用神经网络逼近中子散射逆问题
Approaching the Inverse Neutron Scattering Problem with Neural Networks
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中文总结 AI 辅助
本文利用神经网络从非弹性中子散射谱中高效求解量子磁体的哈密顿参数逆问题，在八参数蜂窝晶格海森堡模型上验证了三种网络架构的高精度与抗噪性，为自动化表征量子磁性材料提供了新途径。
中文摘要 AI 辅助
从非弹性中子散射测量中确定量子磁体的微观哈密顿量，仍然是凝聚态物理中的一个核心挑战。虽然动力学自旋结构因子原则上包含了关于底层相互作用的足够信息，但由于参数空间庞大且存在实验噪声，从实验谱中提取哈密顿参数构成一个高度非平凡的逆问题。在此，我们证明神经网络可以高效地解决一类广泛的量子磁体的这一逆问题。作为基准，我们考虑完全极化相中蜂窝晶格海森堡自旋模型的八参数族，在该相中，动力学自旋结构因子可以在线性自旋波理论内精确计算。利用大型合成中子散射谱数据集，我们训练神经网络直接从动力学响应推断底层哈密顿参数。我们比较了三种不同架构的性能——全连接神经网络（FCNN）、一维卷积神经网络（CNN1D）和二维卷积神经网络（CNN2D）——并发现所有架构都达到了较高的预测精度。值得注意的是，训练后的模型在存在显著实验不确定性的情况下仍然稳健，即使输入谱被幅度高达信号强度$10\%$的随机噪声污染，也能可靠地恢复哈密顿参数。我们的结果确立了机器学习作为从中子散射数据定量重建哈密顿量的强大框架，并为量子磁性材料的自动化表征提供了实用途径。
英文摘要
Determining the microscopic Hamiltonian of a quantum magnet from inelastic neutron scattering measurements remains a central challenge in condensed matter physics. While the dynamical spin structure factor contains, in principle, sufficient information about the underlying interactions, extracting Hamiltonian parameters from experimental spectra constitutes a highly nontrivial inverse problem due to the large parameter space and the presence of experimental noise. Here we demonstrate that neural networks can efficiently solve this inverse problem for a broad class of quantum magnets. As a benchmark, we consider an eight-parameter family of honeycomb lattice Heisenberg spin models in the fully polarized phase, where the dynamical spin structure factor can be computed exactly within linear spin-wave theory. Using a large synthetic dataset of neutron scattering spectra, we train neural networks to infer the underlying Hamiltonian parameters directly from the dynamical response. We compare the performance of three different architectures---fully connected neural networks (FCNNs), one-dimensional convolutional neural networks (CNN1Ds), and two-dimensional convolutional neural networks (CNN2Ds)---and find that all achieve high predictive accuracy. Remarkably, the trained models remain robust in the presence of substantial experimental uncertainty, reliably recovering the Hamiltonian parameters even when the input spectra are contaminated by random noise with amplitudes reaching $10\%$ of the signal intensity. Our results establish machine learning as a powerful framework for quantitative Hamiltonian reconstruction from neutron scattering data and provide a practical route toward automated characterization of quantum magnetic materials.
发表机构
- University of Tennessee（田纳西大学）
- Oak Ridge National Laboratory（橡树岭国家实验室）
机构由 AI 辅助整理，请以论文原文为准。
