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arxiv: 2604.08928 · v1 · submitted 2026-04-10 · 🌌 astro-ph.SR

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A Convolutional Neural Network-Derived Catalog of Solar Flares from Soft X-Ray Observations

Andrew Melatos, Michael. S. Wheatland, Nastaran Farhang

Authors on Pith no claims yet

Pith reviewed 2026-05-10 18:01 UTC · model grok-4.3

classification 🌌 astro-ph.SR
keywords solar flaresconvolutional neural networkGOES observationspower-law distributionflare catalogwaiting time distributionobscuration effectsX-ray data
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The pith

A convolutional neural network identifies over seven times more solar flare candidates than the standard GOES catalog, extending the power-law distribution of flare peak fluxes to smaller events.

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

The paper trains a convolutional neural network on high-cadence GOES soft X-ray data to detect flare rise episodes, generating a catalog of 111,580 candidates between 2018 and 2025. Bayesian inference assigns a probability of being a true flare to each candidate using peak flux, rise time, and coincidence with known events. This larger sample shows a steeper power-law index for raw peak fluxes and extends the distribution by one order of magnitude at the small-flux end after background correction. The waiting-time distributions are consistent with a piecewise Poisson process, and apparent size-waiting time correlations are shown to be affected by obscuration effects. Readers care because a more complete flare catalog improves understanding of solar energy release and space weather impacts.

Core claim

The authors demonstrate that a CNN can be used to construct a new solar flare catalog from 1-second GOES soft X-ray observations by identifying rise episodes, resulting in 111,580 candidates compared to 14,612 in the GOES catalog. After applying Bayesian inference to quantify true positive probabilities, the catalog reveals a power-law distribution of peak fluxes that extends one decade lower in flux than the background-subtracted GOES catalog, with consistent indices after correction. Analysis of waiting times supports a piecewise Poisson process, while highlighting how obscuration biases size-waiting time correlations.

What carries the argument

Convolutional neural network trained to detect flare rise episodes in soft X-ray time series data, followed by Bayesian inference to assign true-positive probabilities based on flux, rise time, and temporal coincidence.

If this is right

  • The CNN catalog provides a more complete sample of small solar flares for statistical studies.
  • Power-law indices for background-corrected peak fluxes are similar between CNN and GOES catalogs.
  • Waiting-time distributions from both catalogs are broadly consistent with a piecewise Poisson process.
  • Previously reported correlations between flare sizes and waiting times are significantly influenced by obscuration effects.
  • The new catalog serves as a foundation for complete and consistent studies of solar flare statistics.

Where Pith is reading between the lines

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

  • This method could be extended to other time-series datasets from different instruments to create more comprehensive flare catalogs.
  • Improved detection of small flares may help quantify their contribution to total solar energy output and coronal heating.
  • Accounting for obscuration suggests that flare occurrence rates during active periods are higher than previously measured.

Load-bearing premise

The Bayesian inference accurately quantifies the true positive probability for each candidate based on peak flux, rise time, and temporal coincidence without significant false positives or missed events distorting the distributions.

What would settle it

Independent verification with higher-resolution instruments or multi-wavelength observations showing that a majority of the low-flux CNN candidates are not real flares would falsify the claimed extension of the power-law distribution.

Figures

Figures reproduced from arXiv: 2604.08928 by Andrew Melatos, Michael. S. Wheatland, Nastaran Farhang.

Figure 1
Figure 1. Figure 1: Top panel: GOES SXR data on 13 January 2024 with 83 manually selected rise episodes marked in red, and the remaining signal shown in blue. Vertical dashed lines indicate the peak times of the two events listed in the GOES catalog. Bottom panels: PDFs of the raw peak fluxes (left panel) and waiting times (right panel) for events in the reference catalog. The reference catalog includes 145 randomly selected … view at source ↗
Figure 2
Figure 2. Figure 2: An example of applying the CNN to GOES SXR data on 23 March 2024. Detected flare candidates (rise episodes) are marked in red, while the remaining signal is shown in blue. Peak times of events registered in the GOES, HEK, and SolO catalogs are indicated by vertical dashed gray lines in the top, middle, and bottom panels, respectively. Vertical dashed red lines mark CNN candidates below the confidence level… view at source ↗
Figure 3
Figure 3. Figure 3: Event count per flare class for GOES (left two histograms) and CNN (right two histograms) catalogs. Flare classes are color-coded according to the legend. For each catalog, separate histograms are graphed for raw and background-subtracted peak fluxes. the scattering of events). The lower envelope is defined as the value below which the lowest 1% of the peak fluxes fall, averaged within each three-month per… view at source ↗
Figure 4
Figure 4. Figure 4: Raw (top panel) and background-subtracted (bottom panel) peak fluxes versus time for events in the CNN catalog. The blue dashed lines mark the lower envelope of event sizes, corresponding to the 1st % quantile of peak fluxes within each three-month period. 4.5. Size and Waiting-Time Distributions The PDF of solar flare peak fluxes is often characterized as a power law over several orders of magnitude (M. S… view at source ↗
Figure 5
Figure 5. Figure 5: Flare peak flux distribution: PDF of raw (left panel) and background-subtracted (right panel) SXR peak flux for the GOES (blue histograms) and CNN (green histograms) Catalogs. The dashed curves indicate the fitted power laws over the applicable ranges. For ease of comparison, the left and right scales are the same. the varying lengths of the Bayesian blocks. The standard deviations are comparable to or exc… view at source ↗
Figure 6
Figure 6. Figure 6: Flare waiting time statistics. Top and middle panels: flare rates derived from applying the Bayesian block algorithm to the waiting-time distributions of the GOES (blue) and CNN (green) catalogs. Bottom panels: waiting-time distributions for both catalogs, along with the piecewise Poisson models of Equation (6), plotted on linear-log (left) and log-log (right) scales. diverges slightly more. We note that t… view at source ↗
Figure 7
Figure 7. Figure 7: Difference between mean waiting times after and before an event, as a function of SXR peak flux. The left and right columns show results for raw and background-subtracted peak fluxes, respectively. The top row includes all events, while the bottom row is restricted to events with peak flux above some threshold. Blue and green markers represent GOES and CNN data, respectively [PITH_FULL_IMAGE:figures/full_… view at source ↗
read the original abstract

A convolutional neural network (CNN) is used to construct a new catalog for solar flares based on high resolution (1-s cadence) Geostationary Operational Environmental Satellites (GOES) soft X-ray data. The CNN is trained to identify flare rise episodes. From 1 January 2018 to 22 August 2025, the algorithm detects 111,580 flare candidates, compared with 14,612 events in the corresponding GOES catalog. For each candidate, the probability of being a true positive is quantified by Bayesian inference based on the peak flux, rise time, and temporal coincidence with cataloged events where available. The flare size and waiting-time distributions are studied and compared with the GOES catalog. The CNN catalog shows a steeper power-law index for raw peak fluxes (-2.59 -\+ 0.02) than GOES (-2.25 -\+ 0.04), indicating the CNN's higher sensitivity to small events. After background correction, the indices are -1.97 -\+ 0.02 (CNN) and -2.05 -\+ 0.04 (GOES). The CNN catalog extends the power-law distribution of flare peak fluxes by one order of magnitude at the small-flux end compared with the GOES background-subtracted catalog. A Bayesian blocks analysis of the waiting-time distributions from the GOES and CNN catalogs indicates broad consistency with a piecewise Poisson process. We find that previously reported correlations between flare sizes and waiting times are significantly influenced by obscuration, that is, under-counting weaker or overlapping flares during periods of elevated flux. The new CNN catalog provides a foundation for complete and consistent studies of solar flare statistics.

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 paper trains a convolutional neural network on 1-s cadence GOES soft X-ray data to detect flare rise episodes, producing a catalog of 111,580 candidates from 2018–2025 versus 14,612 events in the official GOES catalog. Bayesian inference assigns true-positive probabilities to each candidate using peak flux, rise time, and temporal coincidence (where available). The authors compare power-law indices of raw and background-corrected peak-flux distributions, finding a steeper index (-2.59 ± 0.02) and one-order-of-magnitude extension at the low-flux end for the CNN catalog relative to GOES (-2.25 ± 0.04 raw; -2.05 ± 0.04 corrected). Waiting-time distributions are analyzed via Bayesian blocks, and previously reported size–waiting-time correlations are attributed to obscuration effects.

Significance. If the CNN detections and Bayesian probabilities are reliable, the work supplies a substantially larger flare catalog that extends statistical studies of flare energetics and occurrence rates to smaller events. The reported difference in power-law indices and the waiting-time analysis could inform flare-triggering models and space-weather statistics. However, the significance is limited by the absence of detailed validation for the CNN and the extrapolation of the Bayesian model below the GOES threshold.

major comments (3)
  1. [Methods (CNN training)] Methods section (CNN architecture and training): The manuscript provides no description of the CNN architecture, training set composition, loss function, hyperparameters, or quantitative validation metrics (e.g., precision-recall, confusion matrix, or cross-validation scores). These details are required to evaluate whether the network systematically over-detects small, non-GOES-coincident events that drive the steeper power-law index.
  2. [Bayesian inference] Bayesian inference section: For the 111k candidates lacking temporal coincidence with GOES events, the true-positive probability is computed from peak flux and rise time alone. No calibration or hold-out test is reported that validates the likelihood model or prior at fluxes an order of magnitude below the GOES threshold. This extrapolation is load-bearing for the claimed raw index of -2.59 ± 0.02 and the one-order extension of the background-corrected distribution.
  3. [Results (power-law analysis)] Results (power-law fits): The steeper CNN index and extended low-flux tail rest on the assumption that the Bayesian posterior correctly classifies the majority of small non-coincident candidates as true flares. Without an independent small-flare reference set or a sensitivity test that varies the Bayesian model, the difference from the GOES index (-2.25 ± 0.04) cannot be unambiguously attributed to higher sensitivity rather than false-positive contamination.
minor comments (2)
  1. [Abstract] Abstract: the notation “-2.59 -/+ 0.02” should be rendered as ±0.02 for clarity.
  2. [Results] The manuscript should include a table or figure summarizing CNN performance metrics on a held-out test set and the fraction of candidates accepted at different probability thresholds.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for their thorough and constructive review. The comments highlight important areas for clarification and strengthening of the validation. We address each major comment below and will incorporate revisions as noted.

read point-by-point responses

  1. Referee: Methods section (CNN architecture and training): The manuscript provides no description of the CNN architecture, training set composition, loss function, hyperparameters, or quantitative validation metrics (e.g., precision-recall, confusion matrix, or cross-validation scores). These details are required to evaluate whether the network systematically over-detects small, non-GOES-coincident events that drive the steeper power-law index.

    Authors: We agree that the submitted manuscript omitted these essential details. In the revised version we will add a dedicated subsection describing the CNN architecture (convolutional layers, kernel sizes, pooling, fully connected layers, and dropout), the training set construction (positive examples from GOES-flagged rise episodes and negative examples from quiet periods), the loss function (binary cross-entropy with class weighting), all hyperparameters (learning rate schedule, batch size, number of epochs, early stopping), and quantitative metrics including precision-recall curves, confusion matrices, and 5-fold cross-validation scores on held-out data. These additions will allow direct assessment of detection reliability at low fluxes. revision: yes

  2. Referee: Bayesian inference section: For the 111k candidates lacking temporal coincidence with GOES events, the true-positive probability is computed from peak flux and rise time alone. No calibration or hold-out test is reported that validates the likelihood model or prior at fluxes an order of magnitude below the GOES threshold. This extrapolation is load-bearing for the claimed raw index of -2.59 ± 0.02 and the one-order extension of the background-corrected distribution.

    Authors: The Bayesian model was constructed by fitting the likelihoods for peak flux and rise time on the subset of candidates that do coincide with GOES events (where ground truth is available) and then applying the same functional forms to non-coincident candidates. While the original submission did not include an explicit hold-out calibration below the GOES threshold, we will add in revision a sensitivity analysis that varies the prior and likelihood parameters over plausible ranges and recomputes the power-law index, demonstrating that the reported value of -2.59 ± 0.02 remains stable. We will also report the fraction of candidates retained at different probability thresholds. revision: partial

  3. Referee: Results (power-law fits): The steeper CNN index and extended low-flux tail rest on the assumption that the Bayesian posterior correctly classifies the majority of small non-coincident candidates as true flares. Without an independent small-flare reference set or a sensitivity test that varies the Bayesian model, the difference from the GOES index (-2.25 ± 0.04) cannot be unambiguously attributed to higher sensitivity rather than false-positive contamination.

    Authors: We acknowledge that an independent reference catalog of sub-GOES flares does not exist, which limits definitive external validation. However, the steeper index is obtained after applying the same Bayesian procedure to both catalogs and is consistent with the expectation that 1-s cadence data capture rise episodes missed by the standard GOES algorithm. In the revision we will add a sensitivity test that recomputes the power-law index after successively raising the minimum true-positive probability threshold (e.g., >0.5, >0.7, >0.9) and show that the index remains steeper than the GOES value even under conservative cuts. We will also compare the CNN detections against a small manually inspected sample of low-flux events from the same period. revision: partial

Circularity Check

0 steps flagged

No significant circularity in CNN catalog derivation or statistical claims

full rationale

The paper trains a CNN on GOES soft X-ray time series to detect flare rise episodes, generates 111k candidates, applies Bayesian inference using peak flux, rise time and temporal coincidence to assign true-positive probabilities, then fits power-law indices and waiting-time distributions directly to the resulting catalog and compares them to the independent GOES catalog. No equation or step reduces the reported indices (-2.59, -1.97) or the one-order extension claim to a fitted parameter or self-citation by construction. The analysis remains self-contained against external observational benchmarks with no load-bearing self-citations, ansatzes, or uniqueness theorems invoked.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The work relies on standard machine learning assumptions and statistical fitting, with the main additions being the trained CNN and the derived catalog.

free parameters (2)
  • CNN model parameters
    Weights and biases in the neural network are optimized during training on labeled data.
  • Power-law indices
    Fitted to the observed distributions in the catalog.
axioms (2)
  • domain assumption Flare rise episodes can be reliably identified from soft X-ray flux time series
    Core assumption for the CNN training and detection.
  • domain assumption Bayesian inference provides accurate probabilities based on the given features
    Used to validate candidates.

pith-pipeline@v0.9.0 · 5618 in / 1500 out tokens · 75143 ms · 2026-05-10T18:01:27.178416+00:00 · methodology

discussion (0)

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