Graph Neural Network Force Fields for Spin Dynamics in Metallic Magnets

Metallic magnets exhibit complex spin dynamics governed by electronically generated interactions. Predictive simulations of such dynamics typically require repeated solutions of an underlying electronic problem throughout the time evolution, creating a major computational bottleneck. Here we introduce a graph neural network (GNN) magnetic force-field framework that learns the effective magnetic energy functional governing itinerant spin dynamics directly from electronic calculations. Conceptually analogous to machine-learned interatomic potentials, the proposed framework enables efficient evaluation of spin torques while capturing the nonlinear and spatially extended interactions generated by itinerant electrons. We benchmark the method on representative metallic magnetic systems exhibiting collinear, noncollinear, and noncoplanar magnetic order. The learned force fields accurately reproduce electronically generated spin torques and yield nonequilibrium spin dynamics in excellent agreement with direct electronic simulations. Our results establish graph neural networks as a powerful framework for machine-learned magnetic force fields, providing a pathway toward predictive large-scale simulations of nonequilibrium magnetism across multiple length and time scales.

Symmetry-electronic fingerprints reveal competing magnetic phases in two-dimensional materials

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.

Modelling magnetic material properties with uncertainty-aware neural networks

Machine learning is increasingly applied to accelerate the discovery of novel materials by exploring large compositional and structural design spaces. Yet, the scarcity of high-quality data and the frequent need for out-of-distribution prediction introduce substantial uncertainty, making the assessment of model reliability essential. In this work, we investigate uncertainty quantification as a means to evaluate model confidence in the context of permanent magnet research. In a first study, we benchmark classical and modern machine learning models for predicting intrinsic magnetic properties, focusing on the quality of their uncertainty estimates. We apply Gaussian negative log-likelihood loss and dropout-based Bayesian approximation as practical strategies for estimating predictive uncertainty. In a second study, we transfer these architectural features for uncertainty estimation to a more complex task: predicting coercivity from microstructural information using a graph neural network. Together, these studies demonstrate that uncertainty quantification not only enhances the trustworthiness of predictions but is also transferable across different modeling tasks.

Magnetic HIP-NN for spin dynamics in disordered itinerant magnets

We present a magnetic extension of the Hierarchically Interacting Particle Neural Network (HIP-NN) that enables large-scale simulations of electron-mediated spin dynamics in disordered itinerant magnets. The resulting magnetic HIP-NN (mHIP-NN) incorporates rotationally invariant spin correlations directly into hierarchical message-passing layers, enabling the network to learn emergent magnetic energy landscapes and effective local fields from coupled geometric-spin environments while preserving spin-rotation symmetry. As a benchmark application, we consider structurally disordered itinerant $s$-$d$ exchange models in which the effective magnetic forces arise dynamically from the instantaneous electronic structure and are computationally prohibitive to evaluate using conventional exact-diagonalization-based approaches. We show that mHIP-NN accurately reproduces the local torques governing Landau-Lifshitz-Gilbert dynamics and faithfully captures the nonequilibrium evolution of spatial spin correlations following thermal quenches. Our results establish symmetry-aware hierarchical message-passing networks as an efficient and scalable framework for large-scale simulations of frustrated itinerant spin systems and nonequilibrium magnetic dynamics. More broadly, because the learned energy functional remains fully differentiable with respect to both atomic coordinates and spin variables, the framework also provides a natural foundation for spin-dependent interatomic potentials and coupled atom-spin dynamics.