Bayesian with Gaussian process based missing input imputation scheme for reconstructing magnetic equilibria in real time

TL;DR

This paper introduces a Bayesian-Gaussian Process method for real-time imputation of missing magnetic signals in tokamak operations, enabling accurate magnetic equilibrium reconstruction despite signal impairments.

Contribution

The paper develops a novel Bayesian-Gaussian Process numerical method that accurately imputes missing magnetic signals in less than 1 millisecond for real-time magnetic equilibrium reconstruction.

Findings

Imputes missing signals in under 1 millisecond.

Enhances neural network-based magnetic equilibrium reconstruction.

Maintains reconstruction accuracy despite missing signals.

Abstract

A Bayesian with GP(Gaussian Process)-based numerical method to impute a few missing magnetic signals caused by impaired magnetic probes during tokamak operations is developed such that the real-time reconstruction of magnetic equilibria, whose performance strongly depends on the measured magnetic signals and their intactness, are affected minimally. Likelihood of the Bayesian model constructed with the Maxwell's equations, specifically Gauss's law of magnetism and Amp\`ere's law, results in infinite number of solutions if two or more magnetic signals are missing. This undesirable characteristic of the Bayesian model is remediated by coupling the model with the Gaussian process. Our proposed numerical method infers the missing magnetic signals correctly in less than $1$\:msec suitable for real-time reconstruction of magnetic equilibria during tokamak operations. The method can also be used for a neural network that reconstructs magnetic equilibria trained with a complete set of magnetic signals. Without our proposed imputation method, such a neural network would become useless if missing signals are not tolerable by the network.