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Deep Flare Net (DeFN) model for solar flare prediction

Naoto Nishizuka, Komei Sugiura, Yuki Kubo, Mitsue Den, Mamoru Ishii

arXiv:1805.03421v1astro-ph.SR

TL;DR

Solar flares remain difficult to predict within 24 h, even with increasing near-real-time observations. DeFN uses a deep neural network with manually selected solar features and achieves TSS=0.8 for ≥M-class and TSS=0.63 for ≥C-class flares operationally, while retaining feature interpretability.

  • Problem

    Human forecasting remains challenged by the unresolved flare mechanism and difficulty predicting flares within the following 24 h.

  • Method

    DeFN applies a supervised deep neural network to 79-dimensional solar-region feature vectors, using chronological 2010-2014 training and 2015 testing data.

  • Results

    TSS=0.8 for ≥M-class flares and TSS=0.63 for ≥C-class flares were achieved in an operational setting.

  • Takeaways & Limitations

    Because DeFN uses manually selected features, the features most effective for flare prediction can be analyzed after evaluation.

  • Takeaways & Limitations

    Feature-ranking analysis requires an estimated 160-240 GPU-hours, or 7-10 days, for 80 features.

Abstract

from arXiv · show

We developed a solar flare prediction model using a deep neural network (DNN), named Deep Flare Net (DeFN). The model can calculate the probability of flares occurring in the following 24 h in each active region, which is used to determine the most likely maximum classes of flares via a binary classification (e.g., >=M class versus <M class or >=C class versus <C class). From 3x10^5 observation images taken during 2010-2015 by Solar Dynamic Observatory, we automatically detected sunspots and calculated 79 features for each region, to which flare occurrence labels of X-, M-, and C-class were attached. We adopted the features used in Nishizuka et al. (2017) and added some features for operational prediction: coronal hot brightening at 131 A (T>=10^7 K) and the X-ray and 131 A intensity data 1 and 2 h before an image. For operational evaluation, we divided the database into two for training and testing: the dataset in 2010-2014 for training and the one in 2015 for testing. The DeFN model consists of deep multilayer neural networks, formed by adapting skip connections and batch normalizations. To statistically predict flares, the DeFN model was trained to optimize the skill score, i.e., the true skill statistic (TSS). As a result, we succeeded in predicting flares with TSS=0.80 for >=M-class flares and TSS=0.63 for >=C-class flares. Note that in usual DNN models, the prediction process is a black box. However, in the DeFN model, the features are manually selected, and it is possible to analyze which features are effective for prediction after evaluation.

1. Introduction

Solar-flare physics remains unresolved, and predicting flares within the next 24 hours is difficult even with abundant near-real-time observations. This motivates machine-learning approaches designed for operational forecasting, where chronological separation makes prediction harder than random dataset splitting.

  • Motivation: Solar flares arise from stored magnetic energy around sunspots, but their physical mechanism remains unresolved after more than a century.Energy storage and triggering processes are associated with emerging photospheric flux.
  • Motivation: Despite the growth of near-real-time solar observations, human forecasters still struggle to predict flares within the following 24 hours.This forecasting difficulty motivates automated prediction methods.
  • Flare precursors: Larger, more complex sunspots tend to produce larger flares, while rapid magnetic changes and localized brightening can precede eruptions by 2–3 hours.The cited precursors include UV 1600 Å and coronal brightening.
  • Related work: Machine-learning methods for flare prediction include neural networks, regression, k-nearest neighbors, support vector machines, LASSO, random forests, extremely randomized trees, and fuzzy clustering.These approaches were developed to handle the growing volume of solar-observation data.
  • Operational forecasting: Randomly shuffled splits favored k-NN, but chronological operational splits separate similar samples and made earlier k-NN, SVM, and ERT models insufficiently precise.The study therefore focused on DNNs and added temporal-intensity features for operational prediction.

2. Basic Architecture of Neural Networks

A neural network repeatedly applies affine and nonlinear transformations to map inputs into a representation that can be linearly separated. Its layers use weights, biases, and activation functions, with softmax producing binary flare-class probabilities.

  • Neural-network structure: A neural network repeats linear or affine and nonlinear conversions across layers to transform data into a linearly separable representation.Nonlinear activations enable representations unavailable from linear conversions alone.
  • Layer operations: Each layer maps input x to output y using a weight matrix W, bias b, and activation function f.The paper identifies f as the activation function and W and b as the layer parameters.
  • Activation functions: ReLU is used from the first through the second-last layers, providing positive outputs, sparse distributions, and faster calculation.The stated speed advantage follows from its derivative being one.
  • Output layer: Softmax in the last layer converts the network output into probabilities for two flare classes, such as ≥M versus <M.This supports binary flare classification.
  • Architecture depiction: Figure 1 simplifies multilayer connections by representing hidden layers as squares and omitting biases from the displayed nodes.The same simplified style is used later to describe DeFN.

3. Overview of Deep Flare Net (DeFN)

DeFN builds an operational flare-prediction pipeline from SDO and GOES observations: it detects and tracks active regions, then derives features for prediction. The workflow combines magnetograms, ultraviolet and coronal imagery, and soft-X-ray light curves.

  • Data acquisition: The pipeline downloads line-of-sight and vector magnetograms, 1600 Å and 131 Å filter images, and soft-X-ray light curves from SDO and GOES.These observations supply the inputs for subsequent active-region detection and feature extraction.
  • Active-region processing: Active regions are detected from full-disk line-of-sight magnetograms and tracked through their time evolution.Tracking provides the region-level basis for extracting predictive features.
  • Feature extraction: For each active region, the workflow extracts solar features from line-of-sight and vector magnetograms, UV 1600 Å images, GOES 1–8 Å X-rays, and hot coronal 131 Å brightening.The 131 Å channel captures hot coronal emission associated with flaring regions.

4. Details of Deep Flare Net (DeFN) model

DeFN combines 79 standardized solar features with a deep multilayer neural network to estimate binary flare-class probabilities. Its inputs include automatically detected active regions and added hot-coronal and time-lagged emission features, while skip connections, batch normalization, and weighted training support classification.

  • Active-region detection: 3×10^5 full-disk magnetogram images were processed at 1-hour cadence to detect active regions using a 140 G threshold.Detected-region coordinates were transferred to images at other wavelengths.
  • Feature extraction: The feature set added hot coronal brightening above 10^7 K and 131 Å and GOES X-ray emissions measured 1 and 2 hours before each image.Because GOES X-ray intensity is full-disk integrated, maximum 131 Å intensity was calculated for each active region.
  • Classification architecture: DeFN maps 79-dimensional standardized feature vectors to probabilities for ≥M-class and <M-class or non-flare events.The category with the larger probability is selected.
  • Classification architecture: The network uses ReLU activations, a final softmax layer, skip connections, and batch normalization across multiple layers.Skip connections were used to increase precision and avoid divergence in deeper networks.
  • Training: Training used weighted cross-entropy because flare occurrence ratios are imbalanced, with class weights set as inverse occurrence ratios.Architectures with 5–9 layers and different skip-connection configurations were surveyed.

5. Results

DeFN was evaluated for 24-hour flare prediction using chronological training on 2010–2014 data and testing on 2015 data. It achieved TSS=0.80 for ≥M-class flares and TSS=0.63 for ≥C-class flares, although the imbalanced evaluation favored increased detection when overpredicting flares.

  • Operational evaluation: 2010–2014 data were used for training and validation, while 2015 data were reserved for chronological testing in the operational evaluation.Chronological separation makes prediction more difficult than random dataset splitting.
  • Prediction tasks: The model performed two binary tasks: ≥M-class versus <M-class/non-flare and ≥C-class versus <C-class/non-flare.X-class flares were not predicted separately because too few training examples were available.
  • Evaluation behavior: Overprediction increased TSS because missed flares decreased while the false-positive term changed only slightly under the highly imbalanced event distribution.The contingency tables contained many more true negatives than flare events.
  • Skill scores: TSS=0.80 was achieved for ≥M-class flare prediction in the operational setting.The reported evaluation also included POD, CSI, FAR, HSS, and accuracy.
  • Skill scores: TSS=0.63 was achieved for ≥C-class flare prediction in the operational setting.The reported results were compared with human forecasts and baseline SVM, kNN, and ERT algorithms.

6. Summary and Discussion

DeFN predicts whether active regions will produce flares within 24 h using a supervised DNN and manually selected solar features. In chronological operational testing, it achieved TSS=0.8 for ≥M-class flares and TSS=0.63 for ≥C-class flares, while retaining feature interpretability.

  • Model and operational prediction: DeFN predicts maximum flare classes within the following 24 h using active-region probabilities and binary classifications for ≥M-class or ≥C-class flares.The model uses manually selected features derived from solar observation images and active-region detection.
  • Operational results: TSS=0.8 for ≥M-class flares and TSS=0.63 for ≥C-class flares in the operational setting.The dataset from 2010–2014 was used for training and validation, while 2015 was reserved for testing.
  • Operational results: The operational evaluation used chronological training and testing datasets, which are more difficult than randomly shuffled splits.The model was evaluated on the 2015 dataset after training and validation on 2010–2014 data.
  • Interpretability: Manually selected features can be analyzed to identify those most effective for flare prediction.Feature ranking can be investigated by removing features individually and measuring skill-score variation.
  • Operational comparison: The reported DeFN TSS values are compared with operational forecasting results from NICT, Belgium, and NOAA.The paper notes that TSS is recommended for space-weather forecasting but that suitable measures for rare-event forecasts remain under discussion.
  • Interpretability: Feature-ranking analysis requires an estimated 7–10 days of GPU computation for 80 features.The estimated total is 160–240 h, or 2–3 h per feature multiplied by 80 features.

A.1. Skip Connection (Residual Network)

The DeFN model uses skip connections that learn residual functions between layers, allowing deeper networks while avoiding ineffective layer transformations. The connection adds the input to the learned residual output.

  • Purpose: Residual networks were introduced because simply increasing the number of layers decreases model precision.The residual formulation enabled the number of layers to increase successfully.
  • Residual mapping: Skip connections learn a residual function between the input and output instead of requiring every intervening layer to transform the signal directly.The residual function F uses parameters λ to connect the layers between input x and output.
  • Residual mapping: The skip connection is represented by y = F(x; λ) + x, adding the input x to the residual transformation.This identity mapping is the defining operation of the residual connection.
  • Purpose: Layers that are not worth learning can be skipped, enabling deeper networks and more complicated model representations.The passage describes this as neglecting or skipping the S layers between the input and output of the connection.

A.2. Batch Normalization (BN)

Batch normalization standardizes layer inputs during training to stabilize the training process. Its output rescales normalized mini-batch values using learnable parameters.

  • Purpose: Batch normalization standardizes input parameters at each layer during training and stabilizes the training process.The mini-batch is normalized during each training pass.
  • Normalization: The normalization uses the mini-batch average µ_B and dispersion σ_B, with ϵ preventing division by zero.The mini-batch corresponds to the training examples processed in one forward/backward pass.
  • Output transformation: The output applies learnable scale γ and offset β to each normalized hidden-layer node.γ and β are optimized like weight parameters, while i indexes hidden-layer nodes.
  • Training objective: The model uses weighted cross entropy because imbalanced flare occurrence makes unweighted cross entropy inadequate for better precision.The class weights w_k may use the inverse class-occurrence ratio.

B.1. Definitions of Skill Scores

The paper evaluates flare predictions with standard contingency-table skill scores, including discrimination, false-alarm, agreement, and accuracy measures. These scores are computed from true and false positives and negatives.

  • Skill scores: The evaluation includes POD, CSI, FAR, HSS, TSS, and accuracy as flare-prediction skill scores.These metrics are presented as established measures for evaluating prediction results.
  • Detection and success: POD measures detection using true positives and false negatives.Its contingency-table terms are TP and FN.
  • Detection and success: CSI measures critical success using true positives, false positives, and false negatives.Its contingency-table terms are TP, FP, and FN.
  • False alarms: FAR measures false alarms using false positives and true positives.Its contingency-table terms are FP and TP.
  • Agreement and accuracy: HSS and TSS evaluate forecast skill using combinations of TP, FP, FN, and TN.Accuracy also uses all four contingency-table counts.
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