  Entanglement in quantum many-body systems is required for a variety of
quantum information tasks, making it crucial to identify the parameter space in
which the ground state is fully separable, known as the factorization surface
(FS). Nonetheless, the tuning parameters indicating FS for several quantum spin
models remain unknown. We employ symbolic regression (SR), a supervised
learning technique, to determine a closed-form expression in the parameter
regime corresponding to FS of quantum many-body Hamiltonians. We verify the
effectiveness of this method by examining the analytically tractable models,
namely a nearest-neighbor (NN) quantum transverse XY model with additional
Kaplan-Shekhtman-Entin-Aharony interactions, for which the FS is well-known. We
construct an accurate expression for the FS of the XYZ model by providing the
parameter set through the SR algorithm in which the ground state is derived by
matrix product state formalism. With a satisfactory level of accuracy, we
estimate the FS for the long-range XY model, and the NN XY model with
Dzyaloshinskii-Moriya type asymmetric interaction for which the factorization
surface is not known.
