weather forecasting centers

Abstract: Neural operators enable fast PDE forecasting, but repeated predictions accumulate errors and fine-scale structures remain difficult to resolve. We introduce a frequency-decomposed finite-time flow-map neural operator (F$^3$NO) that leverages updated low-frequency features to guide nonlinear refinement of high-frequency information. Within each layer, this cross-scale conditioning connects global spectral processing with local detail refinement. The model directly predicts states at specified future times and adjusts the contributions of the two branches according to the prediction interval. For longer trajectories, it combines parallel predictions within short temporal segments with recursive propagation between segments. Experiments on five PDE benchmarks demonstrate improved forecasting accuracy over autoregressive and direct-prediction baselines. Ablations show that frequency-decomposed refinement can improve accuracy with fewer parameters, while the benefits of segmentation depend on spatial resolution and dynamical regime.

Abstract: Deep generative networks have recently achieved unprecedented performance in precise image and video editing using sophisticated textual prompts. However, the effectiveness of such models heavily depends on access to very large supervised and annotated image datasets, which can be very difficult to obtain. This is particularly true for satellite instruments, which very rarely overlap with labelled data, and suffer from domain shifts in the rare occasions they do. In this paper, we investigate the potential of flow matching models for unsupervised domain adaptation of satellite radiometer images. Our main contribution is a novel unsupervised method that achieves precise domain alignment by leveraging parts of the deterministic ordinary differential equations in flow matching models, conditioned on different satellite instruments. A key strength of our approach is its ability to preserve essential information while adapting across any domains since the perturbations are in theory bijective. Extensive experiments conducted on the GPM-Core constellation show the benefit of our conditional domain adaptation, particularly in improving rain precipitation estimation from radiometer imagery.

Abstract: Diffusion models generate data by reversing a forward corruption process that typically approaches a simple Gaussian prior. Recent work has extended this framework to signals supported on fixed graphs, e.g., road-network traffic and sensor-network measurements. Many graph signals have nonuniform spectral energy, whereas isotropic corruption adds the same conditional noise variance to every graph-frequency mode. Driving all modes to near-zero terminal signal-to-noise ratio (SNR) requires strong corruption, which increases the noise range that must be covered under a fixed sampling budget. We introduce Graph Residual Conjugate Diffusion (GRCD), which replaces the shared clock of graph heat diffusion with a mode-dependent clock that gives every graph-Fourier mode the same conditional SNR. GRCD fits a zero-mean graph-spectral Gaussian reference on the training split and stops at a finite terminal SNR at which the propagated reference still carries the fitted spectral variances. The Gaussian component has an exact modewise propagator in the probability-flow ODE, so sampling advances it analytically and integrates only the learned residual score numerically. We evaluate GRCD on five settings (METR-LA traffic, Molene weather, and three stochastic block models) against seven comparators under a matched protocol: Graph-Aware Diffusion (GAD), EDM (graph backbone), two adaptations of Whitened Score Diffusion (WSD), and three preconditioning controls. At four function evaluations (NFEs), GRCD lowers averaged maximum mean discrepancy (aMMD) by 22 to 36 times over the best comparator on all five settings, reaching 0.054 on METR-LA, where it clears an aMMD 0.1 target with 87% less sampling wall-clock time than the cheapest comparator that reaches it. Fitting the terminal reference reduces aMMD by 2.7 to 7.3 times at finite terminal SNR, while the factors shrink to 1.00 to 1.01 near zero.

Abstract: Data-driven machine-learning weather models now rival, and in some respects surpass, operational numerical weather prediction (NWP), yet no single model dominates across variables, pressure levels, lead times, or regions, and the marginal returns from developing ever-larger individual models are diminishing. We present TaiJi (after the Chinese concept of yin-yang harmony, the complementarity of opposites), a spatiotemporal adaptive ensemble framework that recasts optimal model-weight combination as a learned prediction problem: a lightweight convolutional neural network, conditioned on the recent atmospheric state, predicts at every grid point and lead time a set of affine combination weights and an additive residual for the constituent forecasts. The combiner is trained end-to-end over Pangu-Weather, GraphCast, FuXi, IFS-HRES, and the IFS-ENS ensemble mean, an explicitly hybrid set of ML and NWP constituents, on two consumer-grade RTX 4090 GPUs in about 8 hours, at least an order of magnitude below the training cost of any of its ML constituents. Under the WeatherBench 2 protocol (2020 test year), TaiJi outperforms the strongest baseline for each variable and lead time across the eight core variables and lead times of up to 10 days, under both RMSE and ACC, with a near-100% win rate, and this advantage is preserved across extreme scenarios, including tropical-cyclone tracks and heavy precipitation. We further show that the learned weights vary coherently with latitude, season and lead time rather than following a single fixed rule. TaiJi thus offers a computationally inexpensive route to improving global forecast skill that builds on, rather than replaces, the substantial investment already made in existing forecast models.