Addressing nonlinearities in Monte Carlo

Abstract : 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.
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Article dans une revue
Scientific Reports, Nature Publishing Group, 2018, 8 (1), art.13302-11 p. 〈10.1038/s41598-018-31574-4〉
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Soumis le : lundi 10 septembre 2018 - 16:41:26
Dernière modification le : jeudi 21 mars 2019 - 16:20:10


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Jeremi Dauchet, Jean-Jacques Bézian, Stephane Blanco, Cyril Caliot, Julien Charon, et al.. Addressing nonlinearities in Monte Carlo. Scientific Reports, Nature Publishing Group, 2018, 8 (1), art.13302-11 p. 〈10.1038/s41598-018-31574-4〉. 〈hal-01871366〉



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