%0 Journal Article %T Addressing nonlinearities in Monte Carlo %+ Institut Pascal (IP) %+ Centre de recherche d'Albi en génie des procédés des solides divisés, de l'énergie et de l'environnement (RAPSODEE) %+ Groupe de Recherche Energétique, Plasmas et Hors Equilibre (LAPLACE-GREPHE) %+ Procédés, Matériaux et Energie Solaire (PROMES) %+ Méso-Star %+ Laboratoire Énergies et Mécanique Théorique et Appliquée (LEMTA ) %+ Centre d'Energétique et de Thermique de Lyon (CETHIL) %+ Centre de Recherches sur la Cognition Animale - UMR5169 (CRCA) %+ Education, Formation, Travail, Savoirs (EFTS) %A Dauchet, Jeremi %A Bézian, Jean-Jacques %A Blanco, Stéphane %A Caliot, Cyril %A Charon, Julien %A Coustet, Christophe %A El-Hafi, Mouna %A Eymet, Vincent %A Farges, Olivier %A Forest, Vincent %A Fournier, Richard, A %A Galtier, Mathieu %A Gautrais, Jacques %A Khuong, Anais %A Pelissier, Lionel %A Piaud, Benjamin %A Roger, Maxime %A Terrée, Guillaume %A Weitz, Sebastian %Z This work was sponsored by the French National Centre for Scientific Research (CNRS) through the PEPS-JCJC OPTISOL_Mu program, by the French Agence Nationale de la Recherche (ANR) under grant ANR-16-CE01-0010 (project High-Tune), by the Region Occitanie under grant CLE-2016-EDStar and by the French government research-program “Investissements d’avenir” through the LABEXs ANR-10-LABX-16-01 IMobS3 and ANR-10-LABX-22-01 SOLSTICE and the ATS program ALGUE of IDEX ANR-11-IDEX-02 UNITI. %< avec comité de lecture %Z KTK-3692 %Z DOCA-01 %@ 2045-2322 %J Scientific Reports %I Nature Publishing Group %V 8 %N 1 %P art.13302-11 p. %8 2018-12 %D 2018 %R 10.1038/s41598-018-31574-4 %K Bioenergetics %K Planetary science %K Statistical physics %K Statistics %K Applied optics %Z Engineering Sciences [physics]Journal articles %X 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. %G English %2 https://imt-mines-albi.hal.science/hal-01871366/document %2 https://imt-mines-albi.hal.science/hal-01871366/file/s41598-018-31574-4.pdf %L hal-01871366 %U https://imt-mines-albi.hal.science/hal-01871366 %~ INSTITUT-TELECOM %~ UNIV-TLSE2 %~ UNIV-TLSE3 %~ PRES_CLERMONT %~ MINES-ALBI %~ CNRS %~ UNIV-BPCLERMONT %~ UNIV-LYON1 %~ UNIV-PERP %~ INSA-LYON %~ CRCA %~ EMAC %~ INSTITUT_PASCAL %~ EFTS %~ RAPSODEE %~ UNIV-LORRAINE %~ ACL-SPI %~ PROMES %~ LEMTA-UL %~ CETHIL %~ INSA-GROUPE %~ UDL %~ UNIV-LYON %~ LAPLACE %~ INSTITUTS-TELECOM %~ LAPLACE_GREPHE %~ ANR %~ TOULOUSE-INP %~ UNIV-UT3 %~ UT3-INP %~ UT3-TOULOUSEINP