Bayesian and Deterministic Neural Network approaches to Faraday Cup calibration and plasma parameter estimation

TL;DR

This work tackles the challenge of calibrating in situ plasma measurements across spacecraft in similar orbits by leveraging a ground-truth reference (Wind) and dynamic time warping (DTW) to align temporal sequences. An artificial neural network (ANN) is trained to reproduce Wind-ground-truth solar wind parameters ($N_p$, $w$, $v$) from uncalibrated DSCOVR PlasMag FC spectra, eliminating reliance on perfect calibration of the target instrument. The authors compare deterministic and Bayesian neural network (BNN) approaches, finding that the DTW+ANN framework yields higher correlation and lower RMSE than traditional pipelines, while the BNN provides calibrated uncertainty estimates that are broadly consistent with ground truth. The method shows promise for multi-spacecraft missions (e.g., HelioSwarm, IMAP) by enabling end-to-end calibration and uncertainty quantification directly from raw spectra, and it may improve data coverage and reliability under anomalous conditions. Key contributions include a practical DTW-guided ground-truth generation, a lightweight NN architecture (50-input spectra to 1-output per parameter), significant RMSE improvements over conventional methods, and a probabilistic extension that delivers actionable confidence intervals for solar wind parameter estimates.

Abstract

We describe a novel scheme for analyzing particle detector measurements when a well-calibrated, similarly instrumented spacecraft is present in a similar orbit. To prepare ground truth from measurements provided by a reference spacecraft, the method uses dynamic time warping (DTW)--a technique often used for pattern-matching in time series data. An artificial neural network (ANN) is created and trained to reproduce this ground truth from measurements at the target spacecraft. Unlike previous approaches, this procedure is insensitive to calibration errors in the target data stream, as the neural network may be trained from poorly calibrated particle spectra or even directly from low-level data in engineering units. We demonstrate a proof-of-concept by training an ANN to estimate solar wind proton densities, temperatures, and speeds from the DSCOVR PlasMag Faraday Cup, using the \textit{Wind} Solar Wind Experiment as a reference. We present both deterministic and Bayesian neural network approaches. Applications for Parker Solar Probe, HelioSwarm, and other missions are discussed.

Figures (11)

• Figure 1: Sample DSCOVR FC spectra data for a brief period in February 2019. Raw charge flux measurements, rescaled roughly to current, are plotted as a function of the voltage step. The ANNs are trained with current spectra as the input data, predicting solar wind parameters as an output.
• Figure 2: Flow chart for the data pipeline. The well-calibrated reference (Wind) is time-adjusted using magnetometry and used as ground truth for training the target experiment (DSCOVR FC). Note that the target experiment inputs are [re-formatted] uncalibrated telemetry.
• Figure 3: Contemporaneous L1 orbits of Wind (blue) and DSCOVR (orange), in GSE coordinates and in units of Earth radii ($R_{E}$).
• Figure 4: Heuristic diagram of the Artificial Neural Networks architecture. A network of an Input Layer with input neurons in blue, Hidden layer with neurons in pink, Output Layer with an output neuron in green.
• Figure 5: Left illustration of DTW between a segment of magnetic field time series data from two nearby spacecraft. Right: the data sets are shown with connections indicating the derived DTW mapping.