DSO: Dual-Scale Neural Operators for Stable Long-term Fluid Dynamics Forecasting

Abstract

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.

Figures (8)

• Figure 1: Temporal evolution of vortex dipole under close (top) vs. far (bottom) perturbations. The curve represents a streamline of the flow field. The red-blue vortex pair on the left represents the dipole, while the isolated vortex on the right is the perturbing vortex.
• Figure 2: Overview of DSO architecture. The model consists of three components: (1) an encoder $\mathcal{E}$ that extracts multi-scale spatial features, (2) a translator $\mathcal{T}$ composed of stacked dual-pathway blocks, and (3) a decoder $\mathcal{D}$ that reconstructs the predicted field. Each block contains a Local Pathway (convolution) for fine-scale features and a Global Pathway (MLP-Mixer) for domain-wide information aggregation. The curved arrows connecting the encoder and decoder represent skip connections.
• Figure 3: We selected predictions from selected models on the NS-Decaying dataset, computed and analyzed the mean and variance of their SSIM values.
• Figure 4: Comparison of gradient and divergence errors of different methods on the NS-Decaying dataset. (a) Gradient magnitude error quantifies the accuracy of capturing flow deformation features. (b) Divergence error measures physical consistency and mass conservation properties.
• Figure 5: Prediction visualization of selected models across various time steps for the NS-Decaying case, where the top row displays the ground truth values.