  The magnetization process is a very important probe to study magnetic
materials, particularly in search of spin-liquid states in quantum spin
systems. Regrettably, however, progress of the theoretical analysis has been
unsatisfactory, mostly because it is hard to obtain sufficient numerical data
to support the theory. Here we propose a machine-learning algorithm that
produces the magnetization curve and the spin gap well out of poor numerical
data. The plateau magnetization, its critical field and the critical exponent
are estimated accurately. One of the hyperparameters identifies by its score
whether the spin gap in the thermodynamic limit is zero or finite. After
checking the validity for exactly solvable one-dimensional models we apply our
algorithm to the kagome antiferromagnet. The magnetization curve that we obtain
from the exact-diagonalization data with 36 spins is consistent with the DMRG
results with 132 spins. We estimate the spin gap in the thermodynamic limit at
a very small but finite value.
