Learning Effective Soliton Dynamics from Scattering Data

In such settings, the inverse scattering transform (IST) of Ablowitz, Kaup, Newell, and Segur [2] has enjoyed a rich and successful history, and is now the standard theoretical framework for deriving reduced-order evolution equations for soliton dynamics. Although these derivations are traditionally of an analytical - rather than data-driven - nature, recent work has employed the IST formalism as a tool for experimental data analysis, using the technique to analyze soliton content from empirical measurements [8, 15, 24]. Moreover, recent approaches using alternative parameterization techniques have demonstrated that the learning of reduced-order, interpretable equations of motion for solitons is tenable in a data-driven setting [6, 26, 27]. Despite the success of this recent work, however, little effort has been devoted to developing a data-driven modeling approach based on the IST itself, most likely due to the fact that the framework is fundamentally problem-specific. In this paper, we address the question of whether effective soliton dynamics can be inferred directly from observed scattering data (as opposed to being derived or approximated analytically).