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The magnetization process is a very important probe to study magneticmaterials, particularly in search of spin-liquid states in quantum spinsystems. Regrettably, however, progress of the theoretical analysis has beenunsatisfactory, mostly because it is hard to obtain sufficient numerical datato support the theory. Here we propose a machine-learning algorithm thatproduces the magnetization curve and the spin gap well out of poor numericaldata. The plateau magnetization, its critical field and the critical exponentare estimated accurately. One of the hyperparameters identifies by its scorewhether the spin gap in the thermodynamic limit is zero or finite. Afterchecking the validity for exactly solvable one-dimensional models we apply ouralgorithm to the kagome antiferromagnet. The magnetization curve that we obtainfrom the exact-diagonalization data with 36 spins is consistent with the DMRGresults with 132 spins. We estimate the spin gap in the thermodynamic limit ata very small but finite value.

Machine learning as an improved estimator for magnetization curve and spin gap