arXiv：cs.LG· Jing Xu, Zenglin Xu, Li Yi, Ruoxi Jiang, Yuan Qi·· 10 小时前
ReAl：通过对齐动力学流优化神经算子
ReAl: Refine neural operators via aligning dynamical flow
AI 导读
研究者提出模型无关插件 ReAl，通过精炼与对齐两阶段增强预训练 PDE 神经算子代理模型。精炼阶段用条件流匹配模型学习确定性基预测的残差分布，恢复高频精细结构；对齐阶段用轨迹级奖励强化精炼器，实现长时程动力学对齐。实验显示 ReAl 在多种代理架构和 PDE 任务上持续提升高频保真度、预测精度与长期稳定性。
正文
Abstract:Neural partial differential equation (PDE) surrogates trained with mean squared error (MSE) can capture dominant dynamics but often lose high-frequency information and fine-scale structures. Generative models (e.g., Flow Matching) can capture the distribution of fine-scale details, yet stochastic errors may accumulate during autoregressive rollouts and compromise long-term stability. To address these limitations, we introduce Refine and Align(ReAl), a model-agnostic plug-in that augments pretrained PDE surrogates to improve the reconstruction of high-frequency structures associated with complex physical phenomena. In the refinement stage, a conditional flow-matching model learns the residual distribution around the deterministic base prediction, recovering missing fine-scale structures while retaining the dominant dynamics. In the alignment stage, to mitigate the generative discrepancies amplified in the autoregressive rollout, particularly in chaotic systems, we generate multiple trajectories from the same input and reinforce the refiner with trajectory-level rewards, thereby achieving long-horizon dynamical alignment. Experiments across diverse surrogate architectures and PDE tasks demonstrate that ReAl consistently improves high-frequency fidelity, forecasting accuracy, and long-horizon stability.
| Comments: | 20 pages, 8 figures |
| Subjects: | Machine Learning (cs.LG) |
| Cite as: | arXiv:2610.20369 [cs.LG] |
| (or arXiv:2610.20369v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2610.20369 arXiv-issued DOI via DataCite (pending registration) |
Submission history
From: Jing Xu [view email]
[v1]
Wed, 14 Oct 2026 15:41:24 UTC (14,647 KB)
来源：arXiv：cs.LG · arxiv.org