Probabilistic Super-Resolution for Urban Micrometeorology via a Schr"odinger Bridge

This study employs a neural network that represents the solution to a Schr"odinger bridge problem to perform super-resolution of 2-m temperature in an urban area. Schr"odinger bridges generally describe transformations between two data distributions based on diffusion processes. We use a specific Schr"odinger-bridge model (SM) that directly transforms low-resolution data into high-resolution data, unlike denoising diffusion probabilistic models (simply, diffusion models; DMs) that generate high-resolution data from Gaussian noise. Low-resolution and high-resolution data were obtained from separate numerical simulations with a physics-based model under common initial and boundary conditions. Compared with a DM, the SM attains comparable accuracy at one-fifth the computational cost, requiring 50 neural-network evaluations per datum for the DM and only 10 for the SM. Furthermore, high-resolution samples generated by the SM exhibit larger variance, implying superior uncertainty quantification relative to the DM. Owing to the reduced computational cost of the SM, our results suggest the feasibility of real-time ensemble micrometeorological prediction using SM-based super-resolution.