Predicting Goal Error Evolution from Near-Initial-Information: a Learning Algorithm

Publication year: 2011
Source: Journal of Computational Physics, In Press, Accepted Manuscript, Available online 13 June 2011

Florian, Rauser , Peter, Korn , Jochem, Marotzke

We estimate the discretization error of time-dependent goals that are calculated from a numerical model of the spherical shallow-water equations. The goal errors are described as a weighted sum of local model errors. Our algorithm divides goal error estimation into three phases. In phase one, we select deterministic functionals of the flow as a mathematical description of local model error estimators. In phase two, a learning algorithm adapts the selected functionals to the numerical experiment under consideration by determining the free parameters of the functionals. To do this, the learning algorithm analyzes a short numerical simulation at two different resolutions….