Learning Effective Soliton Dynamics from Scattering Data

2026-07-01

AI Summary

This work proposes a novel data-driven approach to directly learn soliton dynamics from scattering data without requiring prior knowledge of the underlying scattering equations. By integrating the inverse scattering transform framework with weak-form system identification, the method constructs low-dimensional, interpretable dynamical models in the scattering domain—eliminating the need to assume explicit analytical equations or fit soliton trajectories. It is applicable to both perturbed and near-integrable systems and has been successfully validated on synthetic and experimental KdV-type shallow water wave data, accurately recovering effective dynamics consistent with classical inverse scattering theory. This demonstrates the method’s innovation and practical utility in data-driven modeling of nonlinear wave phenomena.

Abstract

The inverse scattering transform (IST) provides the standard theoretical framework for deriving soliton dynamics. Traditionally, such derivations have been of an analytical, rather than data-driven, nature. In this paper, we combine the conceptual framework of the IST with weak-form system identification methods to discover effective soliton dynamics directly from observed scattering data, without assuming prior knowledge of the scattering equations. Our method avoids parameterizing solitary waves via ad hoc curve-fitting by working in the scattering domain, yielding interpretable low-dimensional models that remain valid in perturbed and near-integrable regimes. We demonstrate the performance of the proposed approach on synthetic and experimental data governed by shallow-water equations of Korteweg--de Vries-type and recover models that are consistent with canonical IST theory.

Problem

• soliton dynamics
• inverse scattering transform
• scattering data
• data-driven modeling
• weak-form system identification

Innovation

• inverse scattering transform
• system identification
• soliton dynamics
• data-driven modeling
• scattering data