Addressing nonlinearities in Monte Carlo

Monte Carlo is famous for accepting model extensions and model refinements up to infinite dimension. However, this powerful incremental design is based on a premise which has severely limited its application so far: a state-variable can only be recursively defined as a function of underlying state-v...

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Published inarXiv.org
Main Authors Dauchet, Jérémi, Jean-Jacques Bezian, Blanco, Stéphane, Caliot, Cyril, Charon, Julien, Coustet, Christophe, Mouna El Hafi, Eymet, Vincent, Farges, Olivier, est, Vincent, Fournier, Richard, Galtier, Mathieu, Gautrais, Jacques, Khuong, Anaïs, Pelissier, Lionel, Piaud, Benjamin, Maxime, Roger, Terrée, Guillaume, Weitz, Sebastian
Format Paper Journal Article
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 28.10.2018
Subjects
Charon
Computer simulation
Electromagnetic scattering
Monte Carlo simulation
Physics - Computational Physics
Phytoplankton
Planetary atmospheres
Polynomials
Radiative transfer
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Summary:Monte Carlo is famous for accepting model extensions and model refinements up to infinite dimension. However, this powerful incremental design is based on a premise which has severely limited its application so far: a state-variable can only be recursively defined as a function of underlying state-variables if this function is linear. Here we show that this premise can be alleviated by projecting nonlinearities onto a polynomial basis and increasing the configuration space dimension. Considering phytoplankton growth in light-limited environments, radiative transfer in planetary atmospheres, electromagnetic scattering by particles, and concentrated solar power plant production, we prove the real-world usability of this advance in four test cases which were previously regarded as impracticable using Monte Carlo approaches. We also illustrate an outstanding feature of our method when applied to acute problems with interacting particles: handling rare events is now straightforward. Overall, our extension preserves the features that made the method popular: addressing nonlinearities does not compromise on model refinement or system complexity, and convergence rates remain independent of dimension. Published: Dauchet J, Bezian J-J, Blanco S, Caliot C, Charon J, Coustet C, El Hafi M, Eymet V, Farges O, Forest V, Fournier R, Galtier M, Gautrais J, Khuong A, Pelissier L, Piaud B, Roger M, Terrée G, Weitz S (2018) Addressing nonlinearities in Monte Carlo. Sci. Rep. 8: 13302, DOI:10.1038/s41598-018-31574-4
ISSN:2331-8422
DOI:10.48550/arxiv.1610.02684