Solar flare forecasting utilizing deep survival analysis - Probabilistic time-to-event analysis

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Table 1.

Statistical features X₁, …, X_p calculated for each extracted magnetogram feature Y of the SWAN-SF dataset.

Group	Stat. feature X_k	Description
Main	min Y	minimum
	max Y	maximum
	$\bar{Y}$ $\bar{Y}$	mean
	$\tilde{Y}$ $\tilde{Y}$	median
	IQR(Y)	interquartile range
	σ(Y)	standard deviation
	Var(Y)	variance
	γ₁(Y)	skewness
	κ(Y)	kurtosis

Ext 1	min ∂_tY	gradient minimum
	max ∂_tY	gradient maximum
	$\bar{\partial_{t} Y}$ $\overline{\partial_t Y}$	gradient mean
	$\tilde{\partial_{t} Y}$ $\widetilde{\partial_t Y}$	gradient median
	min ∂_t²Y	second derivative minimum
	max ∂_t²Y	second derivative maximum
	$\bar{\partial_{t}^{2} Y}$ $\overline{\partial_t^2 Y}$	second derivative mean
	$\tilde{\partial_{t}^{2} Y}$ $\widetilde{\partial_t^2 Y}$	second derivative median

Ext 2	$\bar{\| \partial_{t} Y \|}$ $\overline{\| \partial_t Y \|}$	average absolute change
	$\bar{\| \partial_{t}^{2} Y \|}$ $\overline{\| \partial_t^2 Y \|}$	average absolute change of gradient
	algorithmic	average slope of monotonically
	increasing sequences
	algorithmic	average slope of monotonically
	decreasing sequences
	algorithmic	slope of longest monotonically
	increasing sequence
	algorithmic	slope of longest monotonically
	decreasing sequence
	Y_\|Y\|	last value

Notes. We distinguish the common (main) summary statistics from extensions that include statistics on time derivatives (Ext 1) and descriptions of long-term trends for the individual features (Ext 2).

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