# Learning Effective Soliton Dynamics from Scattering Data

arXiv: https://arxiv.org/abs/2607.01545 · HTML: https://mlsanity.com/paper/2607.01545/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 26 references that are in the map.
- First posted on arXiv 1 Jul 2026.

## Builds on (most cited first, 6 of 6)

- [Weak SINDy For Partial Differential Equations](https://mlsanity.com/paper/2007.02848/) (2020)
- [Weak-Form Inference for Hybrid Dynamical Systems in Ecology](https://mlsanity.com/paper/2405.20591/) (2024)
- [Combining machine learning with physics: A framework for tracking and sorting multiple dark solitons](https://mlsanity.com/paper/2111.04881/) (2021)
- [Computer Assisted Discovery of Integrability via SILO: Sparse Identification of Lax Operators](https://mlsanity.com/paper/2503.00645/) (2025)
- [Learning effective models from network dynamics data with multiple initial conditions using weak form SINDy](https://mlsanity.com/paper/2605.30432/) (2026)
- [Robust Moment Identification for Nonlinear PDEs via a Neural ODE Approach](https://mlsanity.com/paper/2506.05245/) (2025)

## Abstract (arXiv)

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.