Anantha Babu

Ellery Rajagopal, Anantha N. S. Babu, Tony Ryu et al. · mit

Data-driven, deep-learning modeling frameworks have been recently developed for forecasting time series data. Such machine learning models may be useful in multiple domains including the atmospheric and oceanic ones, and in general, the larger fluids community. The present work investigates the possible effectiveness of such deep neural operator models for reproducing and predicting classic fluid flows and simulations of realistic ocean dynamics. We first briefly evaluate the capabilities of such deep neural operator models when trained on a simulated two-dimensional fluid flow past a cylinder. We then investigate their application to forecasting ocean surface circulation in the Middle Atlantic Bight and Massachusetts Bay, learning from high-resolution data-assimilative simulations employed for real sea experiments. We confirm that trained deep neural operator models are capable of predicting idealized periodic eddy shedding. For realistic ocean surface flows and our preliminary study, they can predict several of the features and show some skill, providing potential for future research and applications.

Anantha Narayanan Suresh Babu, Akhil Sadam, Pierre F. J. Lermusiaux

Typically, numerical simulations of the ocean, weather, and climate are coarse, and observations are sparse and gappy. In this work, 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. The other two conditional approaches, a vanilla variant and classifier-free guidance, require training with paired high-resolution and observation data. We consider eight 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 quantification of the super-resolved probabilistic ensembles and their errors. We also study the sensitivity to tuning parameters such as guidance strength. Results show that SDEdit generates unphysical fields, while DPS generates reasonable reconstructions at low computational cost but with smoothed fine-scale features. Both conditional approaches require re-training, but they reconstruct missing fine-scale features, are cycle-consistent with observations, and possess the correct statistics such as energy spectra. Further, their mean model errors are highly correlated with and predictable from their ensemble standard deviations. Results highlight the trade-offs between ease of implementation, fidelity (sharpness), and cycle-consistency of the diffusion models, and offer practical guidance for deployment in geophysical inverse problems.