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

TL;DR

The paper introduces DSO, a dual-scale neural operator that decouples local and global information processing, significantly improving long-term stability and accuracy in fluid dynamics forecasting.

Contribution

It proposes a novel neural operator architecture with separate modules for local and global features, addressing stability issues in long-term PDE-based predictions.

Findings

DSO reduces prediction error by over 88% compared to existing neural operators.

It maintains stable long-term predictions in turbulent flow benchmarks.

Empirical validation shows local and global perturbations affect vortex structures and motion trends respectively.

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.