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Sparse grid
About: Sparse grid is a research topic. Over the lifetime, 1013 publications have been published within this topic receiving 20664 citations.
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TL;DR: Experiments show that planning on a sparse grid can achieve comparable results with those of a high resolution grid, as long as the bounds are carefully balanced.
Abstract: Purpose: Radiosurgical treatment planning requires a good approximation of the dose distribution which is typically computed on a high resolution grid. However, the resulting optimization problem is large, and leads to substantial runtime. We study a sparse grid approach, for which we estimate and compensate for the expected deviations from the bounds. Methods: We buildup an estimate of the hotspot error distribution by measuring the maximum dose deviation within a voxel for a large number of randomly generated beam configurations. This results in a conservative estimation of overdosage as a function of upper bound reduction for different grid sizes. We adjust the bounds for voxels inside the target volume (PTV) according to our estimation thus maintaining the likelihood of dose deviations within acceptable limits. The approach was applied to a prostate case, where the volumes of interest are large and close to each other. Our planning objective is a prescribed dose of 36.25 Gy to the 87% isodose. We employed constrained optimization to optimize the lower PTV bound on 2, 4, and 8mm isotropic grids. Results were computed on 1mm grid. Results: The initial coverage was 93.7%, 92%, and 91%, and the volume exceeding the upper bound was 0.74%, 1.71%, and 9% for grid sizes of 2, 4, and 8mm, respectively. Changing the upper bound by 0.5% and 2.5% for the 4 and 8 mm grids resulted in only 0.75% and 2.2% of the volume exceeding the bound. The coverage did not change. Mean optimization times were 141.1, 22.6 and 3.4 minutes using the 2, 4 or 8mm grid, respectively. Conclusions: Experiments show that planning on a sparse grid can achieve comparable results with those of a high resolution grid, as long as the bounds are carefully balanced. This leads to substantially lower optimization times which facilitates interactive planning. This work was supported by the Graduate School for Computing in Medicine and Life Sciences funded by Germany’s Excellence Initiative [DFG GSC 235/1]
01 Jan 2021
TL;DR: The question of high-dimensional model representation (HDMR) is of increasing importance in computational mathematics and science as mentioned in this paper, and the question of HDMR has been studied extensively in the literature.
Abstract: The question of high-dimension model representation (HDMR) is of increasing importance in computational mathematics and science.
TL;DR: In this article, a sensitivity-driven approach is employed to study the role of energetic particles in suppressing turbulence-inducing micro-instabilities for a set of realistic JET-like cases with NBI deuterium and ICRH $3$He fast ions.
Abstract: A newly developed sensitivity-driven approach is employed to study the role of energetic particles in suppressing turbulence-inducing micro-instabilities for a set of realistic JET-like cases with NBI deuterium and ICRH $^3$He fast ions. First, the efficiency of the sensitivity-driven approach is showcased for scans in a $21$-dimensional parameter space, for which only $250$ simulations are necessary. The same scan performed with traditional Cartesian grids with only two points in each of the $21$ dimensions would require $2^{21} = 2,097,152$ simulations. Then, a $14$-dimensional parameter subspace is considered, using the sensitivity-driven approach to find an approximation of the parameter-to-growth rate map averaged over nine bi-normal wave-numbers, indicating pathways towards turbulence suppression. The respective turbulent fluxes, obtained via nonlinear simulations for the optimized set of parameters, are reduced by more than two order of magnitude compared to the reference results.