  Designing and optimizing optical amplifiers to maximize system performance is
becoming increasingly important as optical communication systems strive to
increase throughput. Offline optimization of optical amplifiers relies on
models ranging from white-box models deeply rooted in physics to black-box
data-driven and physics-agnostic models. Here, we compare the capabilities of
white-, grey- and black-box models on the challenging test case of optimizing a
bidirectional distributed Raman amplifier to achieve a target
frequency-distance signal power profile. We show that any of the studied
methods can achieve similar frequency and distance flatness of between 1 and
3.6 dB (depending on the definition of flatness) over the C-band in an 80-km
span. Then, we discuss the models' applicability, advantages, and drawbacks
based on the target application scenario, in particular in terms of
flexibility, optimization speed, and access to training data.
