Two-dimensional magnets offer compelling platforms for spintronics and quantum technologies, yet predicting their magnetic ground states, moments, and anisotropy remains challenging. This limitation primarily arises because existing machine-learning representations encode chemical environments without capturing the symmetry or exchange physics that govern magnetism. In this work, we introduce the symmetry-electronic fingerprint (SEF), a physically interpretable representation that encodes crystallographic symmetry operations, Wyckoff-site geometry, together with site-resolved electronic structure. Combined with ensemble learning with random forests, the SEF accurately classifies magnetic ordering while regressing moments alongside anisotropy energies while simultaneously resolving the distinct regimes of itinerant Stoner ferromagnetism from localized superexchange. What sets the SEF-trained models apart is that regions of elevated model uncertainty are not a failure but a diagnostic, identifying materials where these mechanisms compete. First-principles calculations on Co- and Ni-based halides and oxides confirm that these regions correspond to genuine near-degenerate FM and AFM phases with magnetic frustration, suppressed anisotropy, and emergent non-collinear ordering. By encoding symmetry together with exchange physics directly into the representation unlike conventional descriptors, the SEF transforms model uncertainty into a compass pointing toward two-dimensional materials where small perturbations drive transitions between collinear, frustrated, or non-collinear magnetic phases.

翻译：二维磁体为自旋电子学和量子技术提供了极具吸引力的平台，然而预测其磁性基态、磁矩以及各向异性仍颇具挑战。这一局限主要源于现有的机器学习表示法编码了化学环境，却未能捕捉决定磁性的对称性或交换物理机制。在本工作中，我们引入了对称电子指纹（SEF），这是一种物理可解释的表示法，它编码了晶体学对称操作、Wyckoff位点几何结构以及位点分辨的电子结构。结合随机森林的集成学习，SEF能够准确分类磁有序，回归磁矩和各向异性能量，同时解析巡游斯通纳铁磁性局域超交换机制的区分区域。使SEF训练的模型与众不同的是，模型不确定性升高的区域并非失败，而是一种诊断工具，可识别出这些机制相互竞争的材料。基于Co基和Ni基卤化物与氧化物的第一性原理计算证实，这些区域对应着具有磁挫败、抑制各向异性和涌现非共线有序的真实近简并铁磁（FM）与反铁磁（AFM）相。与传统的描述符不同，通过将对称性和交换物理机制直接编码到表示中，SEF将模型不确定性转化为指向二维材料的指南针，在该材料中，微小的扰动可驱动共线、受挫或非共线磁性相之间的转变。