WIAS Preprint No. 2192, (2015)

SDE based regression for random PDEs


  • Anker, Felix
  • Bayer, Christian
    ORCID: 0000-0002-9116-0039
  • Eigel, Martin
    ORCID: 0000-0003-2687-4497
  • Ladkau, Marcel
  • Neumann, Johannes
  • Schoenmakers, John G. M.
    ORCID: 0000-0002-4389-8266

2010 Mathematics Subject Classification

  • 35R60 47B80 60H35 65C20 65N12 65N22 65J10 65C05


  • partial differential equations with random coefficients, random PDE, uncertainty quantification, Feynman-Kac, stochastic differential equations, stochastic simulation, stochastic regression, Monte-Carlo, Euler-Maruyama




A simulation based method for the numerical solution of PDE with random coefficients is presented. By the Feynman-Kac formula, the solution can be represented as conditional expectation of a functional of a corresponding stochastic differential equation driven by independent noise. A time discretization of the SDE for a set of points in the domain and a subsequent Monte Carlo regression lead to an approximation of the global solution of the random PDE. We provide an initial error and complexity analysis of the proposed method along with numerical examples illustrating its behaviour.

Appeared in

  • SIAM J. Sci. Comput., 39 (2017) pp. A1168--A1200.

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