arXiv:2509.18483cs.LGquant-ph2025-09被引 5

用物理约束的KAN网络,少数据高精度预测量子演化。

Physics-informed time series analysis with Kolmogorov-Arnold Networks under Ehrenfest constraints

  • 将柯尔莫哥洛夫-阿诺德网络结合量子力学的艾伦费斯特定理约束。
  • 仅需200样本(5.4%数据)即达优于TCN的精度。
  • 适合需要物理一致性的量子系统时间序列建模研究者。

量子动力学响应的预测是现代物理学的核心挑战。由于量子系统在高维希尔伯特空间中演化,传统数值方法常因计算成本过高而受限。尽管大语言模型在序列预测上表现优异,但量子动力学要求预测整个时间演化过程,而非单一序列元素。现有神经网络如循环与卷积网络通常需大量训练数据,并出现虚假振荡,影响物理可解释性。本文提出一种新方法:引入物理信息损失函数以强制满足艾伦费斯特定理的柯尔莫哥洛夫-阿诺德网络(KANs)。该方法仅需200个样本(仅为时间卷积网络所需3,700样本的5.4%),即可实现更优精度。我们进一步提出链式KAN结构,将时间因果性直接嵌入模型设计,显著提升时序建模能力。结果表明,物理信息引导的KAN在保持数学严谨性与物理一致性的同时,大幅降低数据需求。

原文摘要 · Abstract (English)

The prediction of quantum dynamical responses lies at the heart of modern physics. Yet, modeling these time-dependent behaviors remains a formidable challenge because quantum systems evolve in high-dimensional Hilbert spaces, often rendering traditional numerical methods computationally prohibitive. While large language models have achieved remarkable success in sequential prediction, quantum dynamics presents a fundamentally different challenge: forecasting the entire temporal evolution of quantum systems rather than merely the next element in a sequence. Existing neural architectures such as recurrent and convolutional networks often require vast training datasets and suffer from spurious oscillations that compromise physical interpretability. In this work, we introduce a fundamentally new approach: Kolmogorov Arnold Networks (KANs) augmented with physics-informed loss functions that enforce the Ehrenfest theorems. Our method achieves superior accuracy with significantly less training data: it requires only 5.4 percent of the samples (200) compared to Temporal Convolution Networks (3,700). We further introduce the Chain of KANs, a novel architecture that embeds temporal causality directly into the model design, making it particularly well-suited for time series modeling. Our results demonstrate that physics-informed KANs offer a compelling advantage over conventional black-box models, maintaining both mathematical rigor and physical consistency while dramatically reducing data requirements.

量子动力学KAN网络物理信息时间序列

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