CLARE: Classification-based Regression for Electron Temperature Prediction

Michael Liang; Blake DeHaas; Naomi Maruyama; Xiangning Chu; Takumi Abe; Koh-Ichiro Oyama

physics.space-phMar 12, 2026

CLARE: Classification-based Regression for Electron Temperature Prediction

Authors: Michael Liang, Blake DeHaas, Naomi Maruyama, Xiangning Chu, Takumi Abe, Koh-Ichiro Oyama

Organizations: Laboratory for Atmospheric and Space Physics, University of Colorado Boulder, Boulder, CO, USA · Japan Aerospace Exploration Agency (JAXA), Sagamihara, Kanagawa, Japan

Abstract

Electron temperature (Te) is an important parameter governing space weather in the upper atmosphere, but has historically been underexplored in the space weather machine learning literature. We present CLARE, a machine learning model for predicting electron temperature in the Earth's plasmasphere trained on AKEBONO (EXOS-D) satellite measurements as well as solar and geomagnetic indices. CLARE uses a classification-based regression architecture that transforms the continuous Te output space into 150 discrete classification intervals. Training the model on a classification task improves prediction accuracy by 6.46% relative compared to a traditional regression model while also outputting uncertainty estimation information on its predictions. On a held out test set from the AKEBONO data, the model's Te predictions achieve 69.67% accuracy within 10% of the ground truth and 46.17% on a known geomagnetic storm period from January 30th to February 7th, 1991. We show that machine learning can be used to produce high-accuracy Te models on publicly available data.

Figures & tables

Figure 1: The distributions of in situ observations of the electron temperature (Te) with respect to (a) L shell (between 1 and 12), (b) MLAT (between -90° to 90°), and (c) GMLT. The colorbar shows the number of observations in each bin on a log10 scale.

Figure 2: Model architecture for CLARE. The model consists of multiple feedforward blocks, with a detailed view of a single feedforward block shown on the right. Gray components represent neural network layers, while yellow components indicate input data and output logits.

Panel of Figure 3 — Figure 3: Correlation between observed and predicted electron temperature on the (a) test dataset of 50,000 randomly held out samples and (b) the held out known solar storm period (January 30th through February 7th, 1991).

Model	test-quiet			test-storm
Model	Accuracy	R 2	RMSE	Accuracy	R 2	RMSE
Titheridge	11.90%	-0.7196	3615.9753	4.96%	-1.2208	4304.8868
Titheridge-IRI	13.49%	-0.4455	3335.7404	12.26%	-0.3274	3170.2374
CLARE	69.67%	0.7829	1292.6217	46.17%	0.6647	1593.4668

Table 1: Results between the Titheridge models and CLARE on quiet solar activity and solar storm test sets. Metrics include accuracy within 10% of the observed value (higher is better), coefficient of determination

R^{2}

(higher is better) and root mean square error RMSE (lower is better). Bolded results indicate the best result in the column.

Figure 4: Prediction accuracy of CLARE within 10% of observed electron temperature against Titheridge and Titheridge-IRI baselines on test-quiet and test-storm sets.

Figure 5: (a) Low confidence probability distribution during high solar storm activity time instant compared to (b) high confidence probability distribution during quiet solar storm activity time instant.

Model	test-quiet		test-storm
Model	Accuracy	RMSE	Accuracy	RMSE
CLARE	69.67%	1292.6217	46.17%	1593.4668
CLARE-continuous	65.17%	1132.0842	45.95%	1340.6564

Table 2: Ablation results for CLARE variants with different training objectives. Bolded results indicate the best result in the column.

Model	test-quiet			test-storm
Model	Accuracy	R 2	RMSE	Accuracy	R 2	RMSE
CLARE	69.67%	0.7829	1292.6217	46.17%	0.6647	1593.4668
CLARE-solar	66.69%	0.7504	1385.9779	13.79%	-0.5679	3445.5452
CLARE-spatial	58.38%	0.6492	1643.2788	47.38%	0.6254	1684.1300

Table 3: Ablation results for CLARE trained on different datasets. Bolded results indicate the best result in the column.

Figure 6: Model predicted $T_{e}$ values during a moderate intensity solar storm between January 30th and February 7th, 1991, for altitudes between 1000 km and 8000 km fixed above Millstone Hill Observatory (geographic latitude 43 ∘ , longitude 289 ∘ ). The plot contains (a) the predicted $T_{e}$ value, (b) the peak model prediction confidence for the corresponding predicted $T_{e}$ value, and solar features from the NASA OMNI dataset, including (c) Kp index, (d) SYM-H, (e) F10.7 index, and (f) AL index.

Appendix figures & tables2 assets

Supplementary material from the paper’s appendix.

Appendix

Figure 7: Electron temperature to altitude comparisons for Titheridge and Titheridge-IRI for nighttime and daytime at (a) ILAT = 20, (b) ILAT = 30, (c) ILAT = 40, and (d) ILAT = 50.

Model	test-quiet			test-storm
Model	Accuracy	R 2	RMSE	Accuracy	R 2	RMSE
Titheridge	12.34%	-0.7115	3610.7134	3.46%	-1.5314	3918.1794
Titheridge-IRI	13.55%	-0.5086	3389.9854	12.53%	-0.7376	3246.2239
CLARE	69.84%	0.7936	1253.8517	22.91%	-0.6071	3121.9749

Appendix

Table 4: Results between the Titheridge models and CLARE on quiet solar activity and solar storm test sets filtered on the day-night times of the original Titheridge paper. Bolded results indicate the best result in the column.

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Abstract

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