  End-to-end learning has become a popular method for joint transmitter and
receiver optimization in optical communication systems. Such approach may
require a differentiable channel model, thus hindering the optimization of
links based on directly modulated lasers (DMLs). This is due to the DML
behavior in the large-signal regime, for which no analytical solution is
available. In this paper, this problem is addressed by developing and comparing
differentiable machine learning-based surrogate models. The models are
quantitatively assessed in terms of root mean square error and training/testing
time. Once the models are trained, the surrogates are then tested in a
numerical equalization setup, resembling a practical end-to-end scenario. Based
on the numerical investigation conducted, the convolutional attention
transformer is shown to outperform the other models considered.
