用流匹配方法提升高维物理系统时序预测精度与效率
Operator Flow Matching for Timeseries Forecasting
- 基于潜空间流匹配，结合时间条件傅里叶层建模多尺度动态
- 在3个PDE基准数据集上优于当前最优模型，且谱分析显示更优多尺度恢复能力
- 参数与内存占用低，适合高效长序列物理系统建模
高维、由偏微分方程（PDE）驱动的动力系统预测仍是生成建模的核心挑战。现有自回归和扩散方法常因累积误差与离散化伪影，限制长期物理一致性预测。流匹配提供自然替代方案，支持高效确定性采样。我们证明了FNO近似误差的上界，并提出TempO——一种利用通道折叠实现稀疏条件化的潜空间流匹配模型，通过时间条件傅里叶层高效处理三维时空场，以高保真度捕捉多尺度模式。TempO在三个基准PDE数据集上超越当前最优基线，谱分析进一步验证其对多尺度动力学的优越恢复能力；效率分析显示，相比基于注意力或卷积的回归器，其参数与内存开销显著更低。
原文摘要 · Abstract (English)
Forecasting high-dimensional, PDE-governed dynamics remains a core challenge for generative modeling. Existing autoregressive and diffusion-based approaches often suffer cumulative errors and discretisation artifacts that limit long, physically consistent forecasts. Flow matching offers a natural alternative, enabling efficient, deterministic sampling. We prove an upper bound on FNO approximation error and propose TempO, a latent flow matching model leveraging sparse conditioning with channel folding to efficiently process 3D spatiotemporal fields using time-conditioned Fourier layers to capture multi-scale modes with high fidelity. TempO outperforms state-of-the-art baselines across three benchmark PDE datasets, and spectral analysis further demonstrates superior recovery of multi-scale dynamics, while efficiency studies highlight its parameter- and memory-light design compared to attention-based or convolutional regressors.
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