用新型神经网络提升非线性物理系统模型的可解释性
PH-KAN: Port-Hamiltonian Kolmogorov-Arnold Network
- 用KAN网络结构参数化物理系统关键组件
- 学习到的非线性函数可直接查看，提升可解释性
- 适合需要理解系统内在机制的研究者
数据驱动的机器学习在非线性系统辨识中日益重要，但传统模型常无法保持底层物理结构，且难以解释，尤其当无解析模型时。端口-哈密顿（pH）模型提供了自然的物理信息表示。然而，若用标准多层感知机（MLP）参数化，学习到的构成部分仍难解释。本文提出基于柯尔莫哥洛夫-阿诺德网络（KAN）的结构保持型非线性端口-哈密顿系统辨识框架。PH-KAN模型使用专用KAN模块参数化互联矩阵、耗散矩阵、哈密顿量和输入映射，并通过构造方式强制满足端口-哈密顿约束。由此获得的构成表达可显式观测非线性函数，相比标准MLP参数化更具可解释性。
原文摘要 · Abstract (English)
Data-driven machine learning approaches have become increasingly attractive for nonlinear system identification, but standard models often fail to preserve the underlying physical structure and remain difficult to interpret, especially when no analytical model is available. In this context, port-Hamiltonian (pH) models provide a natural physics-informed representation. However, when these models are parameterized with standard multilayer perceptrons (MLPs), the learned constitutive components often remain poorly interpretable. In this paper, we propose a structure-preserving identification framework for nonlinear port-Hamiltonian systems based on Kolmogorov-Arnold Networks (KANs). The proposed PH-KAN model parameterizes the interconnection matrix, dissipation matrix, Hamiltonian, and input mapping using dedicated KAN blocks, while enforcing the port-Hamiltonian constraints by construction. This yields constitutive representations in which the nonlinear functions defining the identified pH components can be explicitly inspected, leading to a more interpretable model than with standard MLP-based parameterizations.
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