Guided Unconditional and Conditional Generative Models for Super-Resolution and Inference of Quasi-Geostrophic Turbulence

TL;DR

The study tackles the challenge of reconstructing high-resolution quasi-geostrophic turbulence fields from coarse and sparsely observed data. It benchmarks four diffusion-model approaches, split between guided unconditional (SDEdit; DPS) and fully conditional (vanilla; classifier-free guidance) methods, across jet and eddy regimes and Reynolds numbers. Conditional diffusion models deliver cycle-consistent, physically faithful super-resolution and turbulence statistics, even with sparse observations, while unconditional methods show limited information propagation and, in some cases, nonphysical results. The work provides practical guidance on method selection and tuning, highlighting trade-offs between ease of implementation, fidelity, and uncertainty quantification for geophysical inference tasks.

Abstract

Typically, numerical simulations of Earth systems are coarse, and Earth observations are sparse and gappy. We apply four generative diffusion modeling approaches to super-resolution and inference of forced two-dimensional quasi-geostrophic turbulence on the beta-plane from coarse, sparse, and gappy observations. Two guided approaches minimally adapt a pre-trained unconditional model: SDEdit modifies the initial condition, and Diffusion Posterior Sampling (DPS) modifies the reverse diffusion process score. Two conditional approaches, a vanilla variant and classifier-free guidance, require training with paired high-resolution and observation data. We consider multiple test cases spanning: two regimes, eddy and anisotropic-jet turbulence; two Reynolds numbers, 10^3 and 10^4; and two observation types, 4x coarse-resolution fields and coarse, sparse and gappy observations. Our comprehensive skill metrics include norms of the reconstructed vorticity fields, turbulence statistical quantities, and quantifications of the super-resolved probabilistic ensembles and their errors. We also study the sensitivity to tuning parameters such as guidance strength. Results show that the generated super-resolution fields of SDEdit are unphysical, while those of DPS are reasonable but with smoothed fine-scale features; however, neither of these lower-cost models propagates observational information effectively to unobserved regions. The two conditional models require re-training, but reconstruct missing fine-scale features, are cycle-consistent with observations, and predict correct turbulence statistics, including the tails. Further, their mean errors are highly correlated with and predictable from their ensemble standard deviations. Results highlight the tradeoffs between ease of implementation, fidelity (sharpness), and cycle-consistency of the diffusion models, and offer practical guidance for deployment.

Figures (16)

• Figure 1: Schematic of the various unconditional diffusion modeling approaches. (Top row) Forward and reverse diffusion process for the unconditional model. (Middle row) Reverse process for guidance by modifying the initial condition (Sect. \ref{['sec: SDEEdit']}). (Bottom row) Reverse process for guidance by modifying the score (Sect. \ref{['sec: DPS']}).
• Figure 2: Schematic of the various conditional diffusion modeling approaches (Sect. \ref{['sec: conditional']}). (Top row) Reverse diffusion process for the vanilla conditional model. (Bottom row) Reverse diffusion process for classifier-free guidance.
• Figure 3: Test case description for super-resolution and inference in the jet (Top row) and eddy (Bottom row) regimes at $Re=10^4$. Column 1: Fully-resolved (FR) vorticity field. Column 2: Filtered-field (FF), which serves as the target for super-resolution. Column 3: Observed field (OF) under coarse-resolution observations. Column 4: Observed field (OF) under coarse, sparse and gappy observations. The observed fields serve as data (input) for super-resolution.
• Figure 4: (a) Reconstructed vorticity fields for the four super-resolution approaches in the jet regime (Re=$10^4$) from coarse-resolution fields for one snapshot (Test Case 2, Table \ref{['table: testcases']}). Column 1: Coarse observed vorticity field (data, OF). Column 2: Corresponding filtered vorticity field (target, FF). Column 3: Ensemble mean of the super-resolved diffusion model outputs. Columns 4 and 5: Two representative ensemble members. Columns 6 and 7: Ensemble point-wise standard deviation (Std.) and root-mean squared error (RMSE), respectively. (b) Zoomed-in view of the upper-right quadrant for the first 5 columns of (a), highlighting fine-scale features. Data and target are identical for all models.
• Figure 5: (a) As Fig. (\ref{['fig: fields_jet_full']} a), but for super-resolution in the eddy regime (Re=$10^4$) from coarse-resolution fields (Test Case 4, Table \ref{['table: testcases']}). (b) As Fig. (\ref{['fig: fields_jet_full']} b), zoomed-in view of the lower-left quadrant for the first 5 columns of (a), highlighting fine-scale features. Data and target are identical for all models.