  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 h after
observing images, along with the event occurrence probability. We detected
active regions from 3x10^5 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. (2018); for example, line-of-sight/vector
magnetograms in the photosphere, brightening in the corona, and the X-ray
emissivity 1 and 2 h before an image. We adopted a chronological split of the
database into two for training and testing in an operational setting: the
dataset 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.
