240
9 High-Dimension Model Representation via Sparse GridTechniques
Fig. 9.27 Showing the Chebyshev distribution of points in various two-dimensional subsets of the
four-dimensional grid at level 8 (continued)
In this manner we can map the ‘most likely’ regions of the sparse grid in which
the data vector lies, and then compute a compact uniform grid for interpolation in
NLSE within these regions. If the uniform grid is much smaller than the sparse grid,
we would expect to get tighter estimations of confidence intervals when we perform
a stochastic inversion with NLSE.
9.9 A Five-Dimensional Inverse Problem
The proof-of-the-pudding with sparse grids is their ability to simplify the solution
of inverse problems that utilize internal interpolation tables as with NLSE. Our hope
9 High-Dimension Model Representation via Sparse GridTechniques
Fig. 9.27 Showing the Chebyshev distribution of points in various two-dimensional subsets of the
four-dimensional grid at level 8 (continued)
In this manner we can map the ‘most likely’ regions of the sparse grid in which
the data vector lies, and then compute a compact uniform grid for interpolation in
NLSE within these regions. If the uniform grid is much smaller than the sparse grid,
we would expect to get tighter estimations of confidence intervals when we perform
a stochastic inversion with NLSE.
9.9 A Five-Dimensional Inverse Problem
The proof-of-the-pudding with sparse grids is their ability to simplify the solution
of inverse problems that utilize internal interpolation tables as with NLSE. Our hope