  We derived an approximate non-linear interference (NLI) closed-form model
(CFM), capable of handling a very broad range of optical WDM system scenarios.
We tested the CFM over 8500 randomized C-band WDM systems, of which 6250 were
fully-loaded and 2250 were partially loaded. The systems had highly diversified
channel formats, symbol rates, fibers, as well as other parameters. We improved
the CFM accuracy by augmenting the formula with simple machine-learning
factors, optimized by leveraging the system test-set. We further improvedthe
CFM by adding a term which models special situations where NLI has high
self-coherence. In the end, we obtained a very good match with the results
found using the numerically-integrated Enhanced GN-model (or EGN-model). We
also checked the CFM accuracy by comparing its predictions with full-C-Band
split-step simulations of 300 randomized systems. The combined high accuracy
and very fast computation time (milliseconds) of the CFM potentially make it an
effective tool for real-time physical-layer-aware optical network management
and control.
