Pattern recognition in probability spaces for visualization and identification of plasma confinement regimes and confinement time scaling

Abstract

Pattern recognition is becoming an increasingly important tool for making inferences from the massive amounts of data produced in fusion experiments. The purpose is to contribute to physics studies and plasma control. In this work, we address the visualization of plasma confinement data, the (real-time) identification of confinement regimes and the establishment of a scaling law for the energy confinement time. We take an intrinsically probabilistic approach, modeling data from the International Global H-mode Confinement Database with Gaussian distributions. We show that pattern recognition operations working in the associated probability space are considerably more powerful than their counterparts in a Euclidean data space. This opens up new possibilities for analyzing confinement data and for fusion data processing in general. We hence advocate the essential role played by measurement uncertainty for data interpretation in fusion experiments.

Robust scaling in fusion science: case study for the L-H power threshold

“…This realization, that a more complete and rich source of information lies in the probability distribution of a quantity of interest, is at the heart of GLS regression [9,10,11,12,13].…”

“…As opposed to OLS, and, indeed, most existing regression methods, GLS regression does not require both distributions to be the same, but rather it minimizes the difference between them. More precisely, GLS minimizes the geodesic distance between the distributions, which is a natural and mathematically well-founded similarity measure between probability distributions [10,19,20]. As such, GLS does not rigorously impose the assumptions of the regression model on the data, instead leaving sufficient flexibility to allow deviations from the chosen regression model.…”

Robust regression on noisy data for fusion scaling laws

“…Rather, we employ the Rao geodesic distance (GD) as a similarity measure in probability spaces. The GD is defined in the context of the theory of information geometry, which is a geometric approach to probability theory 2,3 . In information geometry, a probability density family is interpreted as a (Riemannian) differentiable manifold (multidimensional surface).…”

Visualization of the operational space of edge-localized modes through low-dimensional embedding of probability distributions

“…This allows fast computation of the distance. Further, in the case of multiple independent Gaussian variables, the squared GD between two sets of products of distributions is given by the sum of the squared GDs between corresponding individual distributions [2][3] . In this paper we present MDS utilizing GDs between PDFs as an information visualization tool for yielding 2D maps for highdimensional plasma data.…”