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arxiv: 2605.15752 · v1 · pith:R6HZ2GWYnew · submitted 2026-05-15 · 🌌 astro-ph.IM · astro-ph.EP

Forecasting megaelectron-volt electron flux in the Earth's outer radiation belt using supervised machine learning algorithms and a timeseries foundation model

Rungployphan Kieokaew , Ryad Guezzi , Fran\c{c}ois Ginisty , Hadrien Mariaccia This is my paper

Pith reviewed 2026-05-19 19:35 UTC · model grok-4.3

classification 🌌 astro-ph.IM astro-ph.EP
keywords radiation belt electronsMeV flux forecastingmachine learningfoundation modelsspace weatherL-shellGOES POES data
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The pith

A hybrid TimesFM foundation model with covariates forecasts 1-MeV electron flux in the outer radiation belt at an average R2 of 0.9 on 2024 data.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper builds a machine-learning pipeline to predict variations in megaelectron-volt electrons trapped in Earth's outer radiation belt, a region that can damage satellites. Inputs include precipitating electrons from POES, near-1-MeV flux from GOES, solar wind data, and geomagnetic indices, all drawn from 2013-2023. Several standard models are trained alongside a hybrid version of the TimesFM timeseries foundation model that adds ridge regression on past covariates. When tested on January-June 2024 data, the hybrid approach reaches the highest skill, with an average R2 of 0.9 across L-shells from 2.8 to 6.0 and larger gains at outer shells. The work shows one practical way to adapt a pretrained foundation model for short-term space-weather forecasting without full retraining on domain data.

Core claim

The hybrid TimesFM+Cov model, which applies ridge regression to past dynamic covariates and then uses TimesFM to predict the residuals, produces 6-hour forecasts of 1-MeV electron flux with an average R2 of 0.9 across L-shells on out-of-sample 2024 data. This exceeds the performance of linear regression, 1-D CNN, LSTM, and Transformer-Encoder models, which average below 0.78. Skill remains above 0.9 from L=2.8 to 4.7 and falls to 0.77 at L=6.0, yielding relative improvements of 12 percent at the lowest L-shell and 48 percent at the highest L-shell compared with the second-best models.

What carries the argument

The TimesFM+Cov hybrid, which combines ridge regression on observed dynamic covariates with TimesFM zero-shot inference applied to the regression residuals.

If this is right

  • Operational 6-hour forecasts of radiation-belt electrons become feasible using only publicly available satellite and solar-wind observations.
  • Pretrained foundation models can be adapted for space-weather tasks by adding a lightweight covariate regression step rather than retraining from scratch.
  • Forecast skill is highest inside L=4.7 and declines outward, pointing to the need for additional inputs or model adjustments near the outer edge of the belt.
  • The same hybrid recipe supplies a concrete benchmark against which future machine-learning or physics-based radiation-belt models can be compared.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The hybrid technique could be tested on other particle species or longer forecast horizons to check whether the same covariate-plus-foundation-model pattern generalizes.
  • If the training-test distribution similarity continues to hold, such models might eventually run in real time to support satellite operators during quiet and moderately active periods.
  • Pairing the machine-learning outputs with physics-based transport codes could provide both rapid updates and physically consistent longer-term evolution.

Load-bearing premise

The statistical properties of electron flux and driving conditions in the January-June 2024 test interval remain close to those seen in the 2013-2023 training record, without large unmeasured changes in magnetospheric state that would dominate errors at higher L-shells.

What would settle it

A major geomagnetic storm or sudden magnetospheric reconfiguration during 2024 that produces flux variations outside the training distribution and causes the hybrid model's R2 to drop well below the reported 0.9 average would falsify the performance claim.

Figures

Figures reproduced from arXiv: 2605.15752 by Fran\c{c}ois Ginisty, Hadrien Mariaccia, Rungployphan Kieokaew, Ryad Guezzi.

Figure 1
Figure 1. Figure 1: Overview of the data between January 2013 and June 2024 (a–f), and their zoom-in (g–l): (a, b, c) the POES [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Schematic diagram of our pipeline for predicting 1-MeV electrons in the outer radiation belt using past [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Schematic illustration of the walk-forward validation. [PITH_FULL_IMAGE:figures/full_fig_p010_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: R2 scores of the test data (January - May 2024) as a function of L-shells of all the models for 6 hours forecast horizon using 6 hours data cadence. In [PITH_FULL_IMAGE:figures/full_fig_p011_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: L-time diagrams (a-d) and the prediction error (e-g): (a) the 1-MeV electron flux observations; (b - d) 6h [PITH_FULL_IMAGE:figures/full_fig_p012_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Comparison between the 1-MeV flux observations (black) and the 6h forecast predictions from TimesFM+CoV [PITH_FULL_IMAGE:figures/full_fig_p013_6.png] view at source ↗
read the original abstract

Accurate forecasting of megaelectron-volt (MeV) electrons in the outer Earth's radiation belt, which can pose significant risks to satellites, is essential for risk mitigation and spacecraft operations. We develop a machine-learning-based pipeline for forecasting 1-MeV electron flux variations, focusing first on a 6-hour forecast horizon. Using precipitating electrons measured by POES NOAA-15, near 1-MeV electron flux measured by GOES, solar wind measurements near L1, and geomagnetic activity indices as inputs in 2013-2023, we train algorithms including linear regression, 1-D convolutional and long short-term memory neural networks, and Transformer-Encoder to forecast 1-MeV electron flux in McIlwain's L-shells between 2.8 and 6.0 with 0.1 bin resolution. Particularly, we exploit the timeseries foundation model TimesFM for (1) a zero-shot prediction and (2) a hybrid application involving the ridge regression on the past dynamic covariates combined with the TimesFM inference on the residuals. Using data from January-June 2024 as an out-of-sample test, we find that the hybrid application of TimesFM, named TimesFM+Cov, yields the best results with an average R2 of 0.9 across L-shells, compared to an average R2 under 0.78 for all other models. The R2 of TimesFM+Cov remains above 0.9 for L-shells between 2.8 and 4.7 and drops to 0.77 at L=6.0, indicating improvements of 12% at the lowest L-shell and 48% at the highest L-shell compared to our second-best models. Our work offers an alternative perspective on how a pretrained foundation model could be adapted for space weather forecasting.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 2 minor

Summary. The manuscript develops a supervised ML pipeline to forecast 1-MeV electron flux at L-shells 2.8–6.0 using POES precipitating electrons, GOES flux, L1 solar-wind data, and geomagnetic indices. Models trained on 2013–2023 data are evaluated on a strictly later January–June 2024 out-of-sample window; the hybrid TimesFM+Cov (ridge regression on covariates followed by zero-shot TimesFM on residuals) is reported to achieve mean R² = 0.9, versus <0.78 for linear regression, 1-D CNN, LSTM, and Transformer-Encoder baselines, with the largest relative gains at higher L.

Significance. If the reported performance advantage proves robust, the work would demonstrate a practical route for adapting pretrained time-series foundation models to space-weather forecasting, potentially improving 6-hour MeV-electron predictions that matter for satellite operations. The temporal train/test split and the hybrid residual approach are methodologically attractive features.

major comments (3)
  1. [§4] §4 (Results, performance tables): the central claim that TimesFM+Cov yields average R² = 0.9 (and 12–48 % relative gains) is presented without error bars, bootstrap intervals, or any statistical test comparing it to the second-best model; this omission is load-bearing because the advantage must be shown to be distinguishable from sampling variability, especially given the drop to R² = 0.77 at L = 6.0.
  2. [§3] §3 (Methods, hybrid pipeline): no ablation is reported that isolates the contribution of the ridge-regression covariates versus the zero-shot TimesFM residual step; without this, it remains unclear whether the hybrid construction is required for the quoted performance or whether a pure TimesFM forecast would suffice.
  3. [§4–5] §4–5 (Results and Discussion): the manuscript does not compare the distributions of key drivers (solar-wind speed, density, Kp) between the 2013–2023 training interval and the 2024 test window, nor does it test sensitivity to solar-cycle phase; because the test set is only six months long and occurs during the ascending phase of cycle 25, unmeasured distribution shift could explain the observed R² values and would undermine the claim of a general methodological advance.
minor comments (2)
  1. [Figure 2] Figure 2 and associated text: the L-shell binning (0.1 resolution) and the exact definition of the 6-hour forecast target should be stated explicitly in the caption for reproducibility.
  2. [Introduction] Introduction: several recent radiation-belt ML forecasting papers that also use GOES/POES inputs are not cited; adding them would better situate the novelty of the TimesFM hybrid.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the detailed and constructive review. The comments highlight important aspects for strengthening the statistical rigor, methodological clarity, and robustness assessment of our work. We address each major comment below and outline the revisions we plan to implement.

read point-by-point responses

  1. Referee: §4 (Results, performance tables): the central claim that TimesFM+Cov yields average R² = 0.9 (and 12–48 % relative gains) is presented without error bars, bootstrap intervals, or any statistical test comparing it to the second-best model; this omission is load-bearing because the advantage must be shown to be distinguishable from sampling variability, especially given the drop to R² = 0.77 at L = 6.0.

    Authors: We concur that uncertainty quantification and statistical comparisons are essential to substantiate the performance claims. In the revised version, we will compute bootstrap resampling-based confidence intervals for the R² scores at each L-shell and across the average. Furthermore, we will apply appropriate statistical tests, such as a paired t-test or Wilcoxon test on the per-sample prediction errors, to assess if the improvements over the second-best model are significant. These additions will be incorporated into the results section and tables. revision: yes

  2. Referee: §3 (Methods, hybrid pipeline): no ablation is reported that isolates the contribution of the ridge-regression covariates versus the zero-shot TimesFM residual step; without this, it remains unclear whether the hybrid construction is required for the quoted performance or whether a pure TimesFM forecast would suffice.

    Authors: We appreciate this suggestion for clarifying the hybrid model's value. We will perform and report an ablation study in the revised manuscript, including results for: (i) ridge regression on covariates alone, (ii) zero-shot TimesFM without covariates, and (iii) the full hybrid TimesFM+Cov. This will allow readers to evaluate the incremental benefit of combining the approaches. revision: yes

  3. Referee: §4–5 (Results and Discussion): the manuscript does not compare the distributions of key drivers (solar-wind speed, density, Kp) between the 2013–2023 training interval and the 2024 test window, nor does it test sensitivity to solar-cycle phase; because the test set is only six months long and occurs during the ascending phase of cycle 25, unmeasured distribution shift could explain the observed R² values and would undermine the claim of a general methodological advance.

    Authors: We recognize the importance of addressing potential distribution shifts and solar cycle effects. In the revision, we will add a new subsection or figure in the Results or Discussion that compares the distributions of solar-wind speed, density, and Kp (using means, standard deviations, and Kolmogorov-Smirnov tests) between the 2013-2023 training period and the 2024 test window. We will also include a discussion on the solar cycle phase, acknowledging that the test period is during the ascending phase of cycle 25 and that the six-month duration limits generalizability. While a full sensitivity analysis across multiple solar cycle phases would require additional data beyond the current scope, we will emphasize the strict temporal out-of-sample split as a key strength and discuss implications for future work. revision: partial

Circularity Check

0 steps flagged

No circularity: strict temporal train/test split yields genuine out-of-sample R²

full rationale

The paper trains linear regression, CNN, LSTM, Transformer-Encoder, and the hybrid TimesFM+Cov pipeline on 2013-2023 data, then evaluates all models on the strictly later January-June 2024 interval. The hybrid step fits ridge regression to historical covariates and applies zero-shot TimesFM only to residuals; because the test window post-dates all fitting and is never used to tune any hyper-parameter or evaluation metric, the reported average R² of 0.9 (versus <0.78 for baselines) does not reduce to the inputs by construction. No self-citations, uniqueness theorems, or ansatzes from prior author work appear in the derivation of the performance claims.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The paper relies on standard supervised-learning assumptions (i.i.d. training samples, stationarity of input-output relationships) and on the external validity of the chosen satellite and index data streams; no new physical entities or ad-hoc constants are introduced.

axioms (1)
  • domain assumption The relationship between the chosen inputs (POES, GOES, solar wind, geomagnetic indices) and 1-MeV flux is learnable from 2013-2023 data and remains stable enough for 2024 forecasts.
    Invoked when the models are trained on the earlier decade and evaluated on the later six months.

pith-pipeline@v0.9.0 · 5897 in / 1435 out tokens · 36337 ms · 2026-05-19T19:35:25.387311+00:00 · methodology

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