提出双尺度神经算子,显著提升流体长期预测的稳定性和精度。
DSO: Dual-Scale Neural Operators for Stable Long-term Fluid Dynamics Forecasting
- 分离局部细节与全局趋势处理,分别用卷积和MLP-Mixer建模。
- 在湍流基准上误差降低超88%,长期滚动预测更稳定。
- 适合需要高精度长期模拟的流体力学研究者使用。
长期流体动力学预测在科学与工程中至关重要。尽管神经算子已成为求解偏微分方程系统的一种有前景范式,但其在长期预测中常面临稳定性与精度不足的问题。我们识别出两类根本性失败模式:(1) 局部细节模糊,即涡核等精细结构和陡峭梯度被逐渐平滑;(2) 全局轨迹漂移,即长时间滚动后整体运动轨迹偏离真实值。我们认为这些失败源于现有神经算子对局部与全局信息处理方式统一,而物理系统中二者演化特性本就不同。为此,我们提出双尺度神经算子(DSO),显式将信息处理分为两个互补模块:深度可分离卷积用于细粒度局部特征提取,MLP-Mixer用于长程全局聚合。在涡旋动力学实验中,我们发现邻近扰动主要影响局部涡结构,而远距离扰动则主导全局运动趋势,为设计提供实证支持。在湍流基准上的大量实验表明,DSO达到当前最优精度,并保持强长期稳定性,相比现有神经算子预测误差降低超过88%。
原文摘要 · Abstract (English)
Long-term fluid dynamics forecasting is a critically important problem in science and engineering. While neural operators have emerged as a promising paradigm for modeling systems governed by partial differential equations (PDEs), they often struggle with long-term stability and precision. We identify two fundamental failure modes in existing architectures: (1) local detail blurring, where fine-scale structures such as vortex cores and sharp gradients are progressively smoothed, and (2) global trend deviation, where the overall motion trajectory drifts from the ground truth during extended rollouts. We argue that these failures arise because existing neural operators treat local and global information processing uniformly, despite their inherently different evolution characteristics in physical systems. To bridge this gap, we propose the Dual-Scale Neural Operator (DSO), which explicitly decouples information processing into two complementary modules: depthwise separable convolutions for fine-grained local feature extraction and an MLP-Mixer for long-range global aggregation. Through numerical experiments on vortex dynamics, we demonstrate that nearby perturbations primarily affect local vortex structure while distant perturbations influence global motion trends, providing empirical validation for our design choice. Extensive experiments on turbulent flow benchmarks show that DSO achieves state-of-the-art accuracy while maintaining robust long-term stability, reducing prediction error by over 88% compared to existing neural operators.
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