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

arXiv: https://arxiv.org/abs/2609.34070 · HTML: https://mlsanity.com/paper/2609.34070/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 45 of its 89 references that are in the map.
- First posted on arXiv 28 Sep 2026.

## Builds on (most cited first, 30 of 45)

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- [Learning Mesh-Based Simulation with Graph Networks](https://mlsanity.com/paper/2010.03409/) (2020)
- [Transolver: A Fast Transformer Solver for PDEs on General Geometries](https://mlsanity.com/paper/2402.02366/) (2024)
- [Flow Matching on General Geometries](https://mlsanity.com/paper/2302.03660/) (2023)
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- [Riemannian Diffusion Models](https://mlsanity.com/paper/2208.07949/) (2022)
- [Forecasting Sequential Data using Consistent Koopman Autoencoders](https://mlsanity.com/paper/2003.02236/) (2020)
- [FlowMM: Generating Materials with Riemannian Flow Matching](https://mlsanity.com/paper/2406.04713/) (2024)
- [A Theoretical Analysis of Deep Neural Networks and Parametric PDEs](https://mlsanity.com/paper/1904.00377/) (2019)
- [Continuous PDE Dynamics Forecasting with Implicit Neural Representations](https://mlsanity.com/paper/2209.14855/) (2022)
- [Benchmarking Autoregressive Conditional Diffusion Models for Turbulent Flow Simulation](https://mlsanity.com/paper/2309.01745/) (2023)
- [Functional Flow Matching](https://mlsanity.com/paper/2305.17209/) (2023)
- [Neural Galerkin Schemes with Active Learning for High-Dimensional Evolution Equations](https://mlsanity.com/paper/2203.01360/) (2022)
- [Generative Modeling of Molecular Dynamics Trajectories](https://mlsanity.com/paper/2409.17808/) (2024)
- [From Zero to Turbulence: Generative Modeling for 3D Flow Simulation](https://mlsanity.com/paper/2306.01776/) (2023)
- [Deep Generative Models through the Lens of the Manifold Hypothesis: A Survey and New Connections](https://mlsanity.com/paper/2404.02954/) (2024)
- [Learning to Accelerate Partial Differential Equations via Latent Global Evolution](https://mlsanity.com/paper/2206.07681/) (2022)
- [Continuous Ensemble Weather Forecasting with Diffusion models](https://mlsanity.com/paper/2410.05431/) (2024)
- [Generative Latent Neural PDE Solver using Flow Matching](https://mlsanity.com/paper/2503.22600/) (2025)
- [Trivialized Momentum Facilitates Diffusion Generative Modeling on Lie Groups](https://mlsanity.com/paper/2405.16381/) (2024)

## 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.