Probabilistic Forecasting

Recent probabilistic weather forecasters train stochastic predictors with the continuous ranked probability score (CRPS) to generate each ensemble member in a single forward pass. These models learn the predictive distribution from the forecast context alone, which becomes difficult at longer forecast horizons where uncertainty is high. To learn the predictive distribution more effectively, we introduce auxiliary conditional denoising tasks that predict the same future state from the context and its corrupted version, which provides partial future information that can reduce prediction ambiguity. Building on distributional diffusion models, we learn the conditional distributions of these tasks with a single stochastic predictor by minimizing a proper scoring rule across noise levels. At inference, the predictor can still generate each ensemble member in a single forward pass at the fully corrupted endpoint. Standard CRPS training is recovered as the endpoint-only special case of our formulation, so our framework extends existing CRPS-based forecasters with only additional conditioning inputs. Controlled experiments show that the auxiliary tasks improve one-step forecasting across architectures, with larger gains at longer forecast horizons. The gains extend to high-dimensional global weather forecasting under both training from scratch and fine-tuning, along with improved calibration and potential benefits for generalization under distribution shift.

Precipitation nowcasting demands accurate short-term forecasts under strong spatiotemporal variability. Diffusion models are well suited to modeling complex precipitation distributions, yet existing approaches often introduce increasingly specialized designs, leaving the capability of a standard diffusion architecture underexplored. We show that a standard Diffusion Transformer already provides a simple and scalable foundation for precipitation nowcasting, with domain-specific requirements accommodated naturally within its design space. Based on this principle, we develop NowcastDiT and instantiate this flexibility through two complementary adaptations: a dynamics-aware noise prior for temporally coherent forecasts, and end-to-end reinforcement learning with timestep-aware rewards for meteorological skill. Experiments on SEVIR and MRMS benchmarks show that NowcastDiT achieves state-of-the-art performance in both perceptual quality and meteorological skill. These results suggest that standard DiT can serve as an effective foundation for precipitation nowcasting.

Large language models have achieved significant progress in event forecasting, yet their probability outputs exhibit systematic calibration bias that varies heterogeneously across different domains and question types, undermining the trustworthiness of probabilistic outputs for decision-making under uncertainty. However, existing calibration methods typically correct probability outputs after prediction is complete, without modeling the structural sources of bias within the prediction process itself. To address this challenge, we decompose probabilistic prediction over causal-temporal hypergraphs into three stages, evidence weighting, evidence aggregation, and source fusion, and propose CHAIN, which designs stage-specific mechanisms to mitigate bias at each stage: (i) modulating the temporal decay function by causal topological distance, (ii) aggregating approximately independent causal chains via Noisy-OR after direction-aware deduplication, and (iii) driving adaptive fusion by causal coverage and directional balance. Experimental results on cross-domain forecasting benchmarks show CHAIN outperforms existing methods in expected calibration error, Brier score, and accuracy. Our project is available at https://github.com/QwenQKing/Chain.

Research agents explain planned experiments. We measure predictive credit with paired forecasts sharing an intervention, forecaster, and outcome while varying description, matched explanation, and donor context. Five checks track commitment, delivery, predictive gain, alignment, and known-signal uptake. Across 336 prospective states in controlled learning, 12 Tox21 endpoints, and 24 OpenML tasks, v5's frozen credit decision was inconclusive. Tox21's preregistered ROC AUC interval-score harm test was unmet ($D-M=-.0026$, 95 percent interval [$-.0174$, .0104]); OpenML's joint formation, point-equivalence, and repeatability rule was unmet. Matched point-accuracy gains over description remained unconfirmed, and Tox21/OpenML seed-donor intervals spanned zero. Under requested DeepSeek V4 Pro, matched and donor cards reduced secondary Tox21 drift by 64.5 and 59.1 percent. A DeepSeek V4 Flash replay raised matched point MAE from .01823 to .02020 and missed matched-donor interval-score equivalence. OpenML full-card assignment widened nominal 80 percent intervals by 21 percent, with 49.3 percent coverage versus 51.4 percent for description and content in 66/144 cards. Direct-text Flash delivered all 144 notes without detectable matched point-accuracy gain. A researcher-authored mechanism positive control lowered point MAE by 2.60 percentage points versus description. The protocol measures predictive credit for research-agent benchmarks and scientific forecasting; natural-explanation credit remained unconfirmed at the tested donor resolutions.

Modern probabilistic machine learning models increasingly produce multivariate outputs with complex dependence structure, from multi-step time-series forecasts to sample path predictions. Understanding which input features drive the predictive uncertainty is important for risk-aware decisions, model diagnostics, and deciding whether the uncertainty should be mitigated or hedged against. This attribution problem requires a choice of how dependencies between output components are treated. Existing approaches reduce the output to a scalar through aggregation or projection before attribution, thereby obscuring whether features affect marginal uncertainty, dependence structure, or both, while component-wise analyses can miss dependence effects entirely. We close this gap by introducing a hierarchy of three entropy-based Shapley games that make this output-side choice explicit for any ordered multivariate outcome, ranging from per-component marginal entropy to fully joint entropy. The hierarchy isolates a cross-component attribution term that captures how each feature shifts the dependence between output components, a quantity invisible to component-wise methods. We establish a chain-rule decomposition of the joint attribution and characterize the cross-component term through conditional total correlation, providing both closed-form and sample-based estimators. Finally, we demonstrate how the framework captures differences in learned joint structure across probabilistic models from distributional regression to a zero-shot time series foundation model.

Extending reliable nowcasting of extreme precipitation could provide critical additional time for warnings and emergency response during high-impact events such as flash floods. Radar-based generative machine-learning models have enabled skilful hyperlocal precipitation nowcasting, but accurate prediction of intense precipitation remains confined to the first few hours. Because storm-scale structure is predictable for longer than individual cells, a natural strategy is to predict that structure while generatively modelling only the uncertain local growth, decay, reorganisation and initiation of storms. Here we present Microsoft Weather Nowcast (MW-Nowcast), a six-hour ensemble radar nowcasting model that jointly learns a deterministic predictor to capture organised precipitation structure shared across ensemble members, and a generator to produce diverse local residuals around this shared prediction. Across independent test data from the United States, Europe and China, MW-Nowcast achieves higher detection skill than leading methods for heavy and extreme precipitation throughout the 6 h horizon. For the most intense rainfall, MW-Nowcast doubles the available warning time across all three regions, delivering 6 h forecasts with skill previously limited to 3 h for the leading generative baseline. A cost-loss decision analysis shows that MW-Nowcast retains substantial value for a broad range of applications even at 4-6 h, where alternative methods offer little benefit. These additional hours can give forecasters and emergency managers the time to warn and act before extreme rainfall strikes, helping to protect lives and property.

The majority of research on electricity consumption forecasting has focused on deterministic approaches, which generate a single point estimate for each time step in the forecasting horizon. However, the increasing penetration of renewable energy sources and the growing complexity of modern smart grids have introduced greater variability and uncertainty into power-system demand and operation. Consequently, probabilistic forecasting, which quantifies the uncertainty and variability associated with future electricity demand, is becoming increasingly important for reliable power-system planning and operation. This study presents an empirical comparison of four contemporary probabilistic forecasting models for electricity consumption, highlighting their respective strengths and limitations. We have performed comparision on real-world power systems related datasets. Across all power-consumption zones, NGBoost demonstrates superior probabilistic forecasting performance, achieving the lowest MAE and RMSE while providing well-calibrated uncertainty estimates with high prediction-interval coverage and reasonably narrow intervals. These results indicate that NGBoost offers a more accurate and reliable forecasting framework than Bayesian, Monte Carlo (MC) Dropout, and Gaussian Process Regression (GPR) models for the considered electricity consumption data.

Many probabilistic predictors must satisfy exact structure in every stochastic realization, yet common hard-constraint approaches form predictions in ambient coordinates and then correct or project them. We introduce SLP-ProbHard, a cross-family, representation-centered framework for probabilistic hard-constrained learning when explicit structural parameterizations are available. Its core object, a Structural Feasible Latent Parameterization (SFLP), combines a structural latent law $Z \sim P^Z_θ(\cdot\mid x)$ with a feasible map $Y=h_φ(x,Z)$ that satisfies the constraint for every latent realization. Together these components define the predictive law itself, including its support and boundary probabilities, rather than serving as a final feasibility wrapper. We study how feasible coordinates and maps affect stochastic dimension, dependence, calibration, expressiveness, and computation. Experiments use Gaussian latent laws and fixed geometry-derived maps across affine equalities, ordering and simplex constraints, nonlinear manifolds, and three structural representations of seven-basin hydrological flow-duration-curve (FDC) data. In an official-source affine comparison with ProbHardE2E/DPPL, both methods achieve zero practical constraint violations. SLP-ProbHard uses 8 instead of 11 stochastic coordinates and improves MSE/MAE, while DPPL yields better marginal CRPS and closer-to-nominal coverage; a paired test detects no Energy Score difference across ten seeds. Real-world affine and nonlinear FDC representations reduce 13 to 7 and 14 to 8 ambient versus computational coordinates, respectively. Exact feasibility alone thus does not determine a predictive law, motivating direct structural generation when meaningful feasible coordinates are available.

Large language models (LLMs) are increasingly used to forecast real-world events, but access to the strongest individual forecaster may be costly or otherwise constrained. We study weak-to-strong forecast aggregation: can individually weaker LLM forecasters be aggregated to outperform a stronger forecaster? Using ForecastBench (Karger et al., 2025), we evaluate 70 LLM forecasters across 16 comparison groups, each with more than 1,000 shared subquestions, yielding 1,121 weaker-model pairs. Within each group, we identify the strongest individual by test Brier score and evaluate aggregates composed exclusively of weaker forecasters, with aggregation weights learned on separate training data. We find substantial evidence of weak-to-strong improvement. Learned linear pooling identifies a weaker pair that matches or outperforms the strongest individual in 11 of 16 groups and comes within 5% of its Brier score in all 16 groups. We also find that these improvements do not rely on having a near-best constituent and are generally accompanied by good calibration. Additional analyses show that adding more models does not consistently improve performance, and competitive weaker-model aggregates also remain available under practical constraints.

Ocean wave forecasting is essential for maritime safety, offshore operations, and coastal resilience, yet remains challenging due to systematic biases in physics-based models. Physical models, while widely used, rely on approximations and parameterizations that limit their accuracy under complex ocean-atmosphere conditions. To enhance ocean wave forecasting, we propose BridgeCast, within a physics-AI hybrid framework for bias correction. BridgeCast is a probabilistic model based on conditional flow matching (CFM) that learns to transform physical model forecasts into reanalysis-like fields. It treats physical forecasts as corrupted observations and employs a continuous-time generative process to bridge their distribution toward that of reanalysis data. BridgeCast is parameterized by a Transformer-based architecture that enables spatiotemporal modeling, incorporation of exogenous atmospheric variables, and flexible inference via both ordinary and stochastic differential equation formulations. Extensive experiments on real-world datasets demonstrate that BridgeCast consistently outperforms state-of-the-art baselines across regions and forecast lead times.

We study whether model upgrades improve probability estimates for prediction-market questions. Our Resolved Market Forecasting (RMF) benchmark contains 3,000 resolved binary questions across nine domains, on which we evaluate six Claude and Qwen model variants using a question-only, zero-shot protocol. We assess Brier scores relative to an empirical base-rate predictor, examine their Murphy decomposition, and compare models through paired differences, with results stratified by event category and timing relative to training cutoffs. In the reported post-cutoff stratum, the four Claude models achieve Brier scores of 0.183-0.192, improving on the base-rate reference by 0.024-0.033. Qwen 32B does not significantly outperform that reference, although its paired Brier is 0.024 lower than that of the 7B checkpoint. The evaluated Claude version and tier upgrades yield no significant improvement. Within-model differences across event categories exceed the observed differences among Claude variants. These results show why forecasting scores should be interpreted alongside simple probability baselines and question composition: under this protocol, newer versions or higher model tiers do not consistently produce more accurate probabilities.

Forecasting short-horizon mid-price movements from limit order book (LOB) data is central to algorithmic trading, yet most deep LOB forecasters are point predictors: they output a direction or a displacement, but never indicate which of their forecasts can be trusted. We introduce UQ-LOB, a lightweight, encoder-agnostic uncertainty quantification module that attaches to any pretrained LOB encoder and, in the spirit of attentive neural processes, conditions each forecast on a context set of recently completed windows whose outcomes are already realised. The UQ-regression variant outputs a calibrated Gaussian over the future tick displacement, while the UQ-classification variant outputs a categorical distribution over down/up/stationary. Both expose a scalar confidence (predicted signal-to-noise ratio or class probability) that supports selective prediction. On 5.2 billion LOB events across seven cryptocurrency assets and horizons of 5, 10 and 15 seconds, UQ-regression attains near-nominal 68% interval coverage, and restricting to the most confident 10% of predictions raises directional macro F1 by 0.11-0.15 for UQ-regression and 0.05-0.11 for UQ-classification, at every horizon. On large, economically meaningful moves, the tightest confidence tier reaches a directional F1 of 0.88 (down) and 0.83 (up) at the 5-second horizon.

Space weather disturbances driven by the solar wind can degrade satellite navigation, disrupt radio communications, and threaten power infrastructure, making accurate forecasting of the high-latitude ionosphere's response a critical operational need. Existing approaches, empirical climatological models and physics-based magnetohydrodynamic simulations, either smooth out the ionosphere's time-dependent, non-linear response or are too computationally expensive for real-time use, while prior machine learning efforts have mostly targeted scalar indices rather than the full spatial structure of ionospheric convection. Here we train and compare three deep learning architectures, a probabilistic diffusion model conditioned on multi-variate solar wind and interplanetary magnetic field measurements at the L1 Lagrange point, an unconditioned diffusion ablation, and a deterministic U-Net baseline, to forecast Southern Hemisphere high-latitude electric potential maps derived from SuperDARN radar observations. Using five years (2020--2025) of SuperDARN data synchronised with DSCOVR L1 measurements, we evaluate the models under a single-pass regime, an extended autoregressive rollout of up to 350 frames, and an out-of-distribution case study on the intense March 2015 St.\ Patrick's Day storm, unseen during training. We find that the relative advantage of the deterministic and probabilistic approaches is not fixed: the deterministic model is competitive over short horizons and calm conditions, while the diffusion model's advantage grows and eventually dominates as the forecast horizon lengthens and the event becomes more dynamic, evidence that probabilistic, sample-based generative models are the more promising direction for operational, long-horizon space weather forecasting.

Artificial intelligence (AI)-based weather prediction is approaching the skill of physical numerical weather prediction (NWP) systems at a fraction of the computational cost. This is particularly promising for Africa, where rainfall extremes are intensifying and many forecasting centres lack the infrastructure to run physical models at extended lead times. We present a calibrated comparison of GraphCast, GenCast and the Functional Generative Network (FGN) against the physical NWP model IFS for rainfall prediction across Africa. Deterministic and probabilistic forecasts are postprocessed using Isotonic Distributional Regression and evaluated with the Continuous Ranked Probability Score against IMERG, RFEv2 and CHIRPS across seasons, wet and dry regimes, elevation zones and lead times. All models retain skill beyond climatology across most seasons and at extended lead times. AI models generally outperform IFS in wet regions, whereas IFS performs better in dry, high-elevation areas, where its finer resolution better represents orographic controls on rainfall. Across observational datasets and seasons, AI models achieve a median improvement of approximately 5% over IFS. GraphCast achieves calibrated skill comparable to the ensemble-based FGN, although FGN provides greater significant skill at longer lead times. These results highlight the potential of calibrated AI weather prediction to provide accessible and computationally efficient rainfall forecasts across Africa, while demonstrating the continuing importance of spatial resolution, ensemble design and regional characteristics.

Climate data downscaling is the task of increasing the spatial resolution of climate data, typically by generating fine-resolution regional climate data from coarse global model output. Recent machine learning (ML) work in the related task of weather forecasting has seen significant improvements due to newly devised training methods and architectural components, but these have not yet benefited downscaling. We adapt two of these methods to create a family of lightweight probabilistic ML downscaling models built on a modified U-Net backbone and evaluate them on the CORDEX-ML-Bench suite for daily maximum temperature and precipitation across three geographic regions: the Alps, New Zealand and South Africa. We find that a two-stage training curriculum, combining deterministic pretraining with probabilistic tuning, transfers well to downscaling, beating the state-of-the-art for RMSE. Our work provides an advancement towards lightweight, probabilistic downscaling models, reducing the current trade-off between computational intensity and distributional fit.

Long-term autonomy in human-populated environments requires anticipating whether and how people will move at times a robot has not yet observed. Existing representations of pedestrian motion face a tradeoff: they either forecast future activity, reducing each location to a scalar rate, or model the full directional distribution, holding it fixed in time. We present Kairos, a predictive directional-flow memory that extends a hierarchical 3D scene graph (3DSG) to a 4D scene graph (4DSG). Every observed voxel of the reconstructed geometry stores a directional mixture and a presence rate, and spectral predictors forecast, for any future query time, both the probability that people are present and the full directional distribution of their motion. Pairwise flow dependence between adjacent voxels supports conditional queries, and per-voxel predictive variances yield calibrated credible intervals that tighten as observations accumulate. We evaluate Kairos on three real pedestrian environments: a robot-collected campus dataset, a shopping mall, and a station concourse recorded continuously for eleven months. Its learned state remains consistent under loop-closure corrections, and its forecasts are competitive with dedicated occupancy and flow models trained on the full detection stream, although Kairos learns from only the small fraction available to a patrolling robot. Finally, we validate the representation on a downstream encounter-probability planning task, where plans computed over the Kairos forecasts encounter more people than plans computed over any time-invariant map at an equal success rate. We provide the code at https://github.com/IacopomC/kairos.

Probabilistic time series foundation models (TSFMs) provide coordinate-wise predictive distributions, but these marginals do not determine a joint distribution over multivariate future trajectories. We study training-free coupling of frozen TSFM marginals into multivariate forecast sample paths. Our primary evaluation fixes the empirical marginal sample multiset at every channel--horizon coordinate across methods, isolating the effect of coupling alone. Historical temporal and channel relations substantially improve their corresponding dependence diagnostics. The same pattern persists when the fixed-marginal constraint is removed and paths are sampled directly, and remains present under native multivariate backbone inference. These results support treating dependence reconstruction as a distinct post-processing problem for probabilistic TSFMs.

Rapid intensification (RI) remains one of the most consequential and difficult aspects of tropical cyclone (TC) forecasting. Although full-physics numerical weather prediction models can represent the processes governing RI, resolving storm-environment interactions remains computationally expensive, while purely data-driven approaches often lack physical interpretability. We present FAST-ML, a hybrid framework that bridges data-driven efficiency with physical constraints. A physically informed dual-stream neural parameterization ingests 3D ERA5 fields to diagnose ventilation controls---environmental wind shear and mid-level entropy deficit. By optimizing these parameters end-to-end through a differentiable FAST intensity model, this architecture establishes a robust new paradigm for observation-driven parameter optimization, ensuring storm evolution remains strictly governed by thermodynamic principles. By better capturing the storm's continuous intensity evolution, FAST-ML improves upon its physical baseline, reducing ensemble CRPS across forecast lead times, with a reduction of approximately 31% at 60 h and nearly halving the RI false alarm ratio without sacrificing detection skill. In a 100-member ensemble configuration, FAST-ML produces intensity forecasts comparable to FNV3 for selected storms under the evaluated input configurations. Furthermore, zero-shot tests on selected Eastern Pacific storms provide encouraging evidence of cross-basin transferability. FAST-ML provides a modular intensity forecasting framework that can be coupled with externally supplied storm tracks and environmental fields. It demonstrates that observation-driven parameter learning within physically constrained dynamics simultaneously enhances accuracy, interpretability, and computational efficiency.

Renewable forecasts are evaluated by statistical skill (e.g., CRPS), but grid operators pay for realized dispatch cost. We diagnose what drives dispatch value in a single-period newsvendor-style economic dispatch using real public data from two European transmission systems (CWE, DE-4TSO). Spatial coherence across forecast sites falls below the pre-specified 1% practical-significance threshold: a controlled ablation holding per-zone marginal forecasts bit-identical and varying only cross-zone dependence (10 configurations, 3 seeds, paired-bootstrap confidence intervals) shows a coherence gain of at most 0.64% of dispatch cost, indistinguishable from zero in 3 of 10 configurations, reached only under an unrealistic 8-fold forecast-error stress test. Decision-focused training, an established paradigm in this venue, delivers a robust 2.82-5.19% gain. A parametric Gaussian-copula approximation matches the empirical copula at realistic error magnitudes but performs worse than no dependence under extreme stress. A single-seed sweep shows that a 12% energy-score gain changes cost by less than 0.1%. Results characterize this single-period dispatch class; a lightweight four-period extension supports the same conclusion. For this dispatch class, spatially-correlated scenario generation provides limited operational value on its own; grid operators and forecast vendors should instead evaluate dependence models by downstream decision value and prioritize decision-focused training.

Operators of service-based systems act on forecasts of how a running execution will continue, and such a forecast is actionable only if its reliability is known. Mainstream deep-learning models for this task are discriminative and deterministic: they emit a single next activity and a single remaining-time estimate, without a distribution to reason over. We instead cast the problem as generative sequence modelling with marked temporal point processes, which define a joint density over the next mark and its inter-event time and therefore deliver predictive distributions by construction. Real event logs violate the simple-point-process assumption these models rest on, since consecutive events frequently carry identical timestamps; we handle such ties explicitly and combine a transformer encoder with a mixture decoder over inter-event times, trained by exact log-likelihood. On ten public logs, the resulting model matches discriminative baselines on point accuracy, dominates them on the calibration and sharpness of remaining-time distributions, and is the cheapest at inference, since a full predictive distribution is obtained in a single forward pass without sampling.

This study analyses kinetic energy (KE) spectra, difference kinetic energy (DKE) spectra, and signatures of KE transfer across spatial scales in four state-of-the-art probabilistic machine learning weather prediction (MLWP) models: NeuralGCM-ENS, FourCastNet 3, AIFS-ENS, and GenCast. Results are compared with those from the physics-based numerical weather prediction model IFS-ENS. While NeuralGCM-ENS successfully reproduces the expected upscale transfer of KE, noise injection at its encoder stage underestimates mesoscale KE. Conversely, AIFS-ENS, GenCast, and FourCastNet 3 produce realistic KE spectral magnitudes but do not capture the expected upscale transfer of KE. In particular, AIFS-ENS and GenCast, which employ spatially uncorrelated stochastic perturbations, exhibit enhanced accumulation of KE at high wavenumbers. All examined models exhibit upscale error growth, reflected by the progressive shift of the DKE spectral peak toward larger wavelengths over time. However, the MLWP models struggle to reproduce the rapid initial growth of ensemble spread at small spatial scales associated with the butterfly effect. The results show that MLWP models can misrepresent the known scale transfer of kinetic energy despite producing skilful weather forecasts.

Probabilistic downscaling must represent kilometer-scale structure left unresolved by a deterministic regional prediction. We introduce an analog-initialized latent transport method that uses historical regional residuals as a meteorologically informed empirical source. A frozen graph neural network predicts the deterministic state from the Integrated Forecasting System (IFS). For each input, residuals from 20 training dates with similar IFS conditions initialize the ensemble. A conditional flow-matching model transports these fields in a carefully designed 65-factor, 100,000-node latent space, and a grid decoder reconstructs 81 atmospheric channels including precipitation at 2.5km spacing. On a season- and cycle-balanced 2025 test, ensemble CRPS improves over deterministic mean absolute error for all 81 variables. Matched analogs improve point and spatial errors over Gaussian initialization and reduce spectral error compared with covariance matching. Comparisons with released CorrDiff, a local CorrDiff-mini model and full grid EDM provide context on the 2023 validation sample. Total training of the downscaling model takes approximately 12h on one NVIDIA H200, and inference takes about 12s per 81-field member. The frozen networks also generate fields over France when supplied with local static data and a high-resolution IFS-derived analog bank. The method combines empirical initialization with whole-domain latent transport for computationally practical regional ensembles.

Efficient physical resource block (PRB) allocation in 5G networks requires accurate demand forecasting. Conventional methods minimize symmetric error metrics (MAE, RMSE), ignoring the operational cost asymmetry where under-provisioning (service degradation) is far costlier than over-provisioning (wasted capacity). We propose a goal-oriented probabilistic forecasting framework that aligns model training with the operator's decision-making objectives. Specifically, we train DeepAR and Temporal Fusion Transformer (TFT) models using the Pinball Loss function and derive the optimal allocation quantile from the operator's cost matrix. Evaluation on a real beam-level 5G traffic dataset shows that the proposed approach reduces operational cost compared to MSE-trained baselines while maintaining calibrated uncertainty estimates. The framework enables dynamic PRB allocation that explicitly balances service reliability against resource efficiency.

We present IRENE (Italian Radar Ensemble Nowcasting Experiment), a deep learning model for probabilistic short-range precipitation nowcasting over the Italian domain at \SI{1}{km} spatial and 5 min temporal resolution. IRENE adopts an encoder--forecaster architecture built on multi-scale Convolutional Gated Recurrent Units (ConvGRUs), trained on the national radar composite produced by the Italian Civil Protection Department (DPC). An importance-sampling scheme focuses training on precipitation-relevant events, while the almost-fair Continuous Ranked Probability Score (afCRPS) is adopted as the primary probabilistic loss function. Two additional training configurations are proposed: an adversarial (GAN) variant, IRENE-GAN, designed to improve the spatial sharpness of the generated forecasts, and a spectrally constrained variant, IRENE-GAN-RAPSD, in which the adversarial objective is complemented by an explicit penalty on the radially averaged power spectral density. The three configurations are evaluated against the stochastic extrapolation method STEPS and the pre-trained deep learning model DGMR. All IRENE configurations attain a lower Continuous Ranked Probability Score than both benchmarks at every lead time and rank histograms closer to uniformity, indicating better probabilistic skill and ensemble calibration. In terms of ensemble-mean mean absolute error the advantage is confined to the first 90 min, beyond which the strongly damped DGMR fields and, to a lesser extent, STEPS become competitive. Spectral analysis shows that the adversarial training removes the progressive loss of small-scale variance exhibited by IRENE, at the cost of an excess of fine-scale power at long lead times that the spectral penalty only partially controls.

We introduce loss-conditioned state execution, a model-agnostic method that decides whether to execute a world model's fixed feasible proposal or retain the current state. Predictive informativeness alone, however, does not establish whether an update will reduce downstream loss. Occurrence ranking can approach perfection while persistence remains the unique absolute-loss Bayes action. Two transition laws can also share occurrence information and conditional variance yet require opposite absolute-loss decisions. We formalize state movability as the existence of a loss-reducing feasible correction and distinguish it from the benefit of a particular proposal. Our method constructs a loss-specific feasible proposal from a predictive distribution and evaluates its groupwise bounded-loss gain over persistence on independent calibration units. The proposal is executed only in groups with a positive simultaneous lower confidence bound. For fixed proposals and groups with bounded unit losses, we prove that every accepted group has lower expected loss than persistence with high probability when calibration units are i.i.d. draws from the target population. Experiments on public forecasting and action-conditioned dynamics benchmarks show supported updates and a trade-off between certification and coverage. On 28,684 held-out M4 Monthly series, the method executes the proposal for 14.0% of series and achieves bounded loss 0.588, compared with 0.599 for persistence and 0.621 for always executing the proposal. The paired 95% bootstrap intervals for both comparisons lie below zero. In constrained forecasting of six unhealthy-inventory types from JD$\mbox{.}$com, a leading e-retailer in China, strong occurrence-ranking signal coexists with a loss-based preference for persistence, illustrating why event predictability and state execution must be evaluated separately.

Understanding and predicting wildlife movement is critical for ecology and conservation. While trajectory forecasting has advanced for human and vehicle movement, wildlife trajectories present distinct challenges: they are unconstrained in space, highly stochastic, and influenced by environmental conditions. We introduce MoveBench, the first large-scale benchmark for probabilistic wildlife movement forecasting, containing 2.6M GPS locations from 800+ individuals across 110 species in 127 countries, paired with 1.6B environmental raster tiles capturing 160 covariates known or hypothesized to influence movement. We propose a probabilistic evaluation protocol for movement trajectory forecasts, addressing limitations of point-prediction metrics for inherently stochastic phenomena. Through comprehensive empirical evaluation of four method families across multiple temporal and spatial scales, we reveal that: (1) existing predictive methods generalize better to future timepoints than to unseen individuals, (2) deep learning approaches do not consistently outperform simpler baselines, and (3) environmental covariate selection significantly impacts performance. MoveBench enables standardized evaluation of movement forecasting methods and provides a foundation for methodological advances on this ecologically important task.

Probabilistic forecasting is central to decision-making under uncertainty, yet its methodological landscape has become increasingly fragmented across temporal and spatiotemporal forecasting, statistical modeling, machine learning, and deep generative modeling. This survey develops a unified perspective by organizing probabilistic forecasting methods according to where and how uncertainty is introduced into the forecasting pipeline. Our taxonomy connects model-agnostic approaches including ensembles and distribution-free calibration, with model-intrinsic approaches spanning Bayesian modeling, parametric predictive distributions, distributional regression, and modern generative models, and further examines the emerging role of time series foundation models. Beyond methodological synthesis, we identify the assumptions, computational demands, and forms of uncertainty represented by different paradigms, and translate these distinctions into data-driven and domain-specific guidance for method selection. We complement the survey with a cross-paradigm empirical study on univariate, multivariate, and spatiotemporal forecasting tasks. The results reveal that no single uncertainty-quantification paradigm dominates across settings. Calibration, sharpness, predictive accuracy, and computational efficiency can lead to substantially different model preferences, while expressive generative models and zero-shot foundation models exhibit markedly different accuracy-efficiency trade-offs. Lastly, we identify unresolved challenges surrounding uncertainty in evolving dependency structures, physics-informed predictive distributions, forecasting extreme events, handling count-valued, directional, and continuous-time series, and the development of unified software resources. Our survey provides both a conceptual framework and a practical roadmap for probabilistic forecasting research.

We present BEAST, the first-ever Bayesian Swin Transformer for atmospheric forecasting on 0.25$^\circ$ global resolution able to accurately quantify both aleatoric and epistemic uncertainty. To overcome the associated computational bottlenecks, we devise an orthogonal 4D-parallelization scheme that introduces a unique domain-tensor-parallelism strategy and a novel uncertainty parallel method, enabling us to fully leverage GPU capacity and efficiently scale model training. For a 2.4-billion-parameter model, we achieve a peak performance of 3.96 EFLOP/s on 20,480 NVIDIA GH200 GPUs on the JUPITER supercomputer. We train BEAST as a 700-million-parameter model with 96 random weight samples on 384 nodes on 40 years of data for nearly one million gradient updates. This model achieves predictive skill scores competitive with state-of-the-art probabilistic atmospheric AI models and numerical models, and can predict extreme events with exceptional skill, while generating large ensembles 3 to 4 times faster than the current-best AI model. Our contribution unlocks the potential of high-fidelity uncertainty quantification in atmospheric AI models, heralding a new era for AI-based models in climate and Earth system sciences.

Large language models are being organized into multi-agent systems with specialized roles, but whether such specialization produces distinct forecasts and whether subsequent synthesis improves utility remains unclear. In this study, we carried out a live, prospective evaluation over the final 56 matches of the information-dense 2026 FIFA World Cup, keeping a frontier foundation model constant while assigning two primary forecasting agents contrasting specialist roles: a quantitative specialist focusing on structured performance statistics and a news specialist focusing on current injuries, tactics and information from press conferences. Their forecasts were then reviewed by a separate critic before being combined by a meta-agent, resulting in a sequential four-agent model. Forecasts from the betting market served as an external benchmark. The news specialist obtained the highest mean probability-weighted Top-3 utility and matched the betting market in Top-3 exact-score hits. Nevertheless, the two specialist forecasters agreed on at least two of the three scorelines in 50 out of 56 matches, and the meta-agent never generated more than one scoreline outside the specialists' forecast set. These findings show that rapidly changing, unstructured information can provide a valuable forecasting signal alongside structured statistics, whereas adding critic and meta-agent stages does not necessarily create complementary information or improve on the strongest specialist.

When a forecasting system already has a prediction from a market, crowd, or statistical model, when should it use a language model? Standalone accuracy cannot answer this question because a less accurate model may still improve the existing forecast. We study this distinction through relative competence, separating a model's replacement advantage from its complementary value. Under Brier loss (squared error between predicted probabilities and binary outcomes), we characterize when model disagreement can correct external forecast errors and derive the population gain from regime-specific affine pooling. We introduce a competence gate that estimates source weights from resolved outcomes, shrinks regime-specific estimates toward a global solution, and chronologically recalibrates the pooled forecast. Across 4,974 resolved binary questions and four language models, the best standalone model has 24.94% higher Brier loss than the calibrated external forecast, yet the gate improves that reference by 3.35% (95% CI, 1.80 to 4.90%). Model contributions vary across forecasting regimes, with larger corrections in thinner markets and forecasting crowds and smaller corrections in higher-participation settings. The gate also shows no statistically detectable performance difference from more flexible contextual aggregators. These results demonstrate that standalone superiority is not necessary for complementary predictive value and that language models should be evaluated relative to the forecasts already available.