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Data-driven model reconstruction for nonlinear wave dynamics

Ekaterina Smolina1, Lev Smirnov1, Daniel Leykam2, Franco Nori3,4,5, and Daria Smirnova3,6

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Phys. Rev. Research 7, 023314 – Published 26 June, 2025

DOI: https://doi.org/10.1103/2jh8-p5y2

Abstract

The use of machine learning to predict wave dynamics is a topic of growing interest, but commonly used deep-learning approaches suffer from a lack of interpretability of the trained models. Here, we present an interpretable machine learning framework for analyzing the nonlinear evolution dynamics of optical wave packets in complex wave media. We use sparse regression to reduce microscopic discrete lattice models to simpler effective continuum models, which can accurately describe the dynamics of the wave packet envelope. We apply our approach to valley-Hall domain walls in honeycomb photonic lattices of laser-written waveguides with Kerr-type nonlinearity and different boundary shapes. The reconstructed equations accurately reproduce the linear dispersion and nonlinear effects, including self-steepening and self-focusing. This scheme is proven free of the a priori limitations imposed by the underlying hierarchy of scales traditionally employed in asymptotic analytical methods. It represents a powerful interpretable machine learning technique of interest for advancing design capabilities in photonics and framing the complex interaction-driven dynamics in various topological materials.

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Phys. Rev. Research 7, 023314– Published 26 June, 2025
  • Received 24 November 2024
  • Accepted 5 June 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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