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Conference Papers Springer Proceedings in Mathematics & Statistics Year : 2020

Stochastic methods for solving high-dimensional partial differential equations

Abstract

We propose algorithms for solving high-dimensional Partial Differential Equations (PDEs) that combine a probabilistic interpretation of PDEs, through Feynman-Kac representation, with sparse interpolation. Monte-Carlo methods and time-integration schemes are used to estimate pointwise evaluations of the solution of a PDE. We use a sequential control variates algorithm, where control variates are constructed based on successive approximations of the solution of the PDE. Two different algorithms are proposed, combining in different ways the sequential control variates algorithm and adaptive sparse interpolation. Numerical examples will illustrate the behavior of these algorithms.

Dates and versions

hal-02140703 , version 1 (27-05-2019)

Identifiers

Cite

Marie Billaud Friess, Arthur Macherey, Anthony Nouy, Clémentine Prieur. Stochastic methods for solving high-dimensional partial differential equations. International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing - MCQMC 2018, Jul 2018, Rennes, France. pp.125-141, ⟨10.1007/978-3-030-43465-6_6⟩. ⟨hal-02140703⟩
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