlo numerical simulations of internal energy relaxation processes in polyatomic gases are shown to fully agree with the theoretical results. The impact of bulk viscosity in fluid mechanics is also addressed as well as various mathematical aspects of internal energy relaxation and Chapman-Enskog asymptotic expansion for a two-temperature fluid model.
• Stochastic calibration of a carbon nitridation model from plasma wind tunnel experiments using a Bayesian formulation
  
  • del Val Anabel
  • Le Maitre Olivier
  • Congedo Pietro Marco
  • Magin Thierry E.
  Carbon, Elsevier, 2022, 200. In this work, we calibrate a carbon nitridation model for a broad span of surface temperatures from existing plasma wind tunnel measurements by accounting for experimental and parametric uncertainties. A chemical non-equilibrium stagnation line model is proposed to simulate the experiments and obtain recession rates and CN densities, the measured model outputs. First, we establish the influence of the experimental boundary conditions and nitridation parameters on the simulated observations through a sensitivity analysis. Results show that such quantities are mostly affected by the efficiency of nitridation reactions at the gas-surface interface. We then perform model calibrations for each experimental condition and compare them based on the experimental data used. This allows us to check the consistency of the experimental dataset. Using only the trustworthy experimental data, we perform a calibration of Arrhenius law parameters for nitridation efficiencies considering all available experimental conditions jointly, allowing us to compute nitridation efficiencies even for surface temperatures for which there are no reliable experimental data available. The stochastic Arrhenius law agrees well with most of the data in the literature. This result constitutes the first nitridation model extracted from plasma wind tunnel experiments with accurate uncertainty estimates. (10.1016/j.carbon.2022.07.069)
  DOI : 10.1016/j.carbon.2022.07.069
• A Proximal Markov Chain Monte Carlo Method for Bayesian Inference in Imaging Inverse Problems: When Langevin Meets Moreau
  
  • Durmus Alain
  • Moulines Éric
  • Pereyra Marcelo
  SIAM Review, Society for Industrial and Applied Mathematics, 2022, 64 (4), pp.991-1028. (10.1137/22M1522917)
  DOI : 10.1137/22M1522917
• McKean–Vlasov Optimal Control: Limit Theory and Equivalence Between Different Formulations
  
  • Djete Mao Fabrice
  • Possamaï Dylan
  • Tan Xiaolu
  Mathematics of Operations Research, INFORMS, 2022, 47 (4), pp.2891-2930. We study a McKean–Vlasov optimal control problem with common noise in order to establish the corresponding limit theory as well as the equivalence between different formulations, including strong, weak, and relaxed formulations. In contrast to the strong formulation, in which the problem is formulated on a fixed probability space equipped with two Brownian filtrations, the weak formulation is obtained by considering a more general probability space with two filtrations satisfying an (H)-hypothesis type condition from the theory of enlargement of filtrations. When the common noise is uncontrolled, our relaxed formulation is obtained by considering a suitable controlled martingale problem. As for classic optimal control problems, we prove that the set of all relaxed controls is the closure of the set of all strong controls when considered as probability measures on the canonical space. Consequently, we obtain the equivalence of the different formulations of the control problem under additional mild regularity conditions on the reward functions. This is also a crucial technical step to prove the limit theory of the McKean–Vlasov control problem, that is, proving that it consists in the limit of a large population control problem with common noise. (10.1287/moor.2021.1232)
  DOI : 10.1287/moor.2021.1232
• Interior point methods are not worse than Simplex
  
  • Allamigeon Xavier
  • Dadush Daniel
  • Loho Georg
  • Natura Bento
  • Vegh Laszlo
  , 2022, pp.267-277. We develop a new interior point method for solving linear programs. Our algorithm is universal in the sense that it matches the number of iterations of any interior point method that uses a self-concordant barrier function up to a factor O(n1.5 log n) for an n-variable linear program in standard form. The running time bounds of interior point methods depend on bit-complexity or condition measures that can be unbounded in the problem dimension. This is in contrast with the simplex method that always admits an exponential bound. Our algorithm also admits a combinatorial upper bound, terminating with an exact solution in O(2n n1.5 log n) iterations. This complements previous work by Allamigeon, Benchimol, Gaubert, and Joswig (SIAGA 2018) that exhibited a family of instances where any path-following method must take exponentially many iterations. (10.1109/FOCS54457.2022.00032)
  DOI : 10.1109/FOCS54457.2022.00032
• A comparative study of polynomial-type chaos expansions for indicator functions
  
  • Bourgey Florian
  • Gobet Emmanuel
  • Rey Clément
  SIAM/ASA Journal on Uncertainty Quantification, ASA, American Statistical Association, 2022, 10 (4), pp.1350-1383. We propose a thorough comparison of polynomial chaos expansion (PCE) for indicator functions of the form 1 c≤X for some threshold parameter c ∈ R and a random variable X associated with classical orthogonal polynomials. We provide tight global and localized L2 estimates for the resulting truncation of the PCE and numerical experiments support the tightness of the error estimates. We also compare the theoretical and numerical accuracy of PCE when extra quantile/probability transforms are applied, revealing different optimal choices according to the value of c in the center and the tails of the distribution of X. (10.1137/21M1413146)
  DOI : 10.1137/21M1413146
• High accuracy analysis of adaptive multiresolution-based lattice Boltzmann schemes via the equivalent equations
  
  • Bellotti Thomas
  • Gouarin Loïc
  • Graille Benjamin
  • Massot Marc
  SMAI Journal of Computational Mathematics, Société de Mathématiques Appliquées et Industrielles (SMAI), 2022, 8, pp.161-199. Multiresolution provides a fundamental tool based on the wavelet theory to build adaptive numerical schemes for Partial Differential Equations and time-adaptive meshes, allowing for error control. We have introduced this strategy before to construct adaptive lattice Boltzmann methods with this interesting feature.Furthermore, these schemes allow for an effective memory compression of the solution when spatially localized phenomena -- such as shocks or fronts -- are involved, to rely on the original scheme without any manipulation at the finest level of grid and to reach a high level of accuracy on the solution. Nevertheless, the peculiar way of modeling the desired physical phenomena in the lattice Boltzmann schemes calls, besides the possibility of controlling the error introduced by the mesh adaptation, for a deeper and more precise understanding of how mesh adaptation alters the physics approximated by the numerical strategy. In this contribution, this issue is studied by performing the equivalent equations analysis of the adaptive method after writing the scheme under an adapted formalism. It provides an essential tool to master the perturbations introduced by the adaptive numerical strategy, which can thus be devised to preserve the desired features of the reference scheme at a high order of accuracy. The theoretical considerations are corroborated by numerical experiments in both the 1D and 2D context, showing the relevance of the analysis. In particular, we show that our numerical method outperforms traditional approaches, whether or not the solution of the reference scheme converges to the solution of the target equation. Furthermore, we discuss the influence of various collision strategies for non-linear problems, showing that they have only a marginal impact on the quality of the solution, thus further assessing the proposed strategy. (10.5802/smai-jcm.83)
  DOI : 10.5802/smai-jcm.83
• Newton method for stochastic control problems
  
  • Gobet Emmanuel
  • Grangereau Maxime
  SIAM Journal on Control and Optimization, Society for Industrial and Applied Mathematics, 2022, 60 (5), pp.2996-3025. We develop a new iterative method based on Pontryagin principle to solve stochastic control problems. This method is nothing else than the Newton method extended to the framework of stochastic controls, where the state dynamics is given by an ODE with stochastic coefficients. Each iteration of the method is made of two ingredients: computing the Newton direction, and finding an adapted step length. The Newton direction is obtained by solving an affine-linear Forward-Backward Stochastic Differential Equation (FBSDE) with random coefficients. This is done in the setting of a general filtration. We prove that solving such an FBSDE reduces to solving a Riccati Backward Stochastic Differential Equation (BSDE) and an affine-linear BSDE, as expected in the framework of linear FBSDEs or Linear-Quadratic stochastic control problems. We then establish convergence results for this Newton method. In particular, sufficient regularity of the second-order derivative of the cost functional is required to obtain (local) quadratic convergence. A restriction to the space of essentially bounded stochastic processes is needed to obtain such regularity. To choose an appropriate step length while fitting our choice of space of processes, an adapted backtracking line-search method is developed. We then prove global convergence of the Newton method with the proposed line-search procedure, which occurs at a quadratic rate after finitely many iterations. An implementation with regression techniques to solve BSDEs arising in the computation of the Newton step is developed. We apply it to the control problem of a large number of batteries providing ancillary services to an electricity network. (10.1137/21M1408567)
  DOI : 10.1137/21M1408567
• Quantification of model-form uncertainties affecting the calibration of a carbon nitridation model by means of Bayesian Model Averaging
  
  • del Val Anabel
  • Magin Thierry
  • Congedo Pietro Marco
  International Journal of Heat and Mass Transfer, Elsevier, 2022, 213, pp.124271. Severe epistemic uncertainties not only can affect the prescription of parameters within a given model but also the choice of models we make to interpret and infer from experimental data. In this work, we incorporate experimental, parametric and model-form uncertainties in the calibration of a carbon nitridation model. The model-form uncertainties considered stem from the different modeling choices that are taken as valid representations of a set of plasma wind tunnel experiments. To this end, we define a Bayesian model averaging strategy where the marginal posteriors of the nitridation reaction efficiencies are weighted by the marginalized likelihoods of the experimental data for each proposed model. First, Bayes factors are computed to possibly discard invalid models. The baseline model, a thermal equilibrium stagnation line flow with nitridation as only surface reaction, performs as well as all the alternative models proposed, which range from adding surface recombination reactions to considering thermal non-equilibrium in the gas and gas-surface interface. The presence of nitrogen recombination reactions is shown to broaden the support of the nitridation marginal posteriors considerably, allowing it to take on larger values. Lastly, a Bayesian model averaged Arrhenius law for the nitridation efficiencies is computed for a range of surface temperatures. (10.1016/j.ijheatmasstransfer.2023.124271)
  DOI : 10.1016/j.ijheatmasstransfer.2023.124271
• Algorithmes de couplage entre neutronique, thermohydraulique et thermique.
  
  • Delvaux Robin
  , 2022. L'idée générale motivant la représentation multiphysique d'un système quelconque est de décrire son état de la manière la plus fidèle possible. Cela passe par la prise en compte des dépendances et contre-réactions existantes entre les différentes disciplines physiques en jeu : ces dernières sont en effet généralement traitées de manière découplée. Cette approche, centrée sur un seul problème physique, introduit des simplifications dans les modélisations et peut limiter la représentativité des résultats obtenus. En physique des réacteurs, l'objectif de ce type de simulations multiphysiques est avant tout d'améliorer la précision des études de sûreté qui sont effectuées au Commissariat à l'énergie atomique et aux énergies alternatives (CEA) ou par EDF par exemple. Concrètement, la mise en place de modélisations multiphysiques doit permettre d'augmenter leur précision ainsi que la confiance placée dans leurs résultats, autorisant ainsi à choisir des marges de sûreté moins contraignantes que celles, conservatives, obtenues à partir de modélisations simplifiées. Il s'agit par exemple de rendre compte des aspects neutroniques, thermohydraulique et thermomécanique d'un cœur de réacteur.L'approche la plus simple pour réaliser ce type de modélisation consiste à faire communiquer des solveurs monophysiques distincts et préexistants, chacun rendant compte d'une partie du problème global. On parle alors de couplage en boîtes noires. Ce type de simulations souffre de limitations en termes de stabilité et de robustesse. Par ailleurs, elles s'accompagnent généralement de temps de calcul importants.L'objectif de cette thèse est d'explorer les méthodes de couplage envisageables entre des solveurs de neutronique et de thermohydraulique, dans le cadre de la modélisation de l'état stationnaire d'un cœur de réacteur à eau pressurisée. Une attention particulière est portée à la généricité des algorithmes de couplage étudiés. On s'intéresse également à leur capacité à accélérer la convergence du problème multiphysique ainsi qu'à minimiser le nombre d'itérations monophysiques effectuées par chacun des solveurs.Après une introduction aux différentes physiques rentrant en jeu dans la description d'un cœur de réacteur ainsi qu'une présentation des algorithmes de couplage usuels entre neutronique, thermohydraulique et thermique, on s'intéresse dans un premier temps à l'optimisation d'un couplage en boîtes noires entre le solveur de neutronique, Apollo3®, et le solveur de thermohydraulique et thermique, Thedi. L'intérêt de la convergence partielle et des méthodes de type Residual Balance pour limiter le temps de calcul total est prouvé. On propose une nouvelle variante de l'Adaptive Residual Balance, la méthode du Dynamic Residual Balance, qui ne nécessite pas d'étape d'optimisation préalable pour garantir son efficacité. On a ensuite implémenté l'accélération d'Anderson dans le solveur neutronique pour accélérer sa convergence. Cela rend envisageable la mise en place de couplages avec convergence fine. Finalement, on a proposé une approche de couplage hybride, plus intrusive, permettant de garantir la cohérence physique entre les différents champs physiques intervenants dans ce problème multiphysique. Cela se traduit par un gain en termes de vitesses de convergence multiphysique et monophysique par rapport aux couplages en boîtes noires.Dans la dernière partie de cette thèse, on cherche à expliquer les différences en termes de vitesses de convergence observées selon la méthode de couplage retenue. On s'intéresse pour cela au cas analytique d'une plaque infinie en une dimension. Cela nous a permis d'apporter des éléments de compréhension quant aux différences observées entre les couplages en boîtes noires et les couplages hybrides. De plus, on a pu démontrer le lien entre convergence partielle du solveur neutronique et introduction d'un facteur de relaxation multiphysique.
• Wasserstein Adversarial Regularization for learning with label noise
  
  • Fatras Kilian
  • Damodaran Bharath Bhushan
  • Lobry Sylvain
  • Flamary Remi
  • Tuia Devis
  • Courty Nicolas
  IEEE Transactions on Pattern Analysis and Machine Intelligence, Institute of Electrical and Electronics Engineers, 2022, 44 (10), pp.7296-7306. (10.1109/TPAMI.2021.3094662)
  DOI : 10.1109/TPAMI.2021.3094662
• Time Series Alignment with Global Invariances
  
  • Vayer Titouan
  • Tavenard Romain
  • Chapel Laetitia
  • Courty Nicolas
  • Flamary Rémi
  • Soullard Yann
  Transactions on Machine Learning Research Journal, [Amherst Massachusetts]: OpenReview.net, 2022, 2022. Multivariate time series are ubiquitous objects in signal processing. Measuring a distance or similarity between two such objects is of prime interest in a variety of applications, including machine learning, but can be very difficult as soon as the temporal dynamics and the representation of the time series, i.e. the nature of the observed quantities, differ from one another. In this work, we propose a novel distance accounting both feature space and temporal variabilities by learning a latent global transformation of the feature space together with a temporal alignment, cast as a joint optimization problem. The versatility of our framework allows for several variants depending on the invariance class at stake. Among other contributions, we define a differentiable loss for time series and present two algorithms for the computation of time series barycenters under this new geometry. We illustrate the interest of our approach on both simulated and real world data and show the robustness of our approach compared to state-of-the-art methods.
• System of radiative transfer equations for coupled surface and body waves
  
  • de Hoop Maarten
  • Garnier Josselin
  • Sølna Knut
  Zeitschrift für Angewandte Mathematik und Physik = Journal of Applied mathematics and physics = Journal de mathématiques et de physique appliquées, Springer Verlag, 2022, 73 (5), pp.177. (10.1007/s00033-022-01813-w)
  DOI : 10.1007/s00033-022-01813-w
• Optimal strokes for the 4-sphere swimmer at low Reynolds number in the regime of small deformations
  
  • Alouges François
  • Lefebvre-Lepot Aline
  • Weder Philipp
  MathematicS In Action, Société de Mathématiques Appliquées et Industrielles (SMAI), 2022, 11, pp.167-192. The paper deals with the optimal control problem that arises when one studies the 4 sphere artificial swimmer at low Reynolds number. Composed of four spheres at the end of extensible arms, the swimmer is known to be able to swim in all directions and orientations in the 3D space. In this paper, optimal strokes, in terms of the energy expended by the swimmer to reach a prescribed net displacement, are fully described in the regime of small strokes. In particular, we introduce a bivector formalism to model the displacements that turns out to be elegant and practical. Numerical simulations are also provided that confirm the theoretical predictions. (10.5802/msia.23)
  DOI : 10.5802/msia.23
• Mean field optimal stopping and approximations of partial differential equations on Wasserstein space
  
  • Talbi Mehdi
  , 2022. This thesis consists in two parts.The first one is concerned with the study of the mean field optimal stopping problem,that is the optimal stopping of a McKean-Vlasov diffusion, when the criterion to optimize is a function of the stopped process. This problem models the situation where a central planner controls a continuous infinity of interacting agents by assigning a stopping time to each of them, in order to optimize some criterion which depends on the distribution of the system.We study this problem via a dynamic programming approach, which allows to characterize its value function by a partial differential equation on the space of probability measures, that we call obstacle problem (or equation) on Wasserstein space by analogy with the classical obstacle problem, which arises in particular in standard optimal stopping. We especially show that, if this equation has a classical solution, then it is equal to the value function of the mean field optimal stopping problem, and that it can be used to characterize optimal stopping policies.We next extend our study to the case where the value function is not necessarily dif- ferentiable. Thus, we introduce a notion of viscosity solution for the obstacle problem on Wasserstein space, for which we prove the properties of consistency with classical solutions, stability and uniqueness.In the second part of the thesis, we are interested in developing approximations for some classes of partial differential equations on the space of probability measures. More precisely, we show that viscosity solutions of these equations can be written as limits of viscosity solutions of equations defined on finite-dimensional spaces.We first focus our study on the case of the obstacle problem on Wasserstein space, for which it turns out that the approximating equation corresponds to the dynamic programming equation associated with the multiple optimal stopping problem, which may be seen as a finite population formulation of the mean field optimal stopping problem.We finally consider a larger class of parabolic equations on Wasserstein space. This class covers in particular the scope of mean field Hamilton-Jacobi-Bellman equations, or the case of equations arising in mean field differential games. We also prove that our results can be extended to the case of path-dependent equations (i.e., when the variables of the solution are not the time and a measure on R^d, but the time and a measure on the space of paths).
• Sparse tree-based initialization for neural networks
  
  • Lutz Patrick
  • Arnould Ludovic
  • Boyer Claire
  • Scornet Erwan
  , 2022. Dedicated neural network (NN) architectures have been designed to handle specific data types (such as CNN for images or RNN for text), which ranks them among state-of-the-art methods for dealing with these data. Unfortunately, no architecture has been found for dealing with tabular data yet, for which tree ensemble methods (tree boosting, random forests) usually show the best predictive performances. In this work, we propose a new sparse initialization technique for (potentially deep) multilayer perceptrons (MLP): we first train a tree-based procedure to detect feature interactions and use the resulting information to initialize the network, which is subsequently trained via standard stochastic gradient strategies. Numerical experiments on several tabular data sets show that this new, simple and easy-to-use method is a solid concurrent, both in terms of generalization capacity and computation time, to default MLP initialization and even to existing complex deep learning solutions. In fact, this wise MLP initialization raises the resulting NN methods to the level of a valid competitor to gradient boosting when dealing with tabular data. Besides, such initializations are able to preserve the sparsity of weights introduced in the first layers of the network through training. This fact suggests that this new initializer operates an implicit regularization during the NN training, and emphasizes that the first layers act as a sparse feature extractor (as for convolutional layers in CNN).
• Statistical Modeling and Inference for Populations of Networks and Longitudinal Data
  
  • Mantoux Clément
  , 2022. The development and massification of medical imaging and clinical followup databases open up new perspectives for understanding complex phenomena such as ageing or neurodegenerative diseases. In particular, brain connectivity, i.e., the study of connections and interactions between brain regions, can now be studied on the scale of a population scale rather than on an individual basis. This framework offers the possibility of better taking into account individual specificities in the development of monitoring tools. In this thesis, we first propose new approaches to model and understand the variability of brain connectivity within a group of subjects. More generally, we are interested in collections of networks where each network describes interactions between the same entities. We rely on the empirical low rank property of the adjacency matrices of these networks to account for their distribution. We propose two approaches, one variational and the other statistical, to account for the heterogeneity of these matrices. In particular, in the second case, we show that a limited number of parameters is sufficient to give a faithful and interpretable description of the variability of brain connectivity. We also show the theoretical consistency and identifiability of our approach. In a second part, we study a longitudinal model for the progression monitoring of Parkinson's disease. In this model, the trajectory of each patient is divided into several pieces that may correspond to the different phases of the disease or of a treatment. We show that it is possible to estimate trajectories consisting of several pieces, and to select the number of breaks best suited to describe the average evolution of the population.
• Boundary conditions for the Boltzmann equation from gas-surface interaction kinetic models
  
  • Aoki Kazuo
  • Giovangigli Vincent
  • Kosuge Shingo
  Physical Review E, American Physical Society (APS), 2022, 106 (3). Boundary conditions for the Boltzmann equation are investigated on the basis of a kinetic model for gassurface interactions. The model takes into account gas and physisorbed molecules interacting with a surface potential and colliding with phonons. The potential field is generated by fixed crystal molecules, and the interaction with phonons represents the fluctuating part of the surface. The interaction layer is assumed to be thinner than the mean free path of the gas and physisorbed molecules, and the phonons are assumed to be at equilibrium. The asymptotic kinetic equation for the inner physisorbate layer is derived and used to investigate gas distribution boundary conditions. To be more specific, a model of the boundary condition for the Boltzmann equation is derived on the basis of an approximate iterative solution of the kinetic equation for the physisorbate layer, and the quality of the model is assessed by detailed numerical simulations, which also clarify the behavior of the molecules in the layer. (10.1103/physreve.106.035306)
  DOI : 10.1103/physreve.106.035306