  A normalized batch gradient descent optimizer is proposed to improve the
first-order regular perturbation coefficients of the Manakov equation, often
referred to as kernels. The optimization is based on the linear
parameterization offered by the first-order regular perturbation and targets
enhanced low-complexity models for the fiber channel. We demonstrate that the
optimized model outperforms the analytical counterpart where the kernels are
numerically evaluated via their integral form. The enhanced model provides the
same accuracy with a reduced number of kernels while operating over an extended
power range covering both the nonlinear and highly nonlinear regimes. A
$6-7$~dB gain, depending on the metric used, is obtained with respect to the
conventional first-order regular perturbation.
