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On the Mathematical foundations of Diffusion Monte Carlo

hal.structure.identifierLaboratoire de Chimie et Physique Quantiques [LCPQ]
dc.contributor.authorCAFFAREL, Michel
hal.structure.identifierMéthodes avancées d’apprentissage statistique et de contrôle [ASTRAL]
dc.contributor.authorDEL MORAL, Pierre
hal.structure.identifierNaval Group
hal.structure.identifierMéthodes avancées d’apprentissage statistique et de contrôle [ASTRAL]
dc.contributor.authorDE MONTELLA, Luc
dc.date.accessioned2024-04-04T02:30:03Z
dc.date.available2024-04-04T02:30:03Z
dc.date.issued2024-01-22
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/190231
dc.description.abstractEnThe Diffusion Monte Carlo method with constant number of walkers, also called Stochastic Reconfiguration as well as Sequential Monte Carlo, is a widely used Monte Carlo methodology for computing the ground-state energy and wave function of quantum systems. In this study, we present the first mathematically rigorous anal- ysis of this class of stochastic methods on non necessarily compact state spaces, including linear diffusions evolving in quadratic absorbing potentials, yielding what seems to be the first result of this type for this class of models. We present a novel and general mathematical framework with easily checked Lyapunov stability conditions that ensure the uniform-in-time convergence of Diffusion Monte Carlo estimates towards the top of the spectrum of Schr ̈odinger operators. For transient free evolutions, we also present a divergence blow up of the estimates w.r.t. the time horizon even when the asymptotic fluctuation variances are uniformly bounded. We also illustrate the impact of these results in the context of generalized coupled quan- tum harmonic oscillators with non necessarily reversible nor stable diffusive particle and a quadratic energy absorbing well associated with a semi-definite positive matrix force.
dc.language.isoen
dc.rights.urihttp://creativecommons.org/licenses/by/
dc.title.enOn the Mathematical foundations of Diffusion Monte Carlo
dc.typeDocument de travail - Pré-publication
dc.subject.halMathématiques [math]/Probabilités [math.PR]
dc.identifier.arxiv2402.04642
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
hal.identifierhal-04409602
hal.version1
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-04409602v1
bordeaux.COinSctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.date=2024-01-22&rft.au=CAFFAREL,%20Michel&DEL%20MORAL,%20Pierre&DE%20MONTELLA,%20Luc&rft.genre=preprint


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