  We present a physics-informed machine learning (PIML) scheme for the feedback
linearization of nonlinear discrete-time dynamical systems. The PIML finds the
nonlinear transformation law, thus ensuring stability via pole placement, in
one step. In order to facilitate convergence in the presence of steep gradients
in the nonlinear transformation law, we address a greedy-wise training
procedure. We assess the performance of the proposed PIML approach via a
benchmark nonlinear discrete map for which the feedback linearization
transformation law can be derived analytically; the example is characterized by
steep gradients, due to the presence of singularities, in the domain of
interest. We show that the proposed PIML outperforms, in terms of numerical
approximation accuracy, the traditional numerical implementation, which
involves the construction--and the solution in terms of the coefficients of a
power-series expansion--of a system of homological equations as well as the
implementation of the PIML in the entire domain, thus highlighting the
importance of continuation techniques in the training procedure of PIML.
