By Jochen Garcke, Dirk Pflüger
This quantity of LNCSE is a set of the papers from the complaints of the 3rd workshop on sparse grids and purposes. Sparse grids are a favored process for the numerical remedy of high-dimensional difficulties. the place classical numerical discretization schemes fail in additional than 3 or 4 dimensions, sparse grids, of their varied guises, are often the strategy of selection, be it spatially adaptive within the hierarchical foundation or through the dimensionally adaptive mixture procedure. Demonstrating once more the significance of this numerical discretization scheme, the chosen articles current contemporary advances at the numerical research of sparse grids in addition to effective facts buildings. The publication additionally discusses more than a few functions, together with uncertainty quantification and plasma physics.
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Additional info for Sparse Grids and Applications - Stuttgart 2014
J. Sci. Comput. 59, 187–216 (2014) 7. P. Chen, A. Quarteroni, G. Rozza, A weighted empirical interpolation method: a priori convergence analysis and applications. ESAIM: Math. Model. Numer. Anal. 48, 943–953, 7 (2014) 8. P. Chen, A. Quarteroni, G. Rozza, Reduced order methods for uncertainty quantification problems. ETH Zurich, SAM Report 03, Submitted, 2015 9. P. Chen, C. Schwab, Sparse grid, reduced basis Bayesian inversion. Comput. Methods Appl. Mech. Eng. 297, 84–115 (2015) 10. P. Chen, C. Schwab, Sparse grid, reduced basis Bayesian inversion: nonaffine-parametric nonlinear equations.
Chen, A. Quarteroni, G. Rozza, A weighted empirical interpolation method: a priori convergence analysis and applications. ESAIM: Math. Model. Numer. Anal. 48, 943–953, 7 (2014) 8. P. Chen, A. Quarteroni, G. Rozza, Reduced order methods for uncertainty quantification problems. ETH Zurich, SAM Report 03, Submitted, 2015 9. P. Chen, C. Schwab, Sparse grid, reduced basis Bayesian inversion. Comput. Methods Appl. Mech. Eng. 297, 84–115 (2015) 10. P. Chen, C. Schwab, Sparse grid, reduced basis Bayesian inversion: nonaffine-parametric nonlinear equations.
In fact, if we use a sparse grid without boundary points for density estimation we match the expectation value of the data as well as the density trees do. However, the cross entropy for this sparse grid density is larger compared to the others (L D 0:2632) indicating a worse estimation. And indeed, with this estimation we overestimate now the variance significantly. Due to these arguments, we question the ground truth, which in this application was based on a very limited data set. Of course, this makes the comparison of different methods difficult.
Sparse Grids and Applications - Stuttgart 2014 by Jochen Garcke, Dirk Pflüger