  The linear response of a photomultiplier tube (PMT) is a required property
for photon counting and reconstruction of the neutrino energy. The linearity
valid region and the saturation response of PMT were investigated using a
linear-alkyl-benzene (LAB)-based liquid scintillator. A correlation was
observed between the two different saturation responses, with pulse-shape
distortion and pulse-area decrease. The observed pulse-shape provides useful
information for the estimation of the linearity region relative to the
pulse-area. This correlation-based diagnosis allows an ${in}$-${situ}$
estimation of the linearity range, which was previously challenging. The
measured correlation between the two saturation responses was employed to train
an artificial-neural-network (ANN) to predict the decrease in pulse-area from
the observed pulse-shape. The ANN-predicted pulse-area decrease enables the
prediction of the ideal number of photoelectrons irrelevant to the saturation
behavior. This pulse-shape-based machine learning technique offers a novel
method for restoring the saturation response of PMTs.
