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Fossà, Alberto. "Propagation multi-fidélité d’incertitude orbitale en présence d’accélérations stochastiques". Electronic Thesis or Diss., Toulouse, ISAE, 2024. http://www.theses.fr/2024ESAE0009.
Pełny tekst źródłaThe problem of nonlinear uncertainty propagation (UP) is crucial in astrodynamics since all systems of practical interest, ranging from navigation to orbit determination (OD) and target tracking, involve nonlinearities in their dynamics and measurement models. One topic of interest is the accurate propagation of uncertainty through the nonlinear orbital dynamics, a fundamental requirement in several applications such as space surveillance and tracking (SST), space traffic management (STM), and end-of-life (EOL) disposal. Given a finite-dimensional representation of the probability density function (pdf) of the initial state, the main goal is to obtain a similar representation of the state pdf at any future time. This problem has been historically tackled with either linearized methods or Monte Carlo (MC) simulations, both of which are unsuitable to satisfy the demand of a rapidly growing number of applications. Linearized methods are light on computational resources, but cannot handle strong nonlinearities or long propagation windows due to the local validity of the linearization. In contrast, MC methods can handle any kind of nonlinearity, but are too computationally expensive for any task that requires the propagation of several pdfs. Instead, this thesis leverages multifidelity methods and differential algebra (DA) techniques to develop computationally efficient methods for the accurate propagation of uncertainties through nonlinear dynamical systems. The first method, named low-order automatic domain splitting (LOADS), represents the uncertainty with a set of second-order Taylor polynomials and leverages a DA-based measure of nonlinearity to adjust their number based on the local dynamics and the required accuracy. An adaptive Gaussian mixture model (GMM) method is then developed by associating each polynomial to a weighted Gaussian kernel, thus obtaining an analytical representation of the state pdf. Going further, a multifidelity method is proposed to reduce the computational cost of the former algorithms while retaining a similar accuracy. The adaptive GMM method is in this case run on a low-fidelity dynamical model, and only the expected values of the kernels are propagated point-wise in high-fidelity dynamics to compute a posteriori correction of the low-fidelity state pdf. If the former methods deal with the propagation of an initial uncertainty through a deterministic dynamical model, the effects of mismodeled or unmodeled forces are finally considered to further enhance the realism of the propagated statistics. In this case, the multifidelity GMM method is used at first to propagate the initial uncertainty through a low-fidelity, deterministic dynamical model. The point-wise propagations are then replaced with a DA-based algorithm to efficiently propagate a polynomial representation of the moments of the pdf in a stochastic dynamical system. These moments model the effects of stochastic accelerations on the deterministic kernels’ means, and coupled with the former GMM provide a description of the propagated state pdf that accounts for both the uncertainty in the initial state and the effects of neglected forces. The proposed methods are applied to the problem of orbit UP, and their performance is assessed in different orbital regimes. The results demonstrate the effectiveness of these methods in accurately propagating the initial uncertainty and the effects of process noise at a fraction of the computational cost of high-fidelity MC simulations. The LOADS method is then employed to solve the initial orbit determination (IOD) problem by exploiting the information on measurement uncertainty and to develop a preprocessing scheme aimed at improving the robustness of batch OD algorithms. These tools are finally validated on a set of real observations for an object in geostationary transfer orbit (GTO)
Soret, Émilie. "Accélération stochastique dans un gaz de Lorentz inélastique". Thesis, Lille 1, 2015. http://www.theses.fr/2015LIL10054/document.
Pełny tekst źródłaIn this thesis, we study the dynamics of a particle in an inelastic environment composed of scatterer which is commonly known as inelastic Lorentz gas. In the inert case, the environment is not affected by the particle. The kinetic energy of the latter grows with the time and this phenomenon is called « stochastic acceleration ». We approximate the particle's motion by a Markov chain where each step corresponds to a unique collision of the particle with a scatterer. We show that the particle's averaged kinetic energy grows with the time with the exponent 2/5. The result is proved by using probabilistic arguments, bringing into weak convergence theorems of Markov chain as well as the weak convergence of the chain, correctly rescaled in time and space, to a Bessel process.We thus obtain a convergence result for the velocity vector. Under a different rescaling that the one used for the kinetic energy, the latter converges weakly to a spherical brownian motion. In the dynamical case, the evolution of the degrees of freedom of the Lorentz gas is affected by the particle and the dynamical system considered is constitued of the particle and the environment. In such a system, the stochastic acceleration phenomenon cannot be observed. However, we show that the velocity distribution admits a stationnary state
Kulunchakov, Andrei. "Optimisation stochastique pour l'apprentissage machine à grande échelle : réduction de la variance et accélération". Thesis, Université Grenoble Alpes, 2020. http://www.theses.fr/2020GRALM057.
Pełny tekst źródłaA goal of this thesis is to explore several topics in optimization for high-dimensional stochastic problems. The first task is related to various incremental approaches, which rely on exact gradient information, such as SVRG, SAGA, MISO, SDCA. While the minimization of large limit sums of functions was thoroughly analyzed, we suggest in Chapter 2 a new technique, which allows to consider all these methods in a generic fashion and demonstrate their robustness to possible stochastic perturbations in the gradient information.Our technique is based on extending the concept of estimate sequence introduced originally by Yu. Nesterov in order to accelerate deterministic algorithms.Using the finite-sum structure of the problems, we are able to modify the aforementioned algorithms to take into account stochastic perturbations. At the same time, the framework allows to derive naturally new algorithms with the same guarantees as existing incremental methods. Finally, we propose a new accelerated stochastic gradient descent algorithm and a new accelerated SVRG algorithm that is robust to stochastic noise. This acceleration essentially performs the typical deterministic acceleration in the sense of Nesterov, while preserving the optimal variance convergence.Next, we address the problem of generic acceleration in stochastic optimization. For this task, we generalize in Chapter 3 the multi-stage approach called Catalyst, which was originally aimed to accelerate deterministic methods. In order to apply it to stochastic problems, we improve its flexibility on the choice of surrogate functions minimized at each stage. Finally, given an optimization method with mild convergence guarantees for strongly convex problems, our developed multi-stage procedure, accelerates convergence to a noise-dominated region, and then achieves the optimal (up to a logarithmic factor) worst-case convergence depending on the noise variance of the gradients. Thus, we successfully address the acceleration of various stochastic methods, including the variance-reduced approaches considered and generalized in Chapter 2. Again, the developed framework bears similarities with the acceleration performed by Yu. Nesterov using the estimate sequences. In this sense, we try to fill the gap between deterministic and stochastic optimization in terms of Nesterov's acceleration. A side contribution of this chapter is a generic analysis that can handle inexact proximal operators, providing new insights about the robustness of stochastic algorithms when the proximal operator cannot be exactly computed.In Chapter 4, we study properties of non-Euclidean stochastic algorithms applied to the problem of sparse signal recovery. A sparse structure significantly reduces the effects of noise in gradient observations. We propose a new stochastic algorithm, called SMD-SR, allowing to make better use of this structure. This method is a multi-step procedure which uses the stochastic mirror descent algorithm as a building block over its stages. Essentially, SMD-SR has two phases of convergence with the linear bias convergence during the preliminary phase and the optimal asymptotic rate during the asymptotic phase.Comparing to the most effective existing solution to the sparse stochastic optimization problems, we offer an improvement in several aspects. First, we establish the linear bias convergence (similar to the one of the deterministic gradient descent algorithm, when the full gradient observation is available), while showing the optimal robustness to noise. Second, we achieve this rate for a large class of noise models, including sub-Gaussian, Rademacher, multivariate Student distributions and scale mixtures. Finally, these results are obtained under the optimal condition on the level of sparsity which can approach the total number of iterations of the algorithm (up to a logarithmic factor)
Patin, David. "Le chauffage stochastique dans l'interaction laser-plasma à très haut flux". Paris 11, 2006. http://www.theses.fr/2006PA112020.
Pełny tekst źródłaThis thesis takes place in the field of high intensity laser-plasma interaction. The aim was to highlight the stochastic heating effect. This phenomenon comes from the chaotic behavior of the plasma electrons. In order to have a simple theoretical model, two assumptions were made : underdense plasma and high intensity laser. The second one is equivalent to a>1 (where a is the normalized vector potential, a=eE0/mcw0 with (-e) the electron charge, E0 the electric field of the laser, m the electron mass, c the speed of light in vacuum and w0 the pulsation of the laser), so we need a relativistic approach of the system. The hamiltonian formalism is used in order to get information from our system. Using the Chirikov criterion, a set of parameters was deduced in order to get global stochasticity. Then, particle in cell simulations were performed in order to validate theoretical predictions. The influence of several parameters on the energy gain has been studied. Finally, a first numerical test was performed for protons acceleration
Rassou, Sébastien. "Accélération d'électrons par onde de sillage laser : Développement d’un modèle analytique étendu au cas d’un plasma magnétisé dans le régime du Blowout". Thesis, Université Paris-Saclay (ComUE), 2015. http://www.theses.fr/2015SACLS066/document.
Pełny tekst źródłaAn intense laser pulse propagating in an under dense plasma (ne< 10¹⁸ W.cm⁻²) and short(τ₀< 100 fs), the bubble regime is reached. Within the bubble the electric field can exceed 100 GV/m and a trapped electron beam is accelerated to GeV energy with few centimetres of plasma.In this regime, the electrons expelled by the laser ponderomotive force are brought back and form a dense sheath layer. First, an analytic model was derived using W. Lu and S. Yi formalisms in order to investigate the properties of the wakefield in the blowout regime. In a second part, the trapping and injection mechanisms into the wakefield were studied. When the optical injection scheme is used, electrons may undergo stochastic heating or cold injection depending on the lasers’ polarisations. A similarity parameter was introduced to find out the most appropriate method to maximise the trapped charge. In a third part, our analytic model is extended to investigate the influence of an initially applied longitudinal magnetic field on the laser wakefield in the bubble regime. When the plasma is magnetized two remarkable phenomena occur. Firstly the bubble is opened at its rear, and secondly the longitudinal magnetic field is amplified - at the rear of the bubble - due to the azimuthal current induced by the variation of the magnetic flux. The predictions of our analytic model were shown to be in agreement with 3D PIC simulation results obtained with Calder-Circ. In most situations the wake shape is altered and self-injection can be reduced or even cancelled by the applied magnetic field. However, the application of a longitudinal magnetic field, combined with a careful choice of laser-plasma parameters, reduces the energy spread of the electron beam produced after optical injection
Faure, Jérôme. "Accélération de particules par interaction laser-plasma dans le régime relativiste". Habilitation à diriger des recherches, Université Paris Sud - Paris XI, 2009. http://tel.archives-ouvertes.fr/tel-00404354.
Pełny tekst źródłaCastellanos, Lopez Clara. "Accélération et régularisation de la méthode d'inversion des formes d'ondes complètes en exploration sismique". Phd thesis, Université Nice Sophia Antipolis, 2014. http://tel.archives-ouvertes.fr/tel-01064412.
Pełny tekst źródłaDelhome, Raphaël. "Modélisation de la variabilité des temps de parcours et son intégration dans des algorithmes de recherche du plus court chemin stochastique". Thesis, Lyon, 2016. http://www.theses.fr/2016LYSET010/document.
Pełny tekst źródłaThe travel time representation has a major impact on user-oriented routing information. In particular, congestion detection is not perfect in current route planners. Moreover, the travel times cannot be considered as static because of events such as capacity drops, weather disturbances, or demand peaks. Former researches focused on dynamic travel times, i.e. that depend on departure times, in order to improve the representation details, for example concerning the periodicity of congestions. Real-time information is also a significant improvement for users aiming to prepare their travel or aiming to react to on-line events. However these kinds of model still have an important drawback : they do not take into account all the aspects of travel time variability. This dimension is of huge importance, in particular if the user risk aversion is considered. Additionally in a multimodal network, the eventual connections make the travel time uncertainty critical. In this way the current PhD thesis has been dedicated to the study of stochastic travel times, seen as distributed random variables.In a first step, we are interested in the travel time statistical modeling as well as in the travel time variability. In this goal, we propose to use the Halphen family, a probability law system previously developed in hydrology. The Halphen laws show the typical characteristics of travel time distributions, plus they are closed under addition under some parameter hypothesis. By using the distribution moment ratios, we design innovative reliability indexes, that we compare with classical metrics. This holistic approach appears to us as a promising way to produce travel time information, especially for infrastructure managers.Then we extend the analysis to transportation networks, by considering previous results. A set of probability laws is tested during the resolution of the stochastic shortest path problem. This research effort helps us to describe paths according to the different statistical models. We show that the model choice has an impact on the identified paths, and above all, that the stochastic framework is crucial. Furthermore we highlight the inefficiency of algorithms designed for the stochastic shortest path problem. They need long computation times and are consequently incompatible with industrial applications. An accelerated algorithm based on a deterministic state-of-the-art is provided to overcome this problem in the last part of this document. The obtained results let us think that route planners might include travel time stochastic models in a near future
Hajji, Kaouther. "Accélération de la méthode de Monte Carlo pour des processus de diffusions et applications en Finance". Thesis, Paris 13, 2014. http://www.theses.fr/2014PA132054/document.
Pełny tekst źródłaIn this thesis, we are interested in studying the combination of variance reduction methods and complexity improvement of the Monte Carlo method. In the first part of this thesis,we consider a continuous diffusion model for which we construct an adaptive algorithm by applying importance sampling to Statistical Romberg method. Then, we prove a central limit theorem of Lindeberg-Feller type for this algorithm. In the same setting and in the same spirit, we apply the importance sampling to the Multilevel Monte Carlo method. We also prove a central limit theorem for the obtained adaptive algorithm. In the second part of this thesis, we develop the same type of adaptive algorithm for a discontinuous model namely the Lévy processes and we prove the associated central limit theorem. Numerical simulations are processed for the different obtained algorithms in both settings with and without jumps
Zamansky, Rémi. "Simulation numérique directe et modélisation stochastique de sous-maille de l'accélération dans un écoulement de canal à grand nombre de Reynolds". Phd thesis, Ecole Centrale de Lyon, 2011. http://tel.archives-ouvertes.fr/tel-00673464.
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