  We introduce a deep neural network learning scheme to learn the B\"acklund
transforms (BTs) of soliton evolution equations and an enhanced deep learning
scheme for data-driven soliton equation discovery based on the known BTs,
respectively. The first scheme takes advantage of some solution (or soliton
equation) information to study the data-driven BT of sine-Gordon equation, and
complex and real Miura transforms between the defocusing (focusing) mKdV
equation and KdV equation, as well as the data-driven mKdV equation discovery
via the Miura transforms. The second deep learning scheme uses the
explicit/implicit BTs generating the higher-order solitons to train the
data-driven discovery of mKdV and sine-Gordon equations, in which the
high-order solution informations are more powerful for the enhanced leaning
soliton equations with higher accurates.
