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The numerical solution of large-scale PDEs, such as those occurring indata-driven applications, unavoidably require powerful parallel computers andtailored parallel algorithms to make the best possible use of them. In fact,considerations about the parallelization and scalability of realistic problemsare often critical enough to warrant acknowledgement in the modelling phase.The purpose of this paper is to spread awareness of the Probabilistic DomainDecomposition (PDD) method, a fresh approach to the parallelization of PDEswith excellent scalability properties. The idea exploits the stochasticrepresentation of the PDE and its approximation via Monte Carlo in combinationwith deterministic high-performance PDE solvers. We describe the ingredients ofPDD and its applicability in the scope of data science. In particular, wehighlight recent advances in stochastic representations for nonlinear PDEsusing branching diffusions, which have significantly broadened the scope ofPDD.  We envision this work as a dictionary giving large-scale PDE practitionersreferences on the very latest algorithms and techniques of a non-standard, yethighly parallelizable, methodology at the interface of deterministic andprobabilistic numerical methods. We close this work with an invitation to thefully nonlinear case and open research questions.

Hybrid PDE solver for data-driven problems and modern branching