We developed a reliable probabilistic solar-flare forecasting model using a deep neural network, named Deep Flare Net-Reliable (DeFN-R). The model can predict the maximum classes of flares that occur in the following 24 hr after observing images, along with the event occurrence probability. We detected active regions from 3 × 105 solar images taken during 2010-2015 by Solar Dynamic Observatory and extracted 79 features for each region, which we annotated with flare occurrence labels of X-, M-, and C-classes. The extracted features are the same as used by Nishizuka et al.; for example, line-of-sight/vector magnetograms in the photosphere, brightening in the corona, and the X-ray emissivity 1 and 2 hr before an image. We adopted a chronological split of the database into two for training and testing in an operational setting: the data set in 2010-2014 for training and the one in 2015 for testing. DeFN-R is composed of multilayer perceptrons formed by batch normalizations and skip connections. By tuning optimization methods, DeFN-R was trained to optimize the Brier skill score (BSS). As a result, we achieved BSS = 0.41 for ≥C-class flare predictions and 0.30 for ≥M-class flare predictions by improving the reliability diagram while keeping the relative operating characteristic curve almost the same. Note that DeFN is optimized for deterministic prediction, which is determined with a normalized threshold of 50%. On the other hand, DeFN-R is optimized for a probability forecast based on the observation event rate, whose probability threshold can be selected according to users' purposes.
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