Turb-L1: Achieving Long-term Turbulence Tracing By Tackling Spectral Bias

TL;DR

Turb-L1 introduces a multi-grid architecture with hierarchical dynamics synthesis to overcome spectral bias, significantly improving long-term turbulence prediction accuracy and fidelity by capturing high-frequency details.

Contribution

The paper proposes Turb-L1, a novel turbulence prediction method that explicitly addresses spectral bias using a multi-grid approach, enhancing long-term prediction fidelity.

Findings

Reduces MSE by 80.3% in long-term predictions

Increases SSIM over 9 times compared to baseline

Accurately reproduces the enstrophy spectrum and maintains physical realism

Abstract

Accurately predicting the long-term evolution of turbulence is crucial for advancing scientific understanding and optimizing engineering applications. However, existing deep learning methods face significant bottlenecks in long-term autoregressive prediction, which exhibit excessive smoothing and fail to accurately track complex fluid dynamics. Our extensive experimental and spectral analysis of prevailing methods provides an interpretable explanation for this shortcoming, identifying Spectral Bias as the core obstacle. Concretely, spectral bias is the inherent tendency of models to favor low-frequency, smooth features while overlooking critical high-frequency details during training, thus reducing fidelity and causing physical distortions in long-term predictions. Building on this insight, we propose Turb-L1, an innovative turbulence prediction method, which utilizes a Hierarchical Dynamics Synthesis mechanism within a multi-grid architecture to explicitly overcome spectral bias. It accurately captures cross-scale interactions and preserves the fidelity of high-frequency dynamics, enabling reliable long-term tracking of turbulence evolution. Extensive experiments on the 2D turbulence benchmark show that Turb-L1 demonstrates excellent performance: (I) In long-term predictions, it reduces Mean Squared Error (MSE) by $80.3\%$ and increases Structural Similarity (SSIM) by over $9\times$ compared to the SOTA baseline, significantly improving prediction fidelity. (II) It effectively overcomes spectral bias, accurately reproducing the full enstrophy spectrum and maintaining physical realism in high-wavenumber regions, thus avoiding the spectral distortions or spurious energy accumulation seen in other methods.