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. 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, Terr\'ee G, Weitz S (2018) Addressing nonlinearities in Monte Carlo. Sci. Rep. 8: 13302, DOI:10.1038/s41598-018-31574-4
Cite
@article{arxiv.1610.02684,
title = {Addressing nonlinearities in Monte Carlo},
author = {Jérémi Dauchet and Jean-Jacques Bezian and Stéphane Blanco and Cyril Caliot and Julien Charon and Christophe Coustet and Mouna El Hafi and Vincent Eymet and Olivier Farges and Vincent Forest and Richard Fournier and Mathieu Galtier and Jacques Gautrais and Anaïs Khuong and Lionel Pelissier and Benjamin Piaud and Maxime Roger and Guillaume Terrée and Sebastian Weitz},
journal= {arXiv preprint arXiv:1610.02684},
year = {2018}
}
Comments
36 pages, 6 figues