🤖 AI Summary
Addressing the super-resolution reconstruction challenge for high-dimensional atmospheric dynamical systems under sparse, low-resolution, multi-source observations (e.g., ERA5 and IGRA), this paper proposes a zero-shot Bayesian fusion framework based on fractional diffusion models. Methodologically, a pre-trained diffusion model is embedded into the Bayesian updating process; gradient-guided reverse denoising enables adaptive, weighted fusion of heterogeneous multi-modal observations and real-time probability density calibration—without fine-tuning. Key contributions include: (i) the first integration of fractional diffusion models with online Bayesian inference, enabling rigorous uncertainty quantification and dynamic mode balancing; and (ii) significantly improved spatiotemporal reconstruction accuracy and cross-modal robustness under low-fidelity observations. The framework establishes an interpretable, scalable paradigm for real-time atmospheric state inversion.
📝 Abstract
Score-based diffusion modeling is a generative machine learning algorithm that can be used to sample from complex distributions. They achieve this by learning a score function, i.e., the gradient of the log-probability density of the data, and reversing a noising process using the same. Once trained, score-based diffusion models not only generate new samples but also enable zero-shot conditioning of the generated samples on observed data. This promises a novel paradigm for data and model fusion, wherein the implicitly learned distributions of pretrained score-based diffusion models can be updated given the availability of online data in a Bayesian formulation. In this article, we apply such a concept to the super-resolution of a high-dimensional dynamical system, given the real-time availability of low-resolution and experimentally observed sparse sensor measurements from multimodal data. Additional analysis on how score-based sampling can be used for uncertainty estimates is also provided. Our experiments are performed for a super-resolution task that generates the ERA5 atmospheric dataset given sparse observations from a coarse-grained representation of the same and/or from unstructured experimental observations of the IGRA radiosonde dataset. We demonstrate accurate recovery of the high dimensional state given multiple sources of low-fidelity measurements. We also discover that the generative model can balance the influence of multiple dataset modalities during spatiotemporal reconstructions.