Gaël Poëtte

• PhD
• Ingénieur chercheur at Atomic Energy and Alternative Energies Commission

Both accelerated and adaptive gradient methods are among state of the art algorithms to train neural networks. The tuning of hyperparameters is needed to make them work efficiently. For classical gradient descent, a general and efficient way to adapt hyperparameters is the Armijo backtracking. The goal of this work is to generalize the Armijo lines...

Recently, many machine learning optimizers have been analysed considering them as the asymptotic limit of some differential equations when the step size goes to zero. In other words, the optimizers can be seen as a finite difference scheme applied to a continuous dynamical system. But the major part of the results in the literature concerns constan...

Getting an efficient neural network can be a very difficult task for engineers and researchers because of the huge number of hyperparameters to tune and their interconnections. To make the tuning step easier and more understandable, this work focuses on probably one of the most important leverage to improve Neural Networks efficiency: the optimizer...

The Equations Of State (EOS) of materials under extreme conditions of temperature and pressure can be experimentally studied, thanks to intense electron beam-target experiments. The latter are powerful tools to probe materials in the warm dense matter regime. At CEA/CESTA, we use the CESAR pulsed generator (1 MV, 300 kA). During an experimental sho...

Tackling new machine learning problems with neural networks always means optimizing numerous hyperparameters that define their structure and strongly impact their performances. In this work, we study the use of goal-oriented sensitivity analysis, based on the Hilbert–Schmidt independence criterion (HSIC), for hyperparameter analysis and optimizatio...

In this paper, we are interested in propagating uncertainties through the linear Boltzmann equation. Such model is intensively used in neutronics, photonics, socio-economics, epidemiology. It is often solved thanks to Monte-Carlo (MC) schemes. MC codes are reliable and accurate but costly and, as a consequence, propagating uncertainties through the...

In this paper, we are interested in the acceleration of numerical simulations. We focus on a hypersonic planetary reentry problem whose simulation involves coupling fluid dynamics and chemical reactions. Simulating chemical reactions takes most of the computational time but, on the other hand, cannot be avoided to obtain accurate predictions. We fa...

Tackling new machine learning problems with neural networks always means optimizing numerous hyperparameters that define their structure and strongly impact their performances. In this work, we study the use of goal-oriented sensitivity analysis, based on the Hilbert-Schmidt Independence Criterion (HSIC), for hyperparameter analysis and optimizatio...

Laser inertial confinement fusion (ICF) now enters the burning plasma regime, the next step is higher energy yield which requires coupling more energy to the target. Laser direct drive achieves improved coupling as there is no hohlraum acting as an intermediary. However, the Mega-joule laser facilities (National Ignition Facility and Laser Mégajoul...

Monte Carlo-generalized Polynomial Chaos (MC-gPC) has already been thoroughly studied in the literature. MC-gPC both builds a gPC based reduced model of a partial differential equation (PDE) of interest and solves it with an intrusive MC scheme in order to propagate uncertainties. This reduced model captures the behavior of the solution of a set of...

In this paper, we are interested in taking into account uncertainties for keff computations in neutronics. More generally, the material of this paper can be applied to propagate uncertainties in eigenvalue/eigenvector computations for the linear Boltzmann equation. In [1], [2], an intrusive MC solver for the gPC based reduced model of the instation...

In this paper, we build wellposed intrusive generalised Polynomial Chaos (gPC) based reduced models for uncertain photonics. We solve the reduced models with a Monte-Carlo (MC) scheme. Care is taken to highlight under which condition a reduced model (gPC based or not) is wellposed. The analysis is carried out thanks to an analogy between the constr...

Tackling new machine learning problems with neural networks always means optimizingnumerous hyperparameters that define their structure and strongly impact their perfor-mances. In this work, we use a robust system conception approach to build explainablehyperparameters optimization. This approach is defined by the research of a parametrizationof a...

In this document, we revisit classical Machine Learning (ML) notions and algorithms underthe point of view of the numerician, i.e. the one who is interested in the resolution of partialdifferential equations (PDEs). The document provides an original and illustrated state-of-the-art of ML errors and ML optimisers. The main aim of the document is to...

Machine Learning (ML) is increasingly used to construct surrogate models for physical simulations. We take advantage of the ability to generate data using numerical simulations programs to train ML models better and achieve accuracy gain with no performance cost. We elaborate a new data sampling scheme based on Taylor approximation to reduce the er...

In the context of supervised learning of a function by a Neural Network (NN), we claim and empirically justify that a NN yields better results when the distribution of the data set focuses on regions where the function to learn is steeper. We first traduce this assumption in a mathematically workable way using Taylor expansion. Then, theoretical de...

In this paper, we present a new implicit Monte-Carlo scheme for photonics. The new solver combines the benefits of both the IMC solver of Fleck & Cummings and the SMC solver of Ahrens & Larsen. It is implicit hence allows taking affordable time steps (as IMC) and has no teleportation error (as SMC). The paper also provides some original analysis of...

Monte Carlo (MC) schemes for photonics have been intensively studied throughout the past decades. The recent ISMC scheme presents many advantages (no teleportation error, converging behavior with respect to the spatial and time discretisations). But it is rather different from the IMC one (it is based on a different linearization and needs a slight...

In this paper, we consider the linear Boltzmann equation subject to uncertainties in the initial conditions and matter parameters (cross-sections/opacities). In order to solve the underlying uncertain systems, we rely on moment theory and the construction of hierarchical moment models in the framework of parametric polynomial approximations. Such m...

My HDR (Habilitation à Diriger des Recherches) memoir

In this paper, we consider the linear Boltzmann equation subject to uncertainties in the initial conditions and matter parameters (cross-sections/opacities). In order to solve the underlying uncertain systems, we rely on moment theory and the construction of hierarchical moment models in the framework of parametric polynomial approximations. Such m...

In this paper, we are interested in the resolution of the time-dependent problem of particle transport in a media whose composition is uncertain. The most common resolution strategy consists of running, at prescribed points in uncertain space (at experimental designs points), a simulation device as a black-box. This ensures performing the uncertain...

In this paper, we are interested in the resolution of the time-dependent problem of particle transport in a medium whose composition evolves with time due to interactions. As a constraint, we want to use of Monte-Carlo (MC) scheme for the transport phase. A common resolution strategy consists in a splitting between the MC/transport phase and the ti...

In this paper, we perform the numerical analysis of a new moment/generalized polynomial chaos (gPC) based approximation method under finite numerical integration. The paper addresses the impact of this constraint on the method, in particular analyzing the interplay between aliasing and truncation errors, depending on the type of functional to be re...

Various works from the literature aimed at accelerating Bayesian inference in inverse problems. Stochastic spectral methods have been recently proposed as surrogate approximations of the forward uncertainty propagation model over the support of the prior distribution. These representations are efficient because they allow affordable simulation of a...

This paper deals with High Performance Computing (HPC) applied to neutron transport theory on complex geometries, thanks to both an Adaptive Mesh Refinement (AMR) algorithm and a Monte-Carlo (MC) solver. Several Parallelism models are presented and analyzed in this context, among them shared memory and distributed memory ones such as Domain Replica...

In this paper, we consider hyperbolic systems of conservation laws subject to uncertainties in the initial conditions and model parameters. In order to solve the underlying uncertain systems, we rely on moment theory and the construction of a moment model in the framework of parametric polynomial approximations. We prove the spectral convergence of...

In this paper, we consider hyperbolic systems of conservation laws subject to uncertainties in the initial conditions and model parameters. In order to solve the underlying uncertain systems, we rely on moment theory and the construction of a moment model in the framework of parametric polynomial approximations. We prove the spectral convergence of...

In this paper, we propose a new iterative formulation improving the convergence of standard non intrusive stochastic spectral method for uncertainty quantification. We demonstrate that the method is more accurate than the classical approach with the same level of approximation and at no significant additional computational or memory cost, since it...

We propose a stochastic approach for calibration of mixing zone lengths in shock tube experiments. The methodology relies on taking into account uncertain initial data propagated through the basic multifluid Euler equations. In this work, the initial interface position is supposed uncertain, modeled by a stochastic process. The size of the mixing z...

The application of the stochastic Galerkin-generalized Polynomial Chaos approach (sG-gPC) (Wiener, Am. J. Math. 60:897–936, 1938; Cameron and Martin, Ann. Math. 48:385–392, 1947; Xiu and Karniadakis, SIAM J. Sci. Comp. 24(2):619–644, 2002) for Uncertainty Propagation through NonLinear Systems of Conservation Laws (SLC) is known to encounter several...

To treat uncertain interface position is an important issue for complex applications. In this paper, we address the characterization of randomly perturbed interfaces between fluids thanks to stochastic modeling and uncertainty quantification through the 2D Euler system. The perturbed interface is modeled as a random field and represented by a Karhu...

The treatment of uncertain interface positions in complex simulations and the propagation of the latter uncertainty through complex systems is an important issue. In this paper, we tackle the characterization of perturbed interfaces between fluids thanks to stochastic modelization and the propagation of the initial uncertainty through the Euler sys...

Uncertainty quantification through stochastic spectral methods has been recently applied to several kinds of non-linear stochastic PDEs. In this paper, we introduce a formalism based on kinetic theory to tackle uncertain hyperbolic systems of conservation laws with Polynomial Chaos (PC) methods. The idea is to introduce a new variable, the entropic...

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