  In optical fiber communication, system identification (SI) for the nonlinear
Schr\"odinger equation (NLSE) has long been studied mainly for fiber
nonlinearity compensation (NLC). One recent line of inquiry to combine a
behavioral-model approach like digital backpropagation (DBP) and a data-driven
approach like neural network (NN). These works are aimed for more NLC gain;
however, by directing our attention to the learned parameters in such a SI
process, system status information, i.e., optical fiber parameters, will
possibly be extracted. Here, we show that the model-based optimization and
interpretable nature of the learned parameters in NN-based DBP enable
transmission line monitoring, fully extracting the actual in-line NLSE
parameter distributions. Specifically, we demonstrate that longitudinal loss
and dispersion profiles along a multi-span link can be obtained at once,
directly from data-carrying signals without any dedicated analog devices such
as optical time-domain reflectometry. We apply the method to a long-haul
(~2,080 km) link and various link conditions are tested, including excess loss
inserted, different fiber input power, and non-uniform level diagram. The
measurement performance is also investigated in terms of measurement range,
accuracy, and fiber launch power. These results provide a path toward
simplified and automated network management as another application of DBP.
