Learning the inverse scattering map from the continuous Lax spectrum for nonlinear optical communications

Nonlinear effects increasingly limit high speed optical communication and challenge conventional signal processing methods. In this talk, I will present an affine map approximation of the inverse scattering transform. Our key result is that the transmitted signal can be accurately reconstructed using only the continuous part of the Lax spectrum, without explicitly using the discrete soliton spectrum. The learned operator also has a low rank, with its effective rank corresponding to the number of transmitted bits. This allows us to construct an efficient reduced order model. I will conclude with a complete signal recovery workflow and related results using machine learning.

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