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

arXiv 2609.34070 ↗First posted 28 Sep 2026cs.LG cond-mat.mes-hall cs.AIcited by 0

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Abstract (arXiv)

Long-horizon micromagnetic simulation remains expensive because conventional and learned solvers typically propagate Landau--Lifshitz--Gilbert (LLG) dynamics step by step. 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. Against the strongest single-checkpoint external baseline on each metric, FLARE achieves 29.9% lower angular energy distance (15.30^circ), and a 37.3% lower fair energy score (0.393). On a representative composed 5-ns two-segment protocol, FLARE achieves a 3,062× best-batch speedup over the widely used GPU micromagnetic solver MuMax3 on a single GPU.

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References · 45

2022Flow Matching for Generative Modelingcited by 5,702
2020Fourier Neural Operator for Parametric Partial Differential Equationscited by 2,908
2019DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operatorscited by 2,018
2020Learning to Simulate Complex Physics with Graph Networkscited by 880
2023Improving and generalizing flow-based generative models with minibatch optimal transportcited by 879
2020Learning Mesh-Based Simulation with Graph Networkscited by 868
2024Transolver: A Fast Transformer Solver for PDEs on General Geometriescited by 326
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2019A Theoretical Analysis of Deep Neural Networks and Parametric PDEscited by 74
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2013A compact formula for the derivative of a 3-D rotation in exponential coordinatescited by 14
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2026MagneX: A High-Performance, GPU-Enabled, Data-Driven Micromagnetics Solver for Spintronicscited by 1
2026Machine-learning modeling of magnetization dynamics in quasi-equilibrium and driven metallic spin systemscited by 1

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