Data-driven model reconstruction for nonlinear wave dynamics

TL;DR

This paper introduces an interpretable machine learning framework that reconstructs effective models of nonlinear wave dynamics in complex media, enabling accurate predictions and insights without traditional scale assumptions.

Contribution

The authors develop a sparse regression-based approach to derive effective continuum models from microscopic lattice models for nonlinear optical wavepackets.

Findings

Successfully reconstructs models for valley-Hall domain walls in photonic lattices

Accurately captures linear dispersion and nonlinear effects like self-steepening

Demonstrates the method's independence from traditional scale hierarchy limitations

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 wavepackets 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 wavepacket 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.