AI-based separation of turbulence from coherent background flows in decaying hydrodynamic turbulence

TL;DR

This work tackles the problem of disentangling turbulent fluctuations from coherent background flows in hydrodynamic systems. It introduces an AI-based turbulence–background separation model trained on static synthetic images and assesses its robustness by applying it to time-evolving, decaying 2D Navier–Stokes turbulence. The model successfully recovers turbulent structures early and mid evolution, preserving inertial-range spectral scaling, and remains plausible even as nonlinear interactions distort background flows at later times. The study demonstrates the potential of data-driven, nonlocal separation approaches in astrophysical and cosmological contexts while highlighting intrinsic ambiguities that arise in strongly nonlinear regimes.

Abstract

Separating turbulent fluctuations from coherent large-scale background flows is a fundamental challenge in the analysis of numerical simulations and astronomical observations. Traditional approaches to this problem commonly rely on decomposition-based techniques, including scale-based filtering methods such as Fourier or wavelet transforms, as well as adaptive methods like the Hilbert-Huang transformation. In realistic flows, however, coherent motions and turbulent fluctuations often overlap across a broad range of scales and interact nonlinearly, rendering any clear and unique separation inherently ambiguous, particularly in astrophysical settings where data are projected or sparsely sampled. In this work, we assess the robustness of AI-based turbulence-background separation using two-dimensional incompressible Navier-Stokes simulations of decaying hydrodynamic turbulence. The simulations are initialized with a coherent background flow and divergence-free turbulent perturbations with a Kolmogorov-like power spectrum, and evolve without external forcing, providing a conservative physical testbed. A neural network trained exclusively on static synthetic images is applied to simulation snapshots at different evolutionary stages. We find that the model successfully recovers turbulent fluctuations during early and intermediate stages, when partial scale separation is preserved. At later stages, despite the substantial decay of turbulent energy and the resulting reduction in fluctuation strength, the model continues to recover visually and spectrally plausible turbulent structures and preserves inertial-range spectral scaling, demonstrating robust separation under increasingly challenging conditions. These results demonstrate the potential of applying AI models trained on static data to time-evolving turbulent flows, with direct implications for astrophysical and cosmological applications.

Figures (8)

• Figure 1: Representative examples of the synthetic training data used for the AI-based turbulence--background separation. The top row shows input images constructed as linear superpositions of a coherent large-scale background field and a turbulent fluctuation field ($O(x,y) = B(x,y) + I(x,y)$). The bottom row shows the corresponding turbulence-only targets ($I(x,y)$). The background component is dominated by low-wavenumber coherent structures, while the turbulent component exhibits small-scale, nearly isotropic fluctuations with a Kolmogorov-like power spectrum.
• Figure 2: Architecture of the hybrid Swin Transformer–U-Net model used for turbulence–background separation. The Swin-Tiny encoder extracts hierarchical multi-scale features at resolutions $56^2$, $28^2$, $14^2$, and $7^2$, which are passed to a U-Net–style decoder via same-resolution skip connections. The decoder progressively upsamples the latent representation and reconstructs the target field at the original resolution. Both the input and the output are single-channel scalar fields of size $224\times224$.
• Figure 3: Evolution of the loss components during training. The total loss (solid black line) is composed of a pixel-wise mean squared error term, a spectral consistency term, and a leakage penalty that suppresses contamination from background modes. The rapid decrease of the MSE indicates fast convergence in pixel space, while the more gradual decay of the spectral loss reflects the increasing difficulty of matching power spectra across spatial scales.
• Figure 4: Example results of the turbulence--background separation on independent synthetic test samples. From left to right, each column shows the true turbulent field, the model prediction, and the residual. The predicted turbulence closely reproduces the spatial morphology of the true field, while the residuals are largely featureless and dominated by low-amplitude noise, indicating successful suppression of background structures.
• Figure 5: Comparison of the radially averaged power spectra for the true turbulence and the AI-predicted turbulence, averaged over 128 independent test samples. The predicted spectrum closely follows the true spectrum over a broad range of wavenumbers, including the inertial range, with deviations appearing only at the highest wavenumbers where finite-resolution and numerical dissipation effects become significant.