FLARE: Flow Matching with Local Axis-Angle Representations for Stochastic Micromagnetic Evolution
Abstract
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∘), 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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BibTeX
@misc{li2026flare,
title = {{FLARE: Flow Matching with Local Axis-Angle Representations for Stochastic Micromagnetic Evolution}},
author = {Pengyu Li and Renjie Tong and Xuanlue Jiang and Jianmin Li and Yuanyuan Zhou},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.34070},
eprint = {2609.34070},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.34070},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - FLARE: Flow Matching with Local Axis-Angle Representations for Stochastic Micromagnetic Evolution
AU - Pengyu Li
AU - Renjie Tong
AU - Xuanlue Jiang
AU - Jianmin Li
AU - Yuanyuan Zhou
PY - 2026
DA - 2026/09/28
PB - arXiv
DO - 10.48550/arxiv.2609.34070
UR - https://arxiv.org/abs/2609.34070
AB - 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^∘), 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 MuMax^3 on a single GPU.
ER -