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Theses

Sequential Monte Carlo and Applications in Molecular Dynamics

Qiming Du 1, 2, 3 
3 MATHERIALS - MATHematics for MatERIALS
CERMICS - Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique, Inria de Paris
Abstract : This thesis consists in three parts, all connecting to the Sequential Monte Carlo (SMC) framework. The primary motivation is to understand the generalized Adaptive Multilevel Splitting, an algorithm that aims at estimating the rare-event transition probability between metastable states in the context of Molecular Dynamics. In the first part, we deal with the Adaptive SMC framework. We prove that the variance estimator proposed by Lee and Whiteley in the non-adaptive setting, is still consistent in this adaptive setting, under a slightly weaker assumption than the one to establish central limit theorem. In the theoretical perspective, We propose a new strategy that deals with the adaptiveness and genealogy of the particle system separately, based on coalescent tree-based expansions. In the second part, we propose Asymmetric SMC framework, a generalization of the classical SMC framework. The motivation is to reduce the computational burden brought by the mutation kernels. We provide central limite theorem for the assoticated Feynman-Kac measures, along with consistent asymptotic variance estimators. We remark that in some specific setting, the gAMS algorithm enters into the Asymmetric SMC framework, which leads to a consistent variance estimator and asymptotic normality for the gAMS algorithm. However, this result does not cover the general setting of gAMS algorithm. Our analysis is based on generalized coalescent tree-based expansions, which may provide an universal strategy that can be used to derive consistent variance estimators in the general SMC context. In the third part, we propose some strategies that combine the gAMS algorithm and modern statistical/machine learning. We investigate the coupling of gAMS algorithm and a nonparametric regressor---Mondrian Forests (MF), to improve the performance of gAMS algorithm. The proposed iterative updating strategy may be helpful in developing automated and efficient rare-event estimation strategy in a high-dimensional and low temperature setting.
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Submitted on : Thursday, September 16, 2021 - 9:28:40 AM
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Qiming Du. Sequential Monte Carlo and Applications in Molecular Dynamics. Probability [math.PR]. Sorbonne Université, 2020. English. ⟨NNT : 2020SORUS040⟩. ⟨tel-02969115v2⟩

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