6533b85bfe1ef96bd12bbe58
RESEARCH PRODUCT
Adaptive Gaussian particle method for the solution of the Fokker-Planck equation
M.d. ScharpenbergM. Lukáčová-medviovásubject
Mathematical optimizationPartial differential equationApplied MathematicsGaussianComputational MechanicsBasis functionProbability density functionMultivariate normal distributionResidualsymbols.namesakeOrdinary differential equationsymbolsApplied mathematicsFokker–Planck equationMathematicsdescription
The Fokker-Planck equation describes the evolution of the probability density for a stochastic ordinary differential equation (SODE). A solution strategy for this partial differential equation (PDE) up to a relatively large number of dimensions is based on particle methods using Gaussians as basis functions. An initial probability density is decomposed into a sum of multivariate normal distributions and these are propagated according to the SODE. The decomposition as well as the propagation is subject to possibly large numeric errors due to the difficulty to control the spatial residual over the whole domain. In this paper a new particle method is derived, which allows a deterministic error control for the resulting probability density. It is based on global optimization and allows an adaption of an efficient surrogate model for the residual estimation. Copyright line will be provided by the publisher
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2012-06-11 | ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik |