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In fact, considerations about the parallelization and scalability of realistic problems are often critical enough to warrant acknowledgement in the modelling phase. The purpose of this paper is to spread awareness of the Probabilistic Domain Decomposition (PDD) method, a fresh approach to the parallelization of PDEs with excellent scalability properties. The idea exploits the stochastic representation of the PDE and its approximation via Monte Carlo in combination with deterministic high-performance PDE solvers. We describe the ingredients of PDD and its applicability in the scope of data science. In particular, we highlight recent advances in stochastic representations for non-linear PDEs using branching diffusions, which have significantly broadened the scope of PDD. We envision this work as a dictionary giving large-scale PDE practitioners references on the very latest algorithms and techniques of a non-standard, yet highly parallelizable, methodology at the interface of deterministic and probabilistic numerical methods. We close this work with an invitation to the fully non-linear case and open research questions.<\/jats:p>","DOI":"10.1017\/s0956792517000109","type":"journal-article","created":{"date-parts":[[2017,5,22]],"date-time":"2017-05-22T01:51:00Z","timestamp":1495417860000},"page":"949-972","source":"Crossref","is-referenced-by-count":6,"title":["Hybrid PDE solver for data-driven problems and modern branching"],"prefix":"10.1017","volume":"28","author":[{"given":"FRANCISCO","family":"BERNAL","sequence":"first","affiliation":[]},{"given":"GON\u00c7ALO","family":"DOS REIS","sequence":"additional","affiliation":[]},{"given":"GREIG","family":"SMITH","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2017,5,22]]},"reference":[{"key":"S0956792517000109_ref1","doi-asserted-by":"publisher","DOI":"10.1137\/030600692"},{"key":"S0956792517000109_ref39","doi-asserted-by":"publisher","DOI":"10.1016\/j.spa.2009.09.014"},{"key":"S0956792517000109_ref40","doi-asserted-by":"crossref","DOI":"10.1201\/b16332","volume-title":"Nonlinear Option Pricing","author":"Guyon","year":"2013"},{"key":"S0956792517000109_ref17","doi-asserted-by":"publisher","DOI":"10.1051\/proc\/201448020"},{"key":"S0956792517000109_ref20","doi-asserted-by":"publisher","DOI":"10.1002\/cpa.20168"},{"key":"S0956792517000109_ref56","doi-asserted-by":"publisher","DOI":"10.1016\/j.matcom.2009.12.009"},{"key":"S0956792517000109_ref16","doi-asserted-by":"publisher","DOI":"10.4208\/jms.v48n2.15.02"},{"key":"S0956792517000109_ref46","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-12616-5"},{"key":"S0956792517000109_ref47","first-page":"129","article-title":"\u00c9tude de l'\u00e9quation de la diffusion avec croissance de la quantit\u00e9 de matiere et son application a un probleme biologique","volume":"1","author":"Kolmogorov","year":"1937","journal-title":"Moscow Univ. 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