Koopman early warning signals for bifurcation and rate-induced tipping

Abrupt transitions in complex systems are often preceded by early warning signals. However, most indicators rely on the notion of critical slowing down and do not generally extend to rate-induced tipping where transitions can occur without local loss of stability. This is problematic in stochastic, nonautonomous systems where internal variability and time-varying variables interact to shape tipping onset. We use Koopman operator theory to develop a unified early warning framework for both bifurcation and rate-induced tipping in stochastic systems. Our approach builds on residual Koopman mode decomposition that measures discrepancies between dynamics and their finite-dimensional approximation, and extends it to the control setting by augmenting the observable space with time-varying control variables. In idealized examples, the resulting indicators recover expected signatures near bifurcation points and improve detection in rate-induced regimes where classical indicators fail. We further show that learned embeddings through deep learning outperform prescribed dictionaries, especially in a high-dimensional setting. Applied to simulations of the Atlantic Meridional Overturning Circulation, our Koopman-based indicators distinguish tipping from non-tipping trajectories and reveal interpretable spectral signatures prior to critical transition.

Market-Information-Aware Gated-LoRA of Foundation Models for Transferable Day-Ahead Electricity Price Forecasting

Electricity price forecasting is crucial for market participants but remains difficult because prices are volatile, market-specific, and closely tied to anticipated system conditions. Existing supervised methods depend largely on market-specific historical data, limiting their use in newly established or data-scarce markets. This paper proposes a market-information-aware adaptation framework that transfers the Chronos-2 time-series foundation model to day-ahead electricity price forecasting. It first constructs a multi-source market information (MSMI) interface aligning 7-day price context with pre-clearing supply--demand, reserve, maintenance, generator-capacity, and intertie variables, and then trains a source-domain gated low-rank adapter (LoRA), updating about $1\%$ of model parameters without target-market labels. The gate scales the frozen source adapter according to reserve-tightness and operating-state signals. A leave-one-market-out protocol is adopted for evaluating cross-market transferability. Experiments on four Chinese provincial day-ahead spot markets show that the proposed framework reduces the average MAE/RMSE by $6.24\%/7.99\%$ relative to market-information-aware zero-shot Chronos-2 and by $3.05\%/3.52\%$ relative to vanilla Source-LoRA. Experiments show that the gain is not reproduced by a learned global scalar or by random gate initialization, while the additional improvement over Source-LoRA is limited. These results suggest that market-structured inputs and state-dependent gated LoRA can provide a practical transfer path for data-scarce electricity markets.

PARA-PV: Physics-Aware Retrieval-Augmented PV Prediction Based on Frozen Foundation Model and Distribution Shift Correction

Accurate photovoltaic (PV) power forecasting is essential for reliable grid dispatch and renewable energy integration, yet it remains challenging because PV generation is jointly shaped by weather variability, day-night transitions, regime-dependent dynamics, and strict physical constraints. We propose PARA-PV, a Physics-Aware Retrieval-Augmented framework that embeds physical knowledge throughout the forecasting process. The framework first encodes multivariate PV observations into patch-level representations and, through a physics-aware retrieval-augmented learner, retrieves historical patches and analog trajectories that are consistent with the current window in temporal shape, power level, PV operating state, and intra-day period; this yields a physically grounded base forecast. To supplement local memory with broader temporal knowledge, the base forecast is then calibrated against a frozen Chronos time-series foundation-model prior through a lightweight residual adapter, so that general temporal regularities are adapted to PV-specific dynamics without overriding the physically grounded prediction. Because residual conditional distribution shifts persist when weather and diurnal regimes change, a physics-aware distribution shift correction module subsequently adjusts the preliminary forecast using power, weather, timestamp, and day/night conditions, applying gated mean-shift and scale corrections selectively. Finally, a physics-constrained loss function partitions the samples into peak, ramping, night-time, and regular regimes and adaptively reweights their error contributions, preventing the dominant regular regime from suppressing learning of operationally critical states. Our code is available at https://github.com/weican1103/PARA-PV.

In-context learning to predict critical transitions in dynamical systems

Critical transitions - abrupt, often irreversible changes in system dynamics - arise across human and natural systems, often with catastrophic consequences. Real-world observations of such shifts remain scarce, preventing the development of reliable early warning systems. Conventional statistical and spectral indicators, such as increasing variance, tend to fail under realistic conditions of limited data and correlated noise, whereas existing deep learning classifiers do not extrapolate beyond their training data distribution. In this work, we introduce TipPFN, an in-context learning (ICL) framework that uses a prior-data fitted network to infer a system's proximity to a critical transition. Trained on our novel synthetic data generator, which is based on canonical bifurcation scenarios coupled to diverse, randomized stochastic dynamics, TipPFN flexibly capitalizes on contexts of various sizes, complexity and dimensionalities. We demonstrate robust, state-of-the-art early detection of critical transitions in previously unseen tipping regimes, sim-to-real examples, and real-world observations in both ICL and zero-shot settings.

WindINR: Latent-State INR for Fast Local Wind Query and Correction in Complex Terrain

Many downstream decisions in complex terrain require fast wind estimates at a small number of user-specified locations and heights for a given forecast valid time, rather than another dense forecast field on a fixed grid. We present WindINR, a latent-state implicit neural representation framework for continuous high-resolution local wind query and sparse-observation correction. WindINR maps static terrain descriptors, a low-resolution background field, and continuous query coordinates to a high-resolution wind state through a latent-conditioned decoder. To enable rapid inference-time correction, WindINR separates reusable representation learning from sample-specific latent-state correction. During training, a privileged encoder infers a reference latent state from high-resolution supervision, a deployable latent predictor estimates an initial latent state from inference-time inputs alone, and their discrepancies are summarized into a dataset-adaptive Gaussian prior over latent corrections. At inference time, within the WindINR module, network weights remain fixed and only the latent state is updated by minimizing a regularized correction objective using sparse observations and their uncertainty. In controlled OSSEs over the Senja region, including a UAV-aided approach scenario and random-observation robustness tests, WindINR improves local high-resolution wind estimates by updating only a compact latent state rather than the full network. The corrected representation remains continuously queryable at arbitrary coordinates and, in our CPU benchmark, yields about a $2.6\times$ online-correction speedup over full-network fine-tuning, suggesting a practical interface between kilometer-scale background products, sparse local observations, and wind queries in complex terrain.

Earth-o1: A Grid-free Observation-native Atmospheric World Model

Despite the unprecedented volume of multimodal data provided by modern Earth observation systems, our ability to model atmospheric dynamics remains constrained. Traditional modeling frameworks force heterogeneous measurements into predefined spatial grids, inherently limiting the full exploitation of raw sensor data and creating severe computational bottlenecks. Here we present Earth-o1, an observation-native atmospheric world model that overcomes these structural limitations. Rather than relying on conventional atmospheric dynamical modeling systems or traditional data assimilation, Earth-o1 directly learns the continuous, three-dimensional physical evolution of the Earth system from ungridded observational data. By integrating diverse sensor inputs into a unified, grid-free dynamical field, the model autonomously advances the atmospheric state in space and time. We show that this fundamentally distinct paradigm enables direct, real-time forecasting and cross-sensor inference without the overhead of explicit numerical solvers. In hindcast evaluations, Earth-o1 achieves surface forecast skill comparable to the operational Integrated Forecasting System (IFS). These results establish that continuous, observation-driven world models -- a new class of fully observation-native geophysical simulators -- can match the fidelity of established physical frameworks, providing a scalable data-driven foundation for a digital twin of the Earth.

Solar-VLM: Multimodal Vision-Language Models for Augmented Solar Power Forecasting

Photovoltaic (PV) power forecasting plays a critical role in power system dispatch and market participation. Because PV generation is highly sensitive to weather conditions and cloud motion, accurate forecasting requires effective modeling of complex spatiotemporal dependencies across multiple information sources. Although recent studies have advanced AI-based forecasting methods, most fail to fuse temporal observations, satellite imagery, and textual weather information in a unified framework. This paper proposes Solar-VLM, a large-language-model-driven framework for multimodal PV power forecasting. First, modality-specific encoders are developed to extract complementary features from heterogeneous inputs. The time-series encoder adopts a patch-based design to capture temporal patterns from multivariate observations at each site. The visual encoder, built upon a Qwen-based vision backbone, extracts cloud-cover information from satellite images. The text encoder distills historical weather characteristics from textual descriptions. Second, to capture spatial dependencies across geographically distributed PV stations, a cross-site feature fusion mechanism is introduced. Specifically, a Graph Learner models inter-station correlations through a graph attention network constructed over a K-nearest-neighbor (KNN) graph, while a cross-site attention module further facilitates adaptive information exchange among sites. Finally, experiments conducted on data from eight PV stations in a northern province of China demonstrate the effectiveness of the proposed framework. Our proposed model is publicly available at https://github.com/rhp413/Solar-VLM.

Accurate and Efficient Hybrid-Ensemble Atmospheric Data Assimilation in Latent Space with Uncertainty Quantification

Data assimilation (DA) combines model forecasts and observations to estimate the optimal state of the atmosphere with its uncertainty, providing initial conditions for weather prediction and reanalyses for climate research. Yet, existing traditional and machine-learning DA methods struggle to achieve accuracy, efficiency and uncertainty quantification simultaneously. Here, we propose HLOBA (Hybrid-Ensemble Latent Observation-Background Assimilation), a three-dimensional hybrid-ensemble DA method that operates in an atmospheric latent space learned via an autoencoder (AE). HLOBA maps both model forecasts and observations into a shared latent space via the AE encoder and an end-to-end Observation-to-Latent-space mapping network (O2Lnet), respectively, and fuses them through a Bayesian update with weights inferred from time-lagged ensemble forecasts. Both idealized and real-observation experiments demonstrate that HLOBA matches dynamically constrained four-dimensional DA methods in both analysis and forecast skill, while achieving end-to-end inference-level efficiency and theoretical flexibility applies to any forecasting model. Moreover, by exploiting the error decorrelation property of latent variables, HLOBA enables element-wise uncertainty estimates for its latent analysis and propagates them to model space via the decoder. Idealized experiments show that this uncertainty highlights large-error regions and captures their seasonal variability.

Align-DA: Align Score-based Atmospheric Data Assimilation with Multiple Preferences

Data assimilation (DA) aims to estimate the full state of a dynamical system by combining partial and noisy observations with a prior model forecast, commonly referred to as the background. In atmospheric applications, this problem is fundamentally ill-posed due to the sparsity of observations relative to the high-dimensional state space. Traditional methods address this challenge by simplifying background priors to regularize the solution, which are empirical and require continual tuning for application. Inspired by alignment techniques in text-to-image diffusion models, we propose Align-DA, which formulates DA as a generative process and uses reward signals to guide background priors, replacing manual tuning with data-driven alignment. Specifically, we train a score-based model in the latent space to approximate the background-conditioned prior, and align it using three complementary reward signals for DA: (1) assimilation accuracy, (2) forecast skill initialized from the assimilated state, and (3) physical adherence of the analysis fields. Experiments with multiple reward signals demonstrate consistent improvements in analysis quality across different evaluation metrics and observation-guidance strategies. These results show that preference alignment, implemented as a soft constraint, can automatically adapt complex background priors tailored to DA, offering a promising new direction for advancing the field.

Satellite Observations Guided Diffusion Model for Accurate Meteorological States at Arbitrary Resolution

Accurate acquisition of surface meteorological conditions at arbitrary locations holds significant importance for weather forecasting and climate simulation. Due to the fact that meteorological states derived from satellite observations are often provided in the form of low-resolution grid fields, the direct application of spatial interpolation to obtain meteorological states for specific locations often results in significant discrepancies when compared to actual observations. Existing downscaling methods for acquiring meteorological state information at higher resolutions commonly overlook the correlation with satellite observations. To bridge the gap, we propose Satellite-observations Guided Diffusion Model (SGD), a conditional diffusion model pre-trained on ERA5 reanalysis data with satellite observations (GridSat) as conditions, which is employed for sampling downscaled meteorological states through a zero-shot guided sampling strategy and patch-based methods. During the training process, we propose to fuse the information from GridSat satellite observations into ERA5 maps via the attention mechanism, enabling SGD to generate atmospheric states that align more accurately with actual conditions. In the sampling, we employed optimizable convolutional kernels to simulate the upscale process, thereby generating high-resolution ERA5 maps using low-resolution ERA5 maps as well as observations from weather stations as guidance. Moreover, our devised patch-based method promotes SGD to generate meteorological states at arbitrary resolutions. Experiments demonstrate SGD fulfills accurate meteorological states downscaling to 6.25km.