用机器学习重构非线性波动力学方程，实现可解释预测。
Data-driven model reconstruction for nonlinear wave dynamics
- 通过稀疏回归将离散模型简化为连续有效模型。
- 准确复现线性色散与自陡化、自聚焦等非线性效应。
- 适用于光子拓扑材料设计，适合关注可解释性的研究者。
利用机器学习预测波动力学日益受到关注，但常用深度学习方法缺乏模型可解释性。本文提出一种可解释的机器学习框架，用于分析复杂波介质中光波包的非线性演化动力学。通过稀疏回归，将微观离散格点模型降维为更简单的有效连续模型，精确描述波包包络的动力学行为。该方法应用于激光写入波导中的蜂窝光子晶格中的谷霍尔畴壁，具有克尔型非线性及不同边界形状。重建方程能准确再现线性色散和自陡化、自聚焦等非线性效应。该方案摆脱了传统渐近分析方法对尺度层次的先验限制，是一种强大的可解释机器学习技术，对推进光子学设计能力以及揭示各类拓扑材料中驱动相互作用的动力学机制具有重要意义。
原文摘要 · Abstract (English)
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.
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