  We consider the cosmological models based on the scalar-torsion gravity
implying non-minimal coupling between torsion and the scalar field as
modification of teleparallel equivalent of general relativity. Based on
generalized exact solutions of the equations of cosmological dynamics, the type
of scalar-torsion gravity was reconstructed. Also, based on observational
constraints on the values of the parameters of cosmological perturbations, the
type of the coupling function was determined. It was noted that any models of
cosmological inflation obtained on the basis of the proposed approach can be
verified by observational constraints.
