发表机构
University of Wrocław; Institute of Mathematics, Polish Academy of Sciences; Czech Advanced Technology and Research Institute (CATRIN), Palacký University Olomouc; Faculty of Science, Palacký University Olomouc; VŠB–Technical University of Ostrava（弗罗茨瓦夫大学; 波兰科学院数学研究所; 帕拉奇大学奥尔莫乌茨先进技术研究中心; 帕拉奇大学奥尔莫乌茨理学院; 俄斯特拉发理工大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究对比两种机器学习模型从原始电子结构预测磁各向异性能的表现，发现模型仅部分共享光谱依赖，端到端学习可识别磁各向异性的候选电子特征，其解释需多方面收敛证据支持。
AI 中文摘要
直接基于电子光谱训练的机器学习模型可以预测自旋-轨道驱动的性质，但具有相当预测精度的模型可能学习到不同的电子依赖关系。我们利用原子级磁体中的磁各向异性，以及旨在评估所学光谱关系物理相关性的验证策略，来研究这一问题。我们比较了双向门控循环单元和一维卷积神经网络，两者均接受训练以从自旋和轨道分辨的标量相对论态密度（SR-DOS）预测磁各向异性能（MAE）。尽管域内（ID）精度相当，但这些架构仅学习到部分重叠的光谱依赖关系。Shapley加性解释识别出两种架构间共享的光谱特征，这些特征可与符合二阶微扰理论（PT2）的合理自旋-轨道耦合路径相关联。将PT2导出的MAE贡献添加到模型输入中，对域内性能影响甚微，但可提升训练域外的迁移能力，且增益因架构而异。受控光谱扰动进一步表明，相似的归因模式并不意味着预测MAE对光谱权重具有相同的函数依赖关系。这些对比响应为架构依赖的域外迁移提供了功能背景。端到端学习可识别磁各向异性的候选电子特征，然而，其可信的微观解释依赖于预测性能、模型比较、物理理论、受控光谱干预以及分布偏移下评估的收敛证据。
英文摘要
Machine-learning models trained directly on electronic spectra can predict spin--orbit-driven properties, yet models with comparable predictive accuracy may learn different electronic dependencies. We examine this problem using magnetic anisotropy in atomic-scale magnets and a validation strategy designed to assess the physical relevance of learned spectral relationships. We compare a bidirectional gated recurrent unit and a one-dimensional convolutional neural network, both trained to predict magnetic anisotropy energy (MAE) from spin- and orbital-resolved scalar-relativistic densities of states (SR-DOS). Despite comparable in-domain (ID) accuracy, the architectures learn only partly overlapping spectral dependencies. Shapley additive explanations identify spectral features shared between the two architectures that can be associated with plausible spin--orbit-coupling pathways consistent with second-order perturbation theory (PT2). Adding PT2-derived MAE contributions to the model inputs has little effect on ID performance but can improve transfer beyond the training domain, with gains differing between architectures. Controlled spectral perturbations further demonstrate that similar attribution patterns do not imply the same functional dependence of the predicted MAE on spectral weight. The contrasting responses provide a functional context for architecture-dependent out-of-domain transfer. End-to-end learning can identify candidate electronic signatures of magnetic anisotropy. Their credible microscopic interpretation, however, rests on convergent evidence from predictive performance, model comparison, physical theory, controlled spectral interventions, and evaluation under distribution shift.
Comments16 pages, 6 figures, 3 tables, Supporting Information included
