Super-Resolving Coarse-Resolution Weather Forecasts With Flow Matching

Operational weather prediction at kilometer scales remains computationally prohibitive for traditional numerical weather prediction (NWP) models, limiting forecast access for applications in energy, agriculture, and disaster management that require fine-grained spatiotemporal detail. Here we introduce AirCast-SR, a foundation model for atmospheric super-resolution that downscales global AI weather forecasts from 0.25 degree (~28 km) to 1 km horizontal resolution at hourly temporal resolution, producing 67-hour forecasts of eight coupled surface variables simultaneously. EarthMind-SR employs a three-dimensional U-Net conditioned within a Latent Consistency Model (LCM) diffusion framework, trained on patch-based samples over the contiguous United States (CONUS) using GraphCast forecasts as input and NOAA's Analysis of Record for Calibration (AORC) as the target. The model achieves near-zero bias across all variables and lead times, and its radial power spectral density analysis demonstrates preservation of fine-scale atmospheric structure at wavelengths of 10 km to 100 km where coarser models lose spectral power. We validate EarthMind-SR across three CONUS case studies spanning winter, summer, and spring seasons, and demonstrate zero-shot global transferability over India and Germany using independent surface station observations without any retraining or fine-tuning. As an open-weights foundation model, EarthMind-SR establishes a new paradigm for kilometer-scale AI weather prediction and provides a platform for regional fine-tuning, distillation, and downstream applications in climate services and hazard forecasting.

Most super-resolution models learn from paired data by supervising only the final high-resolution output. This provides little control over how the prediction should evolve between the downsampled observation and its fine target. We introduce GalerkinFlow, an equation-agnostic framework that turns each coarse--fine pair into supervision along an entire reconstruction path. At a random sample of intermediate states on the reconstruction path, the model predicts the coarse-to-fine residual velocity and uses coarse-anchor point to define a pseudo-endpoint. We show that the reconstruction loss of this pseudo-endpoint is exactly related to the intermediate velocity loss through a known time-dependent weight. Consequently, every intermediate state contributes supervision toward the same fine target, rather than serving only as an internal step toward an endpoint loss. Because intermediate states already reveal part of the missing fine-scale structure, we additionally supervise the coarse endpoint used during one-step inference. A finite-difference objective further constrains local spatial variation. GalerkinFlow combines convolutional features with scale-conditioned Galerkin operator mixing and requires no governing equation or physical metadata. It achieves the lowest raw-space errors among the evaluated equation-agnostic baselines on Navier--Stokes and Darcy Flow, while remaining competitive on DIV2K.

Recovering high-resolution states from sparse, low-resolution observations is a central challenge in scientific machine learning and data assimilation. Classical data assimilation exploits temporal information through forecast-analysis cycles, but often requires repeated access to expensive high-resolution forecast models. Generative super-resolution can recover unresolved structure from coarse observations, but is commonly used as a one-shot mapping that does not fully exploit constraints from past states. We introduce Iterative Refinement (IR), a learned data assimilation framework that combines these perspectives. Instead of performing a single coarse-to-fine reconstruction, IR decomposes the task into resolution-wise forecast-analysis operations across a multiresolution hierarchy. At each stage, a shared neural operator with resolution-dependent spectral mode slicing provides a dynamical prior, while a shared conditional diffusion corrector uses the current coarser-resolution state to produce a refined posterior at the next finer resolution. We evaluate IR on one-dimensional stochastically forced Burgers dynamics and two-dimensional Kraichnan turbulence. On the challenging 256x256 Kraichnan benchmark, IR achieves an RMSE of 0.184 and an SSIM of 0.836, outperforming spectral upsampling, one-shot diffusion super-resolution, enhanced deep super-resolution, and an autoregressive forecaster. On the more constrained Burgers testbed, IR remains competitive with one-shot diffusion, which achieves the lowest RMSE. These results show that one-shot generative reconstruction can be effective for simpler settings, while hierarchical forecast-analysis refinement becomes advantageous in strongly multiscale and underdetermined regimes. Overall, IR combines temporal priors, generative correction, and multiresolution reconstruction for learned data assimilation in complex physical systems.