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We develop the method based on $ \mathcal{B} $-automorphism for finding newlattice integrable models with various dimensions of local Hilbert spaces. Weinitiate the technique by implementing it to the two-dimensional models andresolve classification problem, which not only confirms known vertex modelsolution space, but also extends to the new $ \mathfrak{sl}_{2} $ deformedsector. The generalisation of the approach for string integrable models isprovided and allows to find new integrable deformations and associated $ R$-matrices. Hence novel integrable solutions appear to be of non-differenceform that admit $ AdS_2 $ and $ AdS_3 $ $ S $-matrices as special cases, wealso obtain embedding of double deformed sigma model $ R $-matrix into one ofthe solutions. The braiding and crossing for the found models as well as theiremergence with respect to the deformation parameter $ k $ are shown.

Automorphic symmetries and $ AdS_n $ integrable deformations