Addressing nonlinearities in Monte Carlo

Jeremi Dauchet (1) , Jean-Jacques Bézian (2) , Stéphane Blanco (3) , Cyril Caliot (4) , Julien Charon (2, 4, 1) , Christophe Coustet (5) , Mouna El-Hafi (2) , Vincent Eymet (5) , Olivier Farges (6) , Vincent Forest (5) , Richard A Fournier (3) , Mathieu Galtier (7) , Jacques Gautrais (8) , Anais Khuong (8) , Lionel Pelissier (9) , Benjamin Piaud (5) , Maxime Roger (7) , Guillaume Terrée (2) , Sebastian Weitz (1, 2)

1 IP - Institut Pascal
2 RAPSODEE - Centre de recherche d'Albi en génie des procédés des solides divisés, de l'énergie et de l'environnement
3 LAPLACE-GREPHE - Groupe de Recherche Energétique, Plasmas et Hors Equilibre
4 PROMES - Procédés, Matériaux et Energie Solaire
5 Meso-Star
6 LEMTA - Laboratoire Énergies et Mécanique Théorique et Appliquée
7 CETHIL - Centre d'Energétique et de Thermique de Lyon
8 CRCA - Centre de Recherches sur la Cognition Animale - UMR5169
9 EFTS - Education, Formation, Travail, Savoirs

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.

Keywords: Bioenergetics; Planetary science; Statistical physics; Statistics; Applied optics

Domains: Engineering Sciences [physics]

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