Declan J. Curran, Sanaa Hobeichi, Hira Saleem, Hao Xue, Flora D. Salim
Downscaling is essential for generating the high-resolution climate data needed for local planning, but traditional methods remain computationally demanding. Recent years have seen impressive results from AI downscaling models, particularly diffusion models, which have attracted attention due to their ability to generate ensembles and overcome the smoothing problem common in other AI methods. However, these models typically remain computationally intensive. We introduce a Hierarchical Diffusion Downscaling (HDD) model, which introduces an easily-extensible hierarchical sampling process to the diffusion framework. A coarse-to-fine hierarchy is imposed via a simple downsampling scheme. HDD achieves competitive accuracy on ERA5 reanalysis datasets and CMIP6 models, significantly reducing computational load by running on up to half as many pixels with competitive results. Additionally, a single model trained at 0.25° resolution transfers seamlessly across multiple CMIP6 models with much coarser resolution. HDD thus offers a lightweight alternative for probabilistic climate downscaling, facilitating affordable large-ensemble high-resolution climate projections. See a full code implementation at: https://github.com/HDD-Hierarchical-Diffusion-Downscaling/HDD-Hierarchical-Diffusion-Downscaling.
Jiayi Li, Penghao Jiang, Baiyu Chen, Yifan Duan, Hira Saleem, Zhaonan Wang, Piotr Koniusz, Flora D. Salim
Neural operators efficiently simulate dynamical systems by repeatedly predicting the next state. However, small errors at each step can accumulate, causing long-term predictions to drift from the true trajectory. Long-term error reflects both the propagation of earlier prediction errors and new errors introduced at each step. How to reduce these errors is therefore a critical question. We propose the Spectral Generator Neural Operator (SGNO), which combines a linear estimate of the next state with a learned correction. The linear component uses consecutive states in the training data to fit a map from the current state to the next. A neural network corrects this prediction by learning changes that the linear model does not capture, including nonlinear interactions. Both components are trained jointly toward the same next-state target. Experiments across 13 periodic PDE configurations in one to three dimensions show that SGNO accurately learns state evolution on linear tasks and reduces 100-step rollout error by 13-74% over the strongest baseline under the main comparison protocol on each nonlinear task. Longer-horizon extrapolation tests show lower late-window prediction errors on several nonlinear tasks. These results show that combining fitted propagation with learned state-dependent correction can improve long-horizon autoregressive prediction on the evaluated PDE tasks. Code is available at https://github.com/cruiseresearchgroup/SGNO.
Hira Saleem, Cormac Purcell, Steven Sherwood, Flora Salim
Physics-based Earth system models (ESMs) are essential for attributing climate change and generating scenario projections, yet their reliance on high-resolution numerical integration makes multi-decadal experiments expensive. In parallel, deep learning has delivered strong gains in short-range weather forecasting; however, auto-regressive roll-outs can accumulate error and become unstable when extended to decade-scale climate emulation. We introduce A-UTE: Advection Informed, Uncertainty Aware Temperature Emulator, aimed at stable multi-year emulation across heterogeneous climate models and grid resolutions. A-UTE is trained on various physics-based models at varying spatial resolutions to emulate temperature fields over a 10-year horizon. A-UTE formulates climate emulation as a forward-time stochastic dynamical system. We propose an auto-regressive ODE-SDE surrogate in which transport dynamics are constrained by an advection consistent ODE component, while a learned neural SDE term models coarse-grained variability and cross-model discrepancy at monthly resolution. We train A-UTE under negative log-likelihood objective for principled uncertainty estimates and probabilistic evaluation. Experiments across 20 climate models show that A-UTE improves long roll-out stability and accuracy relative to relevant baselines, advancing data-driven climate emulation with explicit physical structure and uncertainty-aware predictions.