Inference of m-NLP data using radial basis function regression with center-evolving algorithm

Abstract

An efficient technique is presented to infer space plasma density and satellite potentials from Langmuir probe measurements, using multivariate radial basis function (RBF) regression. This inference technique goes beyond analytic approaches which have been developed over nearly a century, and which remain in use in most lab and space plasma experiments. The method is assessed by applying it to synthetic data sets constructed with three-dimensional particle in cell (PIC) simulations of fixed-bias needle Langmuir probes proposed by Jacobsen, to determine a plasma parameter, independently of the temperature. Our approach follows machine learning techniques, whereby models are constructed on training data sets consisting of the simulated collected currents as a function of voltage, corresponding to known physical parameters such as plasma density and temperature, and satellite potential. Compared to standard approaches used in RBF regression, our approach proves to be particularly efficient when working with large training sets, by implementing an evolutive selection of optimal centers. Program summaryProgram title: CERBFCPC Library link to program files:https://doi.org/10.17632/6bskxt2xjj.1Code Ocean capsule:https://codeocean.com/capsule/3524673/Licensing provisions: MITProgramming language: Fortran 90Nature of problem: When constructing a radial basis function (RBF) regression inference model, the determination of the optimal set of centers in a given training data set can be very time consuming, owing to the large number of possible combinations of centers among entries in the set. The center evolving approach implemented in this program, greatly reduces the training time of a model, with minimal impact on model inference accuracy.Solution method: A new search strategy is implemented for finding an optimal set of centers used in radial basis function regression, which is particularly fast and efficient when working with large data sets. Instead of performing a single exhaustive search among all possible combinations of a given number of centers among a training set, successive exhaustive searches are made in randomly selected small subsets of the training sets, while carrying over optimal centers found in one search, to the next one. Using modest subsets, with a number of entries of order 20, RBF models can be constructed with inference accuracies close to ones obtained with more time consuming exhaustive searches.