Label-free alignment between datasets collected at different times, locations, or by different instruments is a fundamental scientific task. Hyperbolic spaces have recently provided a fruitful foundation for the development of informative representations of hierarchical data. Here, we take a purely geometric approach for label-free alignment of hierarchical datasets and introduce hyperbolic Procrustes analysis (HPA). HPA consists of new implementations of the three prototypical Procrustes analysis components: translation, scaling, and rotation, based on the Riemannian geometry of the Lorentz model of hyperbolic space. We analyze the proposed components, highlighting their useful properties for alignment. The efficacy of HPA, its theoretical properties, stability and computational efficiency are demonstrated in simulations.

Figure 1: Illustration given, depicted and (ii) red/pink.

Accurate atmospheric wind field information is crucial for various applications, including weather forecasting, aviation safety, and disaster risk reduction. However, obtaining high spatiotemporal resolution wind data remains challenging due to limitations in traditional in-situ observations and remote sensing techniques, as well as the computational expense and biases of numerical weather prediction (NWP) models. This paper introduces G-WindCast, a novel deep learning framework that leverages signal strength variations from 5G Global Navigation Satellite System (GNSS) signals to forecast three-dimensional (3D) atmospheric wind fields. The framework utilizes Forward Neural Networks (FNN) and Transformer networks to capture complex, nonlinear, and spatiotemporal relationships between GNSS-derived features and wind dynamics. Our preliminary results demonstrate promising accuracy in real-time wind forecasts (up to 30 minutes lead time). The model exhibits robustness across forecast horizons and different pressure levels, and its predictions for wind fields show superior agreement with ground-based radar wind profiler compared to concurrent European Centre for Medium-Range Weather Forecasts (ECMWF) Reanalysis v5 (ERA5). Furthermore, we show that the system can maintain excellent performance for localized forecasting even with a significantly reduced number of GNSS stations (e.g., around 100), highlighting its cost-effectiveness and scalability. This interdisciplinary approach underscores the transformative potential of exploiting non-traditional data sources and deep learning for advanced environmental monitoring and real-time atmospheric applications.

Since weather forecasts are fundamentally uncertain, reliable decision making requires information on the likelihoods of future weather scenarios. We explore the sensitivity of machine learning weather prediction (MLWP) using the 24h Pangu Weather ML model of Huawei to errors in the initial conditions with a specific kind of Singular Vector (SV) perturbations. Our Arnoldi-SV (A-SV) method does not need linear nor adjoint model versions and is applicable to numerical weather prediction (NWP) as well as MLWP. It observes error growth within a given optimization time window by iteratively applying a forecast model to perturbed model states. This creates a Krylov subspace, implicitly based on a matrix operator, which approximates the local error growth. Each iteration adds new dimensions to the Krylov space and its leading right SVs are expected to turn into directions of growing errors. We show that A-SV indeed finds dynamically meaningful perturbation patterns for the 24h Pangu Weather model, which grow right from the beginning of the forecast rollout. These perturbations describe local unstable modes and could be a basis to initialize MLWP ensembles. Since we start A-SV from random noise perturbations, the algorithm transforms noise into perturbations conditioned on a given reference state - a process that is akin to the denoising process of the generic diffusion based ML model of GenCast, therefor we briefly discuss similarities and differences.

In particular, diffusion models represent fine-scale details wit hout spatial smoothing, which is crucial for mesoscale predictions, such as heavy rainfall fo recasting. However, the applications of diffusion models to mesoscale prediction remain limited. T o address this gap, this study proposes an architecture that combines a diffusion model with Swin-Unet as a deterministic model, achieving mesoscale predictions while maintain ing flexibility. The proposed architecture trains the two models independently, allowin g the diffusion model to remain unchanged when the deterministic model is updated. Comp arisons using the Fractions Skill Score and power spectral analysis demonstrate th at incorporating the diffusion model leads to improved accuracy compared to predictions with out it. These findings underscore the potential of the proposed architecture to enha nce mesoscale predictions, particularly for strong rainfall events, while maintaining flexibility.

Predicting gray swan weather extremes, which are possible but so rare that they are absent from the training dataset, is a major concern for AI weather/climate models. An important open question is whether AI models can extrapolate from weaker weather events present in the training set to stronger, unseen weather extremes. To test this, we train independent versions of the AI model FourCastNet on the 1979-2015 ERA5 dataset with all data, or with Category 3-5 tropical cyclones (TCs) removed, either globally or only over the North Atlantic or Western Pacific basin. We then test these versions of FourCastNet on 2018-2023 Category 5 TCs (gray swans). All versions yield similar accuracy for global weather, but the one trained without Category 3-5 TCs cannot accurately forecast Category 5 TCs, indicating that these models cannot extrapolate from weaker storms. The versions trained without Category 3-5 TCs in one basin show some skill forecasting Category 5 TCs in that basin, suggesting that FourCastNet can generalize across tropical basins. This is encouraging and surprising because regional information is implicitly encoded in inputs. No version satisfies gradient-wind balance, implying that enforcing such physical constraints may not improve generalizability to gray swans. Given that current state-of-the-art AI weather/climate models have similar learning strategies, we expect our findings to apply to other models and extreme events. Our work demonstrates that novel learning strategies are needed for AI weather/climate models to provide early warning or estimated statistics for the rarest, most impactful weather extremes.

Most state-of-the-art AI applications in atmospheric science are based on classic deep learning approaches. However, such approaches cannot automatically integrate multiple complicated procedures to construct an intelligent agent, since each functionality is enabled by a separate model learned from independent climate datasets. The emergence of foundation models, especially multimodal foundation models, with their ability to process heterogeneous input data and execute complex tasks, offers a substantial opportunity to overcome this challenge. In this report, we want to explore a central question - how the state-of-the-art foundation model, i.e., GPT-4o, performs various atmospheric scientific tasks. Toward this end, we conduct a case study by categorizing the tasks into four main classes, including climate data processing, physical diagnosis, forecast and prediction, and adaptation and mitigation. For each task, we comprehensively evaluate the GPT-4o's performance along with a concrete discussion. We hope that this report may shed new light on future AI applications and research in atmospheric science.

This paper presents a family of neural network compression methods of simulated atmospheric states, with the aim of reducing the currently immense storage requirements of such data from cloud scale (petabytes) to desktop scale (terabytes). This need for compression has come about over past 50 years, characterized by a steady push to increase the resolution of atmospheric simulations, increasing the size and storage demands of the resulting datasets (e.g., Neumann et al. (2019), Schneider et al. (2023), Stevens et al. (2024)), while atmospheric simulation has come to play an increasingly critical role in scientific, industrial and policy-level pursuits. Higher spatial resolutions unlock the ability of simulators to deliver more accurate predictions and resolve ever more atmospheric phenomena. For example, while current models often operate at 25 - 50 km resolution, resolving storms requires 1 km resolution (Stevens et al., 2020), while resolving the motion of (and radiative effects due to) low clouds require 100 m resolution (Satoh et al., 2019; Schneider et al., 2017). Machine learning models for weather prediction also face opportunities and challenges with higher resolution: while additional granularity may afford better modeling opportunities, even the present size of atmospheric states poses a significant bottleneck for loading training data and serving model outputs (Chantry et al., 2021). To put the data storage problem in perspective, storing 40 years of reanalysis data from the ECMWF Reanalysis v5 dataset (ERA5, Hersbach et al. (2020)) at full spatial and temporal resolution (i.e.

Alignment training is crucial for enabling large language models (LLMs) to cater to human intentions and preferences. It is typically performed based on two stages with different objectives: instruction-following alignment and human-preference alignment. However, aligning LLMs with these objectives in sequence suffers from an inherent problem: the objectives may conflict, and the LLMs cannot guarantee to simultaneously align with the instructions and human preferences well. To response to these, in this work, we propose a Hybrid Alignment Training (Hbat) approach, based on alternating alignment and modified elastic weight consolidation methods. The basic idea is to alternate between different objectives during alignment training, so that better collaboration can be achieved between the two alignment tasks.We experiment with Hbat on summarization and dialogue tasks. Experimental results show that the proposed \textsc{Hbat} can significantly outperform all baselines. Notably, Hbat yields consistent performance gains over the traditional two-stage alignment training when using both proximal policy optimization and direct preference optimization.

Modern deep learning techniques, which mimic traditional numerical weather prediction (NWP) models and are derived from global atmospheric reanalysis data, have caused a significant revolution within a few years. In this new paradigm, our research introduces a novel strategy that deviates from the common dependence on high-resolution data, which is often constrained by computational resources, and instead utilizes low-resolution data (2.5 degrees) for global weather prediction and climate data analysis. Our main focus is evaluating data-driven weather prediction (DDWP) frameworks, specifically addressing sample size adequacy, structural improvements to the model, and the ability of climate data to represent current climatic trends. By using the Adaptive Fourier Neural Operator (AFNO) model via FourCastNet and a proposed time-sliding method to inflate the dataset of the ECMWF Reanalysis v5 (ERA5), this paper improves on conventional approaches by adding more variables and a novel approach to data augmentation and processing. Our findings reveal that despite the lower resolution, the proposed approach demonstrates considerable accuracy in predicting atmospheric conditions, effectively rivaling higher-resolution models. Furthermore, the study confirms the model's proficiency in reflecting current climate trends and its potential in predicting future climatic events, underscoring its utility in climate change strategies. This research marks a pivotal step in the realm of meteorological forecasting, showcasing the feasibility of lower-resolution data in producing reliable predictions and opening avenues for more accessible and inclusive climate modeling. The insights gleaned from this study not only contribute to the advancement of climate science but also lay the groundwork for future innovations in the field.