WeatherNext 3: Increasing resolution and performance of global weather models with raw observations

State-of-the-art AI weather models have shown impressive medium-range forecast skill and computational efficiency, but suffer two key shortcomings: their forecasts have lower spatial and temporal resolution than the best physics-based models and they are exclusively initialized with and trained on analysis data. As a result, they cannot directly make use of observations, and any biases in the analysis are inherited by the forecast. WeatherNext 3 addresses these shortcomings and establishes a new state-of-the-art for probabilistic medium-range forecasting skill. First, WeatherNext 3 generates new forecasts every hour (rather than every 6 hours like traditional global models) by ingesting low-latency geostationary satellite data. Second, WeatherNext 3's temporal and spatial resolution are on par with physics-based global models, with hourly time steps and 0.1 degree resolution for single-level variables, including solar radiation and cloud cover. Third, WeatherNext 3 moves beyond traditional analysis variables by learning to predict satellite-derived precipitation estimates, as well as tropical cyclone and station observations. Modelling sparse station data allows WeatherNext 3 to make 2m temperature and dewpoint predictions at any location and time, conditioned on local geographical features, with substantially lower error than competing global models, even when evaluated against unseen stations. Together, WeatherNext 3's capabilities move operational AI-based weather forecasting beyond emulating the traditionally distinct stages of data assimilation, forecasting and post-processing, which helps to further push the frontier of performance and granularity for global weather prediction.

Dutch Books for Language Models

People increasingly use language models to support life decisions. Many such decisions involve a probabilistic forecast: How likely is a major life event, a natural disaster, or an economic outcome? Users of language models may implicitly trust that these forecasts fall out of a coherent world model. In this paper, we evaluate the coherence of language model probabilistic forecasts through a procedure that builds on a theorem due to de Finetti. We elicit forecasts from language models across events generated from stock returns data. We then use linear programs to compute the largest Dutch-book profit - the profit an arbitrageur could guarantee by betting against model-generated probabilities - which we use as a measure of incoherence. Our procedure does not require outcome labels, so we can evaluate coherence even in settings where outcomes are not observed or have not yet resolved. We find substantial evidence of incoherence in language model forecasts. Such incoherence increases when there are richer logical relationships between events, and irrelevant contextual details can increase incoherence by an order of magnitude. We conclude by discussing how alternative training strategies may improve probabilistic coherence.

DynG-Diff: A State-Aware Dynamic Guidance Diffusion Framework for Probabilistic Time Series Forecasting

Probabilistic multivariate time series (MTS) forecasting is crucial for modeling complex dynamical systems. However, existing diffusion-based methods rely on task-specific conditional paradigms that lack flexibility and struggle with inherent "information heterogeneity"--the significantly varying noise levels and evolutionary patterns across variables. To address this, we propose DynG-Diff, a variable-sensitive dynamic guidance diffusion framework for probabilistic multivariate time-series forecasting: (1) DynG-Diff adopts a two-stage separated training strategy and uses an unconditional diffusion backbone to model the joint distribution of multivariate time series. (2) DynG-Diff introduces a lightweight state-aware policy network that adaptively infers variable reliability from real-time noisy states and one-step denoising estimates, outputting a dynamic guidance strength matrix. (3) DynG-Diff mathematically formulates this dynamic weight as the local precision of the observation distribution, enabling precise guidance for high-confidence variables during inference while filtering out interference from anomalous noise. Extensive experiments on real-world benchmarks demonstrate competitive probabilistic forecasting performance against state-of-the-art conditional diffusion models and improved robustness under severe observation corruption.The implementation code is available at: https://github.com/TT-20011031/DynG-Diff

LEAP: Likelihood Elicitation and Aggregation for LLM-based Probabilistic Forecasting

LLM-based forecasting systems have improved on real-world tasks such as financial markets and sports outcomes, largely through stronger search and tool use. Many systems still ask an LLM to read all collected evidence together and produce the final forecast. We call this design Monolithic Prediction. It can obscure how individual evidence items affect the result and collapse uncertainty across competing outcomes. We propose LEAP (Likelihood Elicitation and Aggregation for Probabilistic forecasting), which reorganizes how collected evidence is used in the prediction stage. LEAP examines each evidence item separately and elicits likelihood parameters that describe its implications for the target. An explicit prior and a deterministic probabilistic model then combine these likelihoods into a posterior distribution. This procedure supports continuous, single-choice, and multi-choice forecasts while preserving reproducible evidence contributions. We build a benchmark covering forecasting, information-seeking, and browsing tasks, and evaluate LEAP on our own agent loop and several agent CLI frameworks. Given the same evidence, LEAP improves most prediction and calibration metrics across models and remains stronger under controlled comparisons of prior access, inference budget, and aggregation.

Uncertainty-Aware End-to-End AI Weather Forecasting: Disentangling Observation and Model Contributions

End-to-end weather forecasting systems produce skillful global gridded and station forecasts directly from raw Earth observations, replacing the numerical weather prediction pipeline, including data assimilation, at a fraction of its cost. These systems are deterministic and issue no uncertainty. Here we render the Aardvark Weather model probabilistic by attaching one stochastic mechanism to each component: learned, input-dependent noise at the observation encoder, capturing aleatoric uncertainty inherited from the observing system, and Monte Carlo dropout in the processor, capturing epistemic uncertainty in the learned dynamics. The resulting nested ensemble attributes forecast spread to the two sources through a law-of-total-variance decomposition, cross-checked by withholding observation streams. Probabilistic finetuning significantly improves the mean forecast, by 4.2% on average across variables and lead times. The ensemble is calibrated against ERA5 through the medium range (spread-skill ratio 0.98), keeps station RMSE within 2.4% of the deterministic model while beating it in CRPS at every lead time, and trails the operational ECMWF ensemble. The encoder branch behaves as observation-driven uncertainty. Component-attributed uncertainty makes end-to-end forecasts more transparent, a step toward observation-driven digital twins of the atmosphere.

Diffusion-Based Refinement for Kilometer-Scale Probabilistic Precipitation Nowcasting

Localized extreme precipitation is a major trigger of urban flash floods and landslides, yet producing nowcasts that combine fine spatial detail with probabilistic uncertainty remains challenging. Here we introduce exPreCast-ENS, a conditional residual diffusion framework that transforms the deterministic 4 km radar nowcaster exPreCast into a 1 km probabilistic ensemble while correcting systematic forecast errors. Conditioning on both the forecast and preceding radar observations lets the ensemble-mean correct the baseline rather than perturb it, while members represent unresolved fine-scale variability. Over the Korean Peninsula, skill improves with ensemble size. In two high-impact events in 2023, a 30-member ensemble recovers 38-47% of heavy-rain pixels missed by exPreCast while retaining approximately 95% of its correct detections and alarming on under 1% of the pixels it correctly left clear. The method generates a 1-h forecast in 3.4 s on a single GPU and yields consistent improvements on the French regional MeteoNet radar dataset.

SimCast-S2S: An Efficient Generative Model for Subseasonal Precipitation Forecasting via Transfer Learning from Climate Simulations

Subseasonal-to-seasonal (S2S) precipitation forecasting has substantial financial and societal impact, yet remains challenging because of weak predictive signals, high associated uncertainty, and the computational cost of operational systems, which constrains simulation fidelity. We introduce SimCast-S2S, a generative latent-diffusion framework for probabilistic S2S precipitation forecasting that addresses three major bottlenecks in data-driven prediction. First, because S2S prediction requires uncertainty quantification rather than only deterministic point forecasts, SimCast-S2S is the first data-driven system that uses a diffusion-based generative pipeline for S2S prediction, enabling effective sampling from the underlying conditional distribution. Second, since generating large probabilistic ensembles is computationally costly in physical space, SimCast-S2S instead operates in a compact latent space learned by variational autoencoders, enabling efficient large-ensemble generation. Third, diffusion models typically require large training datasets; SimCast-S2S overcomes this via transfer learning with low-rank adaptation (LoRA), pretraining on large ensembles of climate simulations before fine-tuning on limited reanalysis data. On reanalysis data, SimCast-S2S outperforms deep learning baselines, including convolutional neural networks and U-Net architectures. Notably, despite using only a subset of atmospheric input variables and no post-processing, bias correction, or calibration, SimCast-S2S remains competitive with, and in many cases outperforms, state-of-the-art operational systems such as the ECMWF-S2S baseline. These results indicate that latent generative modeling combined with simulation-to-reanalysis transfer learning offers an efficient and scalable path toward data-driven probabilistic S2S precipitation forecasting.

A Behavior-Guided Online Probabilistic Forecasting Method for Electric vehicle Charging Loads

Electric vehicle (EV) charging loads exhibit strong behavioral heterogeneity and temporal variability, posing significant challenges for online probabilistic forecasting under evolving operating conditions. In particular, persistent charging patterns may differ substantially across stations, while recent behavioral changes can continuously alter the underlying load distributions. This paper proposes a behavior-guided online probabilistic forecasting framework that explicitly characterizes persistent station-specific patterns and recent behavioral changes. A dual-timescale behavior representation is constructed to distinguish long-term charging characteristics from recent behavioral states and quantify their deviations. These behavioral changes are further semantically encoded to guide drift-aware forecasting adaptation, while a delayed-feedback mechanism ensures temporally consistent online updates when observations become available across different forecasting horizons. Experiments on ten heterogeneous real-world charging stations demonstrate that the proposed method consistently outperforms conventional forecasting models and concept-drift-aware online baselines in forecasting accuracy and probabilistic reliability. For 1-h-ahead forecasting, the proposed method reduces MSE and Pinball loss by 15.3\% and 17.8\%, respectively, over the corresponding best baselines. For 4-h-ahead forecasting, the improvements further reach 16.8\% and 22.6\%, respectively, demonstrating consistent performance gains under evolving charging behaviors and extended forecasting horizons.

Arbitrage-Aware Multi-Step Forecasting of Implied Volatility Surfaces: Modelling Surface Trajectories Using Latent Diffusion

Implied volatility surfaces summarise the option market and are central to many financial applications. Forecasting their future evolution requires modelling two-dimensional geometry, temporal dependence, and predictive uncertainty while preserving economic admissibility. We propose a conditional latent diffusion framework for generating joint 30-step trajectories of implied volatility surfaces and underlying returns. An arbitrage-aware autoencoder learns a low-dimensional surface representation, while the diffusion model captures the conditional joint evolution. Evaluated on SPX surfaces, the framework generates realistic probabilistic multi-step scenarios while also outperforming the persistence benchmark in point forecasting.

StocBench: A Benchmark for Generative Modeling of Stochastic Dynamics

We benchmark transport-based generative models as well as distillation-based few-step methods for the probabilistic forecasting of stochastic fluid flows, with a particular focus on performance under limited inference budgets. All methods are evaluated on a two-dimensional Kolmogorov flow with stochastic forcing. We measure one-step distributional accuracy against large simulated reference ensembles and assess whether the invariant measure is preserved during autoregressive rollouts via the enstrophy spectrum. On the stochastic task, flow matching achieves the most accurate one-step conditional distribution at high inference budgets, while the second-order exponential integrator DPM-2 is strongest at very low NFE. Few-step distillation methods are competitive with the multi-step methods and preserve the enstrophy spectrum particularly well. A deterministic control task, in which the forcing over the prediction interval is observed, separates aleatoric from epistemic uncertainty. Model performance does not translate between the two settings: the distilled models are competitive on the stochastic task but least accurate on the control task. While stochastic diffusion samplers such as DDPM better preserve the enstrophy spectrum during rollouts in the stochastic setting, deterministic samplers such as DDIM and DPM-2 show better spectral preservation in the deterministic setting.

DecoVAE: a Lightweight Interpretable Trend-Seasonal VAE Framework for Efficient Probabilistic Time Series Forecasting

Probabilistic time series forecasting remains challenging, largely because modeling distinct trend and seasonal dynamics requires specialized approaches. Existing methods often fail to capture the unique inner properties of these components, lack interpretability, or suffer from heavy memory and runtime overhead. To address these limitations, we propose DecoVAE, a lightweight interpretable trend-seasonal VAE framework that explicitly decomposes time series into trend and seasonal components by applying domain-specific inductive biases. The trend stream enforces structural smoothness using a differential regularizer on the latent trajectory, analogous to the Hodrick-Prescott filter. Concurrently, the seasonal stream operates in the frequency domain via a complex Gaussian VAE, natively capturing the amplitude and phase of periodic patterns. Extensive evaluations across seven real-world benchmarks show that DecoVAE consistently outperforms strong baselines. It achieves reductions of up to 14.96\% in CRPS and 23.30\% in NMAE for short-term forecasting, and up to 52.68\% and 26.51\% for long-term horizons. Crucially, DecoVAE yields these accuracy gains while remaining highly efficient, reducing model weight by up to 93\% and accelerating speed by up to 74\% compared to the second-best method.

CLaST: Context-aware Contrastive VAE for Probabilistic Time Series Forecasting

Probabilistic forecasting models are widely used for time series forecasting in domains such as energy systems, finance, medicine, and transportation. In recent years, deep generative models have shown strong results on probabilistic forecasting, yet many conventional approaches struggle to capture internal temporal dependencies, leading to latent representations with limited expressive power. To address this limitation, we propose \textit{CLaST}, a VAE framework for probabilistic multivariate time series forecasting. Unlike existing generative models, CLaST learns embeddings that preserve contextual similarity between observations through our contrastive loss function. Experiments across nine widely adopted benchmarks demonstrate that CLaST consistently surpasses strong baseline methods. In short-term forecasting tasks, our approach achieves improvements of up to $16.4\%$ in CRPS and $14.4\%$ in NMAE over the second-best method. Furthermore, in long-term prediction CLaST attains superior overall performance, exceeding the second-best method by up to $48.6\%$ and $25.1\%$ in CRPS and NMAE, respectively.

Systematic Evaluation of TabPFN-TS for Zero-Shot Probabilistic Heat Load Forecasting in District Heating Networks

District heating energy hubs require reliable heat load forecasts for efficient operational scheduling. Conventional forecasting workflows train system-specific models on historical data, which can become burdensome when networks change through new consumers, retrofits, or changing operating regimes. Zero-shot time-series foundation models and in-context forecasting offer a promising alternative: they can adapt at inference time from recent observations rather than by repeated retraining. This study systematically evaluates TabPFN-TS against time-series foundation models and trained machine-learning baselines for probabilistic heat load forecasting in district heating networks. Unlike foundation models pretrained on large collections of real time series, TabPFN-TS relies on synthetic pretraining data, which avoids direct pretraining-test overlap but raises the question of whether the learned prior captures district heating dynamics. We analyze covariate choice, context length, temporal resolution, and prediction horizon on representative operating weeks, validate the selected configuration over a full year, and test transferability on a second network. The results identify hourly 24-hour forecasting with a 12-week rolling context and ambient temperature as a parsimonious high-performing configuration; longer context windows do not improve accuracy. TabPFN-TS remains close to Chronos-2 in deterministic accuracy, reaching CVRMSE values of 13.06% versus 12.48% on the main dataset, and lies within the critical-difference threshold in the daily-rank comparison. Although Chronos-2 achieves the lowest aggregate full-year error, TabPFN-TS shows better empirical calibration. Finally, the diagnostic findings motivate a Multi-Resolution Residual-Correction Forecaster that combines a low-frequency Base Forecaster with a short-horizon Residual Forecaster to improve longer-horizon planning accuracy.

TinyCast: Probabilistic Zero-Shot Forecasting with Computed Periodicity

We introduce TinyCast, an attention-free zero-shot forecaster that emits a predictive distribution from 146,505 parameters, on the premise that at this size the periodic structure of a context is worth computing rather than learning. A zero-parameter spectral detector supplies the dominant periods, the context is folded on their phase, and a dilated convolutional encoder and a block-autoregressive quantile decoder model the rest. It is smaller than every zero-shot entry on the GIFT-Eval board whose parameter count can be established. On probabilistic accuracy it defines the size-accuracy frontier. Among zero-shot entries declaring no test-data leakage it is the only one below 1.4M parameters that emits a predictive distribution, and every entry scoring better carries at least that budget. On Chronos-ZS and fev-bench every neural model ahead of it carries at least 28 times its parameters. Because the mixing path is convolutions and matrix multiplications only, it exports to static INT8 and forecasts end to end on an embedded device without per-signal fitting.

Defensive Boosting for Online Probabilistic Forecasting

We study online probabilistic forecasting of binary outcomes chosen by an adaptive adversary. Given an online learning algorithm for a weak hypothesis class $H$, we would like to efficiently obtain two incomparable guarantees that existing online boosting techniques provide separately. Online gradient boosting competes in Brier score with the best predictor induced by the span of $H$ on every sequence, but promises nothing when the span does not contain an accurate predictor. Online weak-to-strong boosting drives classification error to zero under a weak-learning condition, but promises little when that condition fails. We give a simple defensive forecasting algorithm, the Defensive Booster, that obtains both guarantees. On every adaptive sequence, its Brier score is competitive with the best prediction induced by the span of $H$ at the same rate as online gradient boosting; simultaneously, whenever the realized transcript satisfies the smooth weak-learning condition, its Brier score and randomized classification error satisfy the same rate guarantee as online classification boosting. This is achieved by operationalizing the "dual view" of boosting: When the algorithm's randomized classification error is persistently high, its mistake weights form a smooth reweighting on which every weak hypothesis has low edge, yielding an ex-post hard-core certificate that the weak-learning condition fails. We also develop a strongly adaptive variant, which satisfies both guarantees on every time interval. The Defensive Booster is very efficient: it accesses just one weak-class learner, whereas the prior online boosting methods we compare against maintain large weak-learner ensembles. Experiments on synthetic and real data streams demonstrate its strong predictive performance (sometimes substantially improving over all prior baselines) coupled with orders-of-magnitude faster runtime.

High-resolution Calibrated Probabilistic Hourly Precipitation from a Deterministic Forecast

An ``Attention Residual U-Net'' method is described for probabilistic quantitative precipitation forecasting (PQPF) that predicts the hourly probability of no precipitation plus the distribution of positive precipitation from a weighted mixture of two Gamma distributions. The neural network is trained on patches of numerical weather prediction (NWP) hourly precipitation from The Weather Company's convection-permitting GRAF (Global high-Resolution Atmospheric Forecasting) model along with terrain information and column-average relative humidity from the National Oceanic and Atmospheric Administration's (NOAA's) Global Forecast System (GFS). The target data are NOAA's Multi-Radar, Multi-Sensor (MRMS) gauge-corrected, quality controlled radar data sampled to the same grid as the GRAF data. The network outputs distributional parameters for each model grid point. Training uses negative log-likelihood as a proper scoring rule, with climatological initialization for stable convergence. Inference is performed as a single forward pass over the contiguous United States (CONUS) domain, with edge-replication padding to satisfy the network's spatial-divisibility requirement. The subsequent forecasts are spatially detailed, highly reliable, and skillful with respect to climatology and a simpler reference forecast method. The method is particularly useful for estimating probabilities in regions with large terrain variation.

Earth observation embeddings are effective sub-grid descriptors for probabilistic weather downscaling

Global weather reanalyses and forecasts resolve the evolving atmospheric state on coarse grids, but site-specific applications require predictions at arbitrary locations where near-surface conditions also depend on unresolved terrain and land-surface properties. Existing probabilistic downscalers address this gap using hand-crafted topographic descriptors. We ask instead whether Earth observation foundation models can provide transferable sub-grid surface representations for probabilistic weather downscaling. We augment a convolutional conditional neural process that downscales coarse ERA5 reanalysis fields at ~25 km resolution with a learned local surface descriptor, obtained by compressing a patch of TESSERA embeddings at 10 m resolution. Although these embeddings summarise surface conditions over annual timescales, they improve downscaling of instantaneous 2 m temperature and 10 m wind speed by encoding persistent surface properties that capture a location's departure from the coarse-grid atmospheric state. Across five climatically diverse regions, the embedding improves point and probabilistic skill at stations held out in both space and time, overall improving CRPS skill by 11.5% for 2 m temperature and 6.2% for 10 m wind speed. We further analyse how its contribution differs by variable, finding that topography explains more of temperature's sub-grid structure, while TESSERA provides additional surface information for wind speed. These improvements persist when the coarse input is changed from ERA5 to forecasts from the Aurora AI forecasting model, and when predicting at newly deployed stations with no regional history. To our knowledge, this is the first evidence that long-timescale Earth-observation embeddings can support short-timescale weather downscaling where sub-grid departures are systematically structured by persistent surface properties.

Two-stage Odd Residual Flows for Mean-Preserving Probabilistic Time Series Forecasting

Probabilistic forecasting plays an essential role in risk-sensitive decision-making, particularly in long-horizon settings. However, existing approaches often face a fundamental trade-off between distributional flexibility and accurate mean prediction. Traditional parametric methods, such as Mean Variance Estimation (MVE), can suffer from degraded point accuracy when trained under joint Negative Log-Likelihood (NLL) objectives, while modern-flexible generative models, including Normalizing Flows and Diffusion Models, typically rely on costly Monte Carlo sampling and may yield suboptimal mean estimates. To address this limitation, we propose Two-stage Odd Residual Flows (TORF), a framework that decouples mean forecasting from uncertainty estimation. In the first stage, a pre-trained deterministic model is used to produce an accurate mean prediction. In the second stage, a Restricted Normalizing Flow, with strictly odd functions learns flexible residual distributions around the point forecast, guaranteeing mean preservation from the first stage without sampling. Experiments show that TORF achieves state-of-the-art deterministic accuracy (NMAE) while providing strong density estimation performance (CRPS) on short and long-horizon forecasting.

Do AI Forecast Ensembles Sample the Correct Conditional Distribution?

Ensemble forecasting aims to sample the conditional distribution of outcomes; whether AI forecast ensembles do this correctly in a joint sense remains largely untested. We train a diffusion model for probabilistic subseasonal coastal sea level forecasts at eight US East Coast tide gauge stations, with sea level derived from reanalysis, and find that marginal and joint forecast quality decouple: positive skill at every station and lead time marginally, while joint spatial structure is worse than climatological draws. A shuffle-based permutation decomposition reveals this failure is invisible to the energy score but detected by the variogram score. Lorenz-96 experiments across 0.7-170 equivalent years show the gap persists regardless of training volume and is reproduced by a linear baseline, indicating structural inadequacy of the learned distribution. A dynamical ensemble does not replicate the failure while a deterministic emulator does, suggesting it is specific to learned emulators rather than ensemble forecasting generally.

Timestep-Conditioned Transformers for Global Weather Forecasting

Existing machine-learning weather forecasting models rely on predetermined and fixed autoregressive timesteps. The choice of model timestep involves a fundamental trade-off: shorter timesteps (e.g. 1 to 6 hours) finely resolve atmospheric dynamics within the diurnal cycle but increase error accumulation for a given forecast horizon, while longer timesteps (e.g. 24 hours) reduce error accumulation but limit the usability of short-range forecasts where sub-daily predictability is high. In this work, we present GEM-3, a probabilistic global weather model that addresses this trade-off through explicit multi-timestep inference. With a single set of trained weights, the model timestep can be configured at inference time to balance predictability and usability across a broad forecast horizon. Additionally, we find that mixed-timestep training consistently improves rollout stability relative to timestep-specialist models. Under the hood, GEM-3 is a lightweight neighborhood-attention transformer with ~134M parameters on an equirectangular grid with a number of architectural advancements beyond its predecessor GEM-2. The result is a practical forecasting system that couples near-SOTA medium-range probabilistic skill, stable extended-range rollouts, efficient training and inference, and decision-relevant diagnostics.

FarSky: Task-Aware Latent-Space Coupling for Generative Intra-Hour Solar Forecasting

Accurate solar irradiance forecasting is essential for the reliable integration of photovoltaic power into modern electricity grids. All-sky imagers (ASI) provide high-resolution observations of clouds, making them well suited for intra-hour forecasting. Recent deep learning approaches have substantially improved forecast accuracy but are often limited by deterministic predictions and a reduced capability to anticipate ramp events. This work proposes FarSky, a generative forecasting framework that leverages latent-space coupling to learn task-aware representations of sky images. A multi-task autoencoder first learns a shared latent representation for image reconstruction and irradiance estimation. A latent diffusion model then generates future latent states conditioned on recent observations, from which irradiance forecasts are directly decoded. Probabilistic forecasts are inherently obtained through stochastic sampling. The framework is developed using a multi-year ASI dataset acquired at the Plataforma Solar de Almería, Spain, and evaluated on two independent test datasets against persistence, state-of-the-art end-to-end, and generative forecasting approaches. FarSky achieves the best overall deterministic and probabilistic forecasting performance, improving forecast skill by up to 11 percentage points. Furthermore, it substantially improves ramp event detection over existing methods, achieving F1-scores above 60%. These results demonstrate the potential of combining generative models with task-aware latent-space coupling for solar forecasting.

Crossing-Free Probabilistic K-Line Forecasts Without Retraining

Probabilistic K-line forecasting describes uncertainty in four complementary prices, namely open--high--low--close (OHLC). However, it introduces two consistency problems: quantile crossing and K-line crossing. Quantile crossing occurs when a higher-quantile forecast falls below a lower-quantile forecast, while K-line crossing occurs when the forecast low exceeds the open or close, or the forecast high falls below the open or close. Existing solutions generally address only one problem through output reordering, specialized architectures, or penalized training objectives. We propose K-line--Quantile Sequential Projection (KQSP), a parameter-free and training-free reconciliation method applicable to forecasts produced by any model. Compared with other crossing solutions, KQSP preserves predictive accuracy while producing substantially smaller corrections to the original forecasts. To mitigate model bias, we evaluate KQSP using various models, including pretrained foundation models. KQSP reduces both quantile and K-line crossing rates to zero for all test data undertaken. These results show that probabilistic K-line consistency can be enforced independently of forecast generation and without retraining.

From Seasonality to Semantics: Benchmarking a Hybrid Probabilistic Forecasting System for Roadblocks in Bolivia

Roadblocks in Bolivia are a social conflict phenomenon with devastating economic impacts, estimated at losses equivalent to 4% of the national Gross Domestic Product. Despite their recurrence and impact, there is a lack of local predictive systems to anticipate these events for logistical decision-making. This paper presents a hybrid probabilistic forecasting system that integrates time series decomposition (Prophet) with natural language processing (NLP) techniques applied to a six-year corpus of Bolivian news coverage. The methodology employs vector semantic embeddings and zero-shot classification models to capture signals of discursive escalation prior to the materialization of the roadblocks. Using an expanding walk-forward validation scheme applied over 1,762 days and seven forecasting horizons (H+1 to H+7), seven internal configurations and four external benchmarks were compared, including SARIMA and LightGBM. The results demonstrate that the hybrid configuration (Prophet + NLP, C6) consistently outperforms purely statistical models, achieving an AUC-ROC of 0.677 at H+1 and reducing the Brier Score by 10.9% relative to the baseline temporal model (0.220 vs. 0.247), maintaining a statistically significant error reduction across all evaluated horizons ($p < 0.02$). This research validates that the integration of semantic news signals allows for the detection of social tension peaks not captured by historical inertia, providing a technical tool for risk management in critical transport corridors.

SPECTRA: State-Space Exogenous Context and Temporal-Frequency Resolution Architecture for Probabilistic Energy Forecasting

Modern power systems increasingly require probabilistic forecasts amid interacting uncertainties from renewable intermittency, flexible demand, market volatility, and weather-dependent generation. However, existing methods often treat multi-scale decomposition, exogenous-variable alignment, and probabilistic output as separate steps, obscuring how predictable structures and uncertainty-bearing fluctuations jointly shape the forecast distribution. This paper proposes a state-space exogenous-context and temporal-frequency resolution architecture for general probabilistic energy forecasting. Its central premise is that trend-periodic components primarily determine the baseline trajectory, whereas high-frequency residuals and external perturbations govern the spread and asymmetry of forecast uncertainty. Accordingly, the architecture adaptively separates deterministic and residual streams, aligns exogenous context with both, refines the deterministic backbone through multi-resolution spectral-temporal state-space modeling, and estimates ordered quantile boundaries from their complementary representations. Experiments on load, price, solar, and wind forecasting achieve the best continuous ranked probability score in 14 of 18 settings, reducing average CRPS by 5.74\% and upper-tail quantile risk by 7.27\% over the strongest baselines. These results support deterministic-stochastic separation as an effective design principle for general probabilistic energy forecasting.

On the sensitivity of machine-learned probabilistic weather forecast models to scale-aware scoring rules

Probabilistic forecast models can be machine-learned from data using loss functions based on scoring rules such as the Continuous Ranked Probability Score (CRPS). This note summarises a preliminary study comparing versions of AIFS-CRPS, a global weather forecast model, trained with different univariate and multivariate scoring rules that aim to explicitly represent scale-awareness in the loss function. In the first part, we compare the (almost) fair CRPS, a fair global energy score, and a graph energy score based on node neighbourhoods. Across standard verification metrics, forecast skill is broadly similar. In the extratropics we find only small differences, while in the tropics the graph energy score setup performs somewhat better and the global energy score shows some degradation. These results suggest that multivariate scores are a viable alternative to CRPS-based training for global machine-learned weather forecasting. In the second part of the study, we analyse how different scoring rules and scale-aware loss constraints shape the spectra of forecast fields. It is apparent that any form of explicit scale-awareness improves realism. Here, the largest differences are likely associated with different effective weights per scale.

Censoring-Aware In-Context Learning for Generalized Supplier Lead Time Estimation in Supply Chain Planning

Supplier lead time forecasting is a central input to material requirements planning, inventory optimization, and supply chain risk management. However, many industrial lead time datasets are naturally right-censored: at the time forecasts are required, some orders have not yet arrived. Standard regression and classification approaches discard this information, while conventional survival models require task-specific modeling. We propose LeadTime-ICL (LT-ICL), a censoring-aware in-context learning model for probabilistic lead time forecasting. LT-ICL combines a transformer backbone with a conditional normalizing-flow head, producing a full predictive distribution over lead times. The model is pretrained on synthetic right-censored lead time tasks, enabling in-context adaptation to new industrial datasets without task-specific parameter updates. We provide theoretical support for this formulation by showing that excess CRPS is bounded by prior misspecification and amortized approximation errors, providing clear direction for improving forecasting performance. We evaluate LT-ICL on 24 proprietary supply-chain datasets spanning seven industries. LT-ICL achieves the lowest point-forecasting error on 15 of the 24 datasets, and the lowest probabilistic forecasting error on 14 datasets, yielding the best average rank across both. These results support right-censored probabilistic forecasting as a practical formulation for supplier lead time prediction and demonstrate that pretrained in-context models can provide accurate, low-adaptation-cost forecasting for industrial planning systems.

Towards Reliable Zero-Shot Crowd Forecasting: Evaluating Time Series Foundation Models for Special Event Pedestrian Forecasting

Managing massive crowds during infrequent special events requires reliable real-time pedestrian-flow forecasting to ensure public safety and operational efficiency. However, supervised forecasting methods face limitations in these contexts due to scarce historical data, heterogeneous data distributions, and short in-event observation windows. To effectively support operational decision-making, forecasts should provide not only accurate point estimates but also informative predictive uncertainty. Probabilistic uncertainty quantification plays a critical role in this aspect, particularly capturing sudden volatility and tail risks. This paper investigates pretrained time series foundation models as a lightweight approach for zero-shot probabilistic forecasting without extensive local retraining. Using decision-oriented metrics tailored to short events, we conduct a comprehensive assessment of two time series foundation models on crowd forecasting, with the SAIL2025 event as a use case. We then distill practical insights for crowd managers, specifying when zero-shot forecasts remain operationally reliable.

Behaviour-Conditioned Neural Processes for Adaptive Residential Short-Term Load Forecasting

Residential short-term load forecasting (STLF) is challenging because household demand is heterogeneous, temporally variable, and shaped by diverse behavioural routines. This work investigates whether inferred behavioural structure can be embedded within the forecasting mechanism of a Neural Process-based probabilistic model, rather than used only as an external grouping signal, for context-conditioned residential STLF. We propose a behaviour-conditioned Attentive Neural Process framework that treats each load profile as a forecasting task. Behavioural structure is represented by a discrete latent variable inferred from the available context and used for behaviour-conditioned decoder conditioning, while a continuous latent variable captures shared functional uncertainty across heterogeneous profiles. To enable conditioning without ground-truth behavioural labels, clustering-derived information provides weak supervision during training, whereas test-time conditioning relies only on context-inferred class distributions. Experiments on the Smart Grid, Smart City (SGSC) dataset use user-disjoint train/validation/test splits, variable context lengths, and multi-step forecast horizons, with comparisons against a label-agnostic ANP baseline and fixed-window deterministic STLF baselines. The proposed variants improve MAE and CRPS over ANP across horizons and context settings, with the largest gains under limited context. The best-performing variant achieves average reductions of 7.9% in MAE and 6.9% in CRPS relative to ANP. Compared with fixed-window baselines, this variant achieves lower RMSE across all evaluated horizons while maintaining competitive MAE, suggesting fewer large prediction deviations under heterogeneous consumption patterns. These results support single-model, uncertainty-aware forecasting across heterogeneous households, contexts, and horizons.

VAIOM: Continuous-Input, Discrete-Output Decoder-Only Financial Sequence Modeling

Financial observations are continuous, heterogeneous, and noisy, whereas decoder-only next-token models are usually built around discrete symbolic inputs. We introduce Vector-Input Autoregressive Inference for Ordinal-Return Modeling (VAIOM), a decoder-only Transformer for probabilistic next-return modeling on one-hour foreign-exchange bars. VAIOM separates input representation from output likelihood: continuous multivariate financial-event vectors preserve numerical structure at the input, while a categorical distribution over the next volatility-normalized return bucket supports cross-entropy training and likelihood evaluation. The selected 0.9M Hybrid Continuous Input model combines continuous event features with categorical asset metadata, a Mixture-of-Market-States return head, Gap, volatility-regime, and Ordinal auxiliary objectives, and full-sequence supervision. Models and preprocessing are fit using pre-2024 Train data; models are selected on 2024H2 Validation and evaluated without refitting on two 2025 Test periods. Across three independent training seeds, every model outperforms fixed single-bar LightGBM baseline in both Test halves. For the canonical checkpoint, paired gains over LightGBM are 0.029 and 0.043 bits per event. Validation experiments show that continuous input improves over discrete-token input under the same categorical return objective, full-sequence supervision improves over last-position training, and auxiliary representation shaping together with a mixture-structured return head improves return likelihood in controlled comparisons. A supporting capacity study finds that the smallest evaluated complete architecture rung achieves the strongest Validation likelihood on the present corpus.

Learning-based Probabilistic Load Forecasting with Post-hoc and In-model Uncertainty

Smart-building load forecasters are often trained offline on dense, multivariate, high-frequency data, but deployment may provide only hourly, feature-limited inputs. Missing features must then be reconstructed, and their errors can propagate through the model. If this input uncertainty is not reflected, prediction intervals may become miscalibrated, affecting demand-response scheduling. Our work examines where uncertainty should be placed once inference inputs are reconstructed. We develop a unified one-day-ahead probabilistic forecasting framework that aligns temporal resolution, reconstructs the unavailable inputs, and derives causal features, and we compare a modular post-hoc residual-quantile scheme with an integrated in-model quantile-learning scheme. The comparison uses three mid-scale Deep Learning (DL) backbones: recurrent, hybrid recurrent, and attention-based Temporal Fusion Transformer (TFT) models, under identical inputs, forecasting horizon, preprocessing rules, and training budgets. Results show that uncertainty placement is backbone-dependent. Integrated quantile learning is most reliable with the TFT, yielding 2.2-3.6% MAPE and 28-83W RMSE on the labeled test window, while producing intervals about 5x narrower than the modular intervals at the closest-to-nominal coverage level. Diebold-Mariano tests support the TFT ranking and the mixed behavior of the recurrent backbones. A reconstruction-sensitivity test shows that reconstructed inputs increase the Quantile Score (QS) by 106% while interval width remains nearly unchanged, indicating that the model does not automatically absorb reconstruction-induced uncertainty. Robustness checks against non-DL baselines and seasonal hold-out weeks support this ranking. Our results expose the limits of post-hoc residual quantiles when inference depends on reconstructed inputs.