FLARE: Flow Matching with Local Axis-Angle Representations for Stochastic Micromagnetic Evolution

Micromagnetic dynamics pose a structured stochastic generative problem: high-dimensional fields of unit-vector magnetizations can evolve into multiple possible futures under the same physical controls. Existing learned approaches generally retain stepwise integration or model deterministic evolution, leaving full-field, direct-horizon stochastic prediction largely unexplored. We propose FLARE, a flow-matching framework that recasts stochastic finite-time magnetization prediction as conditional transport over anchor-relative local axis-angle rotations. This rotation-space formulation respects the intrinsic geometry of magnetization dynamics and preserves pointwise unit norm by construction. By explicitly conditioning on the physical prediction horizon, FLARE directly generates full-field stochastic endpoints across multiple target times without stepwise integration. Across seven author-released learned baselines, FLARE leads all three distributional metrics, including 29.9% lower angular energy distance and 37.3% lower fair energy score than the strongest external baseline on each metric. On a representative composed 5-ns protocol, it further achieves a $3,062\times$ best-batch speedup over MuMax${}_3$ on a single GPU.