Machine learning reveals systematic accumulation of electric current in lead-up to solar flares

Classification of Flaring and Nonflaring Active Regions.

We chronologically split the available AR data into two parts. The training and validation data comprise ARs between May 2010 and December 2013 and the test data comprise ARs between January 2014 and April 2016. We explicitly study the development of newly emerged ARs, identified from the first recorded observation within ±60○ of the central meridian. Between May 2010 and April 2016, only 22 flaring ARs emerged on the visible solar disk, and hence all “emerging ARs” are included in the test data. The total number of ARs considered is listed in Table 2.

We consider observations from flaring ARs which are within ±72 h of M- or X-class flares for training. Note that all magnetic-field observations from ARs in the training and validation data are not needed to optimally train the machines. Instead, we pick an observation every 96 min from within ±6 h of flares and every 864 min otherwise (within ±72 h of flares). For nonflaring ARs, we pick an observation every 900 min for training. The choice of these time intervals is inconsequential to the results as long as the number of AR observation samples is adequate for training. For robust training, we apply 10-fold cross-validation. We randomly split the flaring and nonflaring ARs in the training and validation data in 10 parts and use observations from ARs in 9 parts for training and the remaining part for validation. This process is repeated 10 times. Thus, we avoid mixing AR observations in the training and validation sets and thereby avoid artificially boosting the machine performance (28). Total numbers of observations used for training from flaring ARs and nonflaring ARs are 768 and 4,323, respectively (SI Appendix, Table S2).

A straightforward performance measure for classification problems is accuracy, defined as the fraction of correctly classified observations; i.e., accuracy=(TP+TN)/(TP+FN+FP+TN). However, there are five times as many nonflaring as flaring ARs in the training and validation data. Hence, the classification problem considered here is class imbalanced and accuracy is not useful (24). Recall, defined as the accuracy for each class, is a more relevant performance metric. For the positive class, i.e., flaring ARs, recall=TP/(TP+FN). Using the training and validation dataset, we compare performance of three ML algorithms—logistic regression (Logit), support vector machines (SVM), and gradient boosting (GB)—for classification of flaring and nonflaring ARs (SI Appendix). SVM yields slightly higher 10-fold cross-validation recall value 0.83±0.12 (SI Appendix).

Time Evolution of Machine Prediction.

We are particularly interested in time evolution of magnetic fields in flaring ARs, and hence we obtain recall of the machine prediction on time series of observations from flaring ARs. A time series X(t) of SHARP feature vectors representing continuous AR observations yields a time series of machine prediction Y(t). Flares are known to be temporally clustered (33) and hence we focus on evolution within ±72 h of flares. We compile time series of observations during a window t−TF∈[−72,72]h centered around a flare event TF. Whenever two consecutive flares on an AR are separated by <144 h, we split the observations between the flare events into two halves and consider the first half as the postflare category of the first flare and the second half as belonging to the preflare category of the second flare. We align all such time series from flaring ARs at t−TF=tr=0, the time of flare events, yielding cotemporal X(tr) and Y(tr) time series for time tr with respect to the flare. The machine prediction averaged over the flaring-AR population Y¯(tr)=(1/N(tr))∑i=1N(tr)Yi(tr) gives instantaneous recall or identification rate at time tr. Here, N(tr) is the number of magnetic-field observations available at time tr from the flaring-AR population (SI Appendix, Fig. S2). Thus, recall Y¯(tr) is a measure of the time-evolving correlation between SHARP features and flare activity, obtained using the trained machine. Similarly, the machine predictions can be obtained for all observations from nonflaring ARs. Since there is no characteristic time event on nonflaring ARs, we find the average machine prediction defined as ⟨Y⟩=(1/N)∑iNYi. ⟨Y⟩ is time and population average over all N nonflaring AR observations and gives the false-positive rate.

We can now obtain time evolution of machine prediction for flaring ARs in the test data using the trained SVM. Note that none of the observations from the test data were considered during training and cross-validation of the machine, i.e., SVM, performance. Thus, all observations in the test data are previously “unseen” by the machine. Similar to the training data, recall or identification rate is consistently high (>0.6) for days before and after flares for flaring ARs in the test data (Fig. 1). This indicates that flaring ARs persist in a flare-productive state for days before and after flares. With proximity to flares, identification rate increases to a maximum of 0.91, 24 h before flare. This recall value is comparable to reported results of flare forecasting using ML (24) and significantly higher than recall ∼0.55 obtained through operational forecasts based on subjective AR analyses (as estimated by ref. 9).

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Fig. 1.

Time evolution of recall Y¯(tr)=1/N(tr)∑iN(tr)Yi(tr) for flaring ARs in the test data before and after a flare using SVM. The recall peaks at ∼0.9, 24 h before flares. For comparison, machine identification error rate (false-positive rate) for nonflaring ARs in the test data ⟨Y⟩ is ∼0.1 (Table 3). Shaded area indicates 1σ error bar.

The number of observations separated from flares by >72 h reduces significantly to continue time evolution analysis beyond 72 h before and after flares (SI Appendix, Fig. S2). Hence, we obtain time- and population-averaged machine prediction ⟨Y⟩flaring=(1/Nflaring)∑iNflaringYi, where Nflaring is the number of all flaring AR observations separated from flares >72 h. ⟨Y⟩flaring thus gives recall for such flaring AR observations. Similarly, recall for nonflaring ARs is obtained by 1−⟨Y⟩non flaring. Time- and population-averaged values of recall for flaring and nonflaring ARs are reported in Table 3. The high value of recall ∼0.75 even for observations separated from flares >72 h suggests that SHARP features derived from magnetic fields of flaring ARs are statistically significantly different from those of nonflaring ARs.

Evolution of Magnetic Fields in Flaring Active Regions.

We have trained an SVM to distinguish between SHARP features derived from magnetic fields in flaring and nonflaring ARs with high fidelity. To understand magnetic-field evolution in ARs, we analyze TP and FN populations from flaring ARs and TN and FP populations from nonflaring ARs, as categorized by the machine. We include SHARP features from all ARs in the training and validation data as well as the test data. In Table 4, time- and population-averaged values of SHARP features over flaring AR observations separated from flares >72 h and nonflaring AR observations are listed. As expected, average TP (also FP) values are strikingly higher than average TN (also FN) values. This difference is listed in terms of SD of average TN values for each of the SHARP parameters, in the last column in Table 4. Total unsigned flux (USFLUX) and total unsigned current helicity (TOTUSJH) are leading contributors to machine classification. Whereas mean free energy (MEANPOT) and area with shear >45○ (SHRGT45) minimally influence the classification. Also, SHARP features that lead classification between flaring and nonflaring ARs are an extensive measure of AR magnetic field.

Categories of SHARP features are further highlighted by the Pearson correlation matrix in Fig. 2. Strongly correlated features are divided into the following groups: (i) extensive features (area, total unsigned flux, total free energy, total Lorentz force, total unsigned vertical current, and total unsigned current helicity), (ii) features that scale with electric current in AR (absolute net current helicity and sum of net current per polarity), (iii) measures of AR nonpotential energy (mean free energy and area with shear >45○), (iv) sum of flux near polarity inversion line (15), and (v) vertical Lorentz force on AR. From Table 4, we see that the extensive features dominate machine classification, followed by the features that scale with electric current. Meanwhile, features that scale with AR mean nonpotential energy contribute the least.

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Fig. 2.

Pearson correlation matrix for SHARP features (see Table 1 for description). Based on the degree of correlation, SHARP features group together in categories representing (i) AR magnetic-field scale, (ii) AR energy buildup, (iii) AR nonpotentiality, (iv) Schrijver R value, and (v) Lorentz force on AR. P value of correlation between total vertical Lorentz force (TOTFZ) and R value is 0.09. All other P values are ≪0.001.

SHARP features from each of the groups above characteristically evolve before and after flares. For the mth entry of each SHARP feature vector, we calculate the time evolution of population-averaged value Xm¯(tr), before and after flares, over TP and FN flaring AR observations. SHARP features that scale with AR size are significantly correlated with flare activity. However, similar to total unsigned magnetic flux (Fig. 3A) and total unsigned current helicity (Fig. 3B), average TP values of these SHARP features remain approximately constant before and after flaring and thus characterize flaring AR populations. The average TP value of absolute net current helicity (and also the sum of net current per polarity) systematically increases by about two times during the lead-up to the flare and decreases subsequently (Fig. 3C). This implies that free-energy buildup in large-scale ARs, manifested in field measurements in the form of photospheric electric current, is dominantly responsible for flares (4, 17). The high, distinct average-TP value of flux in the neighborhood of the magnetic polarity inversion line (Fig. 3D) is also a striking feature of flaring ARs (15). AR-associated nonpotential energy, which is weakly correlated with electric current (Fig. 2), is not a leading criterion to discriminate between flaring and nonflaring ARs (Fig. 3E). However, the average FN value of nonpotential energy shows a sharp increase hours before flare. The average TP value of total vertical Lorentz force (Fig. 3F) also systematically decreases from days before flares.

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Fig. 3.

Time evolution of population-averaged values of SHARP features (see Table 1 for description) before and after flares. Average SHARP feature values over true positive (TP) and false negative (FN) flaring AR observations within ±72 h of flare events are obtained. Average TP value of total unsigned flux (A) and total unsigned current helicity (B) remains approximately constant before and after flares. Average TP value of absolute net current helicity (C) shows a characteristic steady preflare increase and decrease postflare. Sum of flux near polarity inversion line (R value) (D) also shows a distinct average TP value. For AR nonpotential energy (E), average FN value undergoes a sharp increase ∼12 h before flares. Average TP value of vertical Lorentz force (F) shows continuous preflare decrease, i.e., increase in downward-directed Lorentz force on the AR. Shaded area indicates 1σ error bars. Key in A applies to A–F.

Development of Emerging Flaring ARs.

Our analysis shows that extensive SHARP features characteristically distinguish flaring and nonflaring AR populations. Also, values of the extensive features remain approximately constant days before and after flares. On the contrary, newly emerged ARs must start with small values of the extensive SHARP features. Therefore, we are interested in understanding how emerging ARs transition to flare-productive states before the first flare. For emerging flaring ARs, we compile observations in a time span tr∈[−72,0] h where tr=t−TF is time with respect to the first-flare event TF and compute recall Y¯(tr) and TP and FN population-average values for each mth SHARP feature Xm¯(tr). We see that the machine identification or recall of newly emerged ARs steadily improves with time and yields a maximum recall value of ∼0.7, 6 h before the first flares (Fig. 4A). In comparison, the false-positive rate for emerging nonflaring ARs is ∼0.1 (recall ∼0.9). For emerging flaring ARs, the population-averaged TP value of absolute net-current helicity (Fig. 4B) shows a steady increase, albeit the error bars are significant. Most notably, the population-averaged TP value of vertically downward-directed Lorentz force increases continuously from days before the flare (Fig. 4C). This may be interpreted as evidence of Maxwell-stress buildup in the corona above flaring active regions, which imparts an enhanced downward-directed Lorentz force on the photosphere. For FNs in the emerging flaring AR observations, area (Fig. 4D) and mean nonpotential energy (Fig. 4E) show marked increase hours before flare.

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Fig. 4.

Machine identification and time evolution of SHARP features for emerging flaring ARs. These emerging ARs are first observed within ±60○ of the central meridian. (A) Evolution of population-averaged identification rate or recall Y¯(tr)=1/N(tr)∑iN(tr)Yi(tr) over emerging flaring ARs before 72 h of first flare is shown. For comparison, machine identification error rate (false-positive rate) ⟨Y⟩ for emerging nonflaring ARs is ∼0.1. (B–F) Time evolution of population-averaged values of SHARP features (see Table 1 for description) over true positive (TP) and false negative (FN) emerging flaring AR observations 72 h before first flare. (B) Average TP value of absolute net current helicity increases steadily before flares. (C) Average TP value of vertical Lorentz force on ARs systematically decreases before flares, i.e., increase in downward-directed Lorentz force. (D and E) Average FN values of area (D) and nonpotential energy (E) increase sharply hours before flares. (F) Average FN value of R value increases gradually before flares. Shaded area indicates 1σ error bars. Key in B applies to B–F.