Probabilistic Forecasting

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Overview

Probabilistic forecasting estimates ranges, quantiles, event probabilities, or full predictive distributions rather than only a single future value. Methods include Bayesian and parametric models, ensemble post-processing and conformal calibration, and neural generative approaches such as diffusion and flow matching; language-model agents also forecast real-world events using evidence and probability aggregation. Researchers evaluate forecasts with proper scores such as CRPS and Brier score, alongside calibration, sharpness, and benchmarks in weather, energy, health, finance, and human mobility. A central challenge is balancing accuracy, reliable uncertainty, computational cost, and usefulness for downstream decisions, since strong average scores may hide failures in extremes or dependencies between outcomes.

Latest papers

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230 papers37 papers in the last four weeks, up 3% on the four weeks before. 0.2% of all new papers.

Sep 8, 2026

Stochastically Perturbed Weights: Ensembles from Deterministic Machine-Learning Weather Models

Machine-learning weather models (MLWMs) now match or outperform operational numerical weather prediction (NWP) at global medium-range forecasting, at far lower inference cost. Many deployed MLWMs are deterministic, producing a single forecast with no estimate of its own uncertainty, whereas a growing family of trained-probabilistic models generate calibrated ensembles directly, at the price of a dedicated training run. We ask instead how much uncertainty can be extracted from a deterministic checkpoint that already exists, without retraining it. Where physical ensembles represent model uncertainty by stochastically perturbing parametrisation tendencies, we perturb the network's raw weight tensors at inference time, a scheme we call stochastically perturbed weights (SPW). We also ask whether it works, where and on which scales to inject the noise, and where it fails. A three-phase ablation across four deterministic backbones, Aurora, GraphCast, SFNO, and AIFS, selects one production baseline per model, benchmarked against the trained-probabilistic AIFS-ENS, FourCastNet 3 and Atlas as well as the operational ECMWF ensemble (IFS-ENS) over 112 initialisation times. At a 240 h (10-day) lead time the SPW ensembles reach continuous ranked probability skill scores (CRPSS) between 0.04 and 0.13 below the best trained-probabilistic baseline, at zero marginal training cost. No injection site works across models: the productive tensor group is architecture-specific, so SPW is at present a tuning procedure rather than a plug-and-play recipe. Its main failure mode is a coherent whole-field offset that overdisperses the domain mean, and restricting the noise to coarse scales or perturbing the initial conditions each repair part of it.

Simon Adamov, Oliver Fuhrer, Reto Knutti +1

Federal Office for Meteorology and Climatology MeteoSwiss, Zurich, Switzerland · Institute for Atmospheric and Climate Science (IAC), ETH Zurich, Zurich, Switzerland · Department of Applied Mathematics and Theoretical Physics, University of Cambridge, United Kingdom

Uncertainty QuantificationEnsemble LearningProbabilistic ForecastingWeather Forecasting
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Sep 7, 2026

Forecasting the Winner of a Live Tennis Match

With the rise of live sports betting in recent years, tennis forecasting has expanded from pre-match prediction to models that update win probabilities as a match unfolds. A central challenge in creating such a model is the constant need for models to adapt to score and performance changes. This study examines how pre-match and live information can be most effectively integrated into a model to produce accurate win-probability estimates. The analysis uses 8,222 Grand Slam matches containing a total of 1,505,355 points. Five models were evaluated using a chronological split, with matches from 2011-2021 used for training, 2022 for validation, and 2023-2024 for testing. Trace, a hybrid model, achieved accuracies of 76.06%, 82.15%, and 88.34% at 25%, 50%, and 75% match progress, suggesting that hybrid modeling is a practical approach to live tennis forecasting.

Charles Xie, Aneesh Muppidi

Natick High School 15 West Street, Natick, Massachusetts 01760, USA · University of Oxford Oxford, United Kingdom

Probabilistic ForecastingSports Outcome Prediction
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Sep 7, 2026

Statistical versus machine learning-based spatial interpolation of post-processed ensemble weather forecasts

Statistical post-processing improves ensemble weather forecasts, but generating calibrated predictions at locations without observations remains challenging. This study compares statistical and machine-learning-based methods for post-processing ECMWF 2-m temperature and 10-m wind speed forecasts at observed and unobserved stations in Germany. We consider EMOS-based approaches, distributional regression networks, Transformers, and graph neural networks under both limited and extended predictor settings. For temperature, we also investigate linear forecast combinations and propose an altitude-aware linear pool (ALP). The results show that post-processing improves upon the raw ensemble in most settings, but no single method performs best across all variables, station groups, and evaluation metrics. The proposed ALP provides a small but significant improvement over the standard linear pool at unobserved locations.

Mária Lakatos

Faculty of Informatics, University of Debrecen, Hungary

Ensemble LearningProbabilistic ForecastingWeather Forecasting
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Sep 7, 2026

Inferring Urban Mobility Interactions from Aggregated Dynamics

Real-time urban governance depends not only on knowing where people are, but on how they move between places, directional flows that could be conventionally resolved by tracking individuals through space, i.e., expensive to sustain and built on traces that are highly unique and readily re-identifiable. Here we show that this directional structure need not be observed to be known: aggregated counts which cities already collect retain enough information to reconstruct the temporal evolution of origin-destination (OD) matrix. Using an uncertainty-aware physics-informed framework, we infer future OD flows from area-level counts alone across twelve mobility datasets from cities in the United States and China, reaching accuracy comparable to models that take historical OD matrices as input. Probabilistic modeling corrects the systematic underestimation of sparse, high-value corridors and yields calibrated predictions consistent with observed flows. Architectures that respect the generation-before-assignment logic of transport planning recover interactions more faithfully, indicating that location-level spatial heterogeneity should be preserved before pairwise interactions are reconstructed. Because inference requires only aggregated observations after training, recovering interactions this way reduces reliance on continuous individual-level tracking, pointing toward a more deployable and less exposure-heavy basis for real-time urban intelligence.

Yi Wang, Jing Li, Jinliang Deng +5

Institute of Remote Sensing and Geographic Information System, School of Earth and Space Sciences, Peking University, Beijing, China · Centre for Frontier AI Research, Institute of High-Performance Computing, Agency for Science, Technology and Research (A*STAR), Singapore · Department of Computer Science and Engineering, Hong Kong University of Science and Technology, Hong Kong, China. +1

Traffic Flow EstimationProbabilistic ForecastingSpatiotemporal Forecasting
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Sep 5, 2026

The Corroboration Illusion: When More News Makes LLM Forecasts Less True

Large language models (LLMs) are increasingly used to forecast real-world events by retrieving and reasoning over news. We show that this dependence on an open, crawlable news corpus creates a new attack surface: an adversary who can merely publish articles--without access to the retriever, the model, or the user's queries--can systematically move the forecaster's output probabilities. We formalize news-corpus poisoning of probabilistic forecasters, a threat model distinct from prior RAG poisoning, which targets factual answers or opinion polarity rather than calibrated probabilities. We evaluate the attack on 500 resolved ForecastBench questions against a 17.4M-article Common Crawl News corpus with a strict crawl-date cutoff, using three retrieval-augmented forecasters built on open 7-8B models. A single LLM-written article per question flips 56% of forecasts across the 0.5 boundary; five articles flip 69-73% and shift probabilities by +0.13 to +0.22 net of a neutral-article placebo, degrading the Brier score from 0.18 to 0.37. The effect is monotone in the number, retrieval rank, query similarity, and context share of injected articles, transfers across model families, and is unaffected by the claimed publisher. We then evaluate three natural defenses--source allow-lists, isolate-then-aggregate forecasting, and perplexity filtering--and show that each has a cheap bypass: spoofed publishers, majority poisoning, and higher-temperature generation, respectively. Our results indicate that probabilistic LLM judgments inherit the full fragility of the information supply chain they consume.

Yuan Lu, Yukuan Zhang

Peking university Beijing, China · University of Central Florida Orlando, FL, USA

LLM SecurityData Poisoning AttacksLLM ReliabilityRAG Poisoning AttacksProbabilistic Forecasting
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Sep 5, 2026

From Narrative to Auditable Forecasts: A Structured Scaffold for Agentic Forecasting

LLM agents are increasingly used for live forecasting, where they retrieve up-to-date information and produce estimates for unresolved future events. However, current agentic forecasting often relies on implicit narrative aggregation: agents collect evidence, discuss it in prose, and often assign a probability without an explicit update path from evidence to forecast. This limits both forecasting accuracy and auditability. We propose AuditForecast, an agentic scaffold for structured probabilistic forecasting. AuditForecast first anchors the forecast with a suitable quantitative baseline model, uses model-guided data retrieval to derive a base probability, and then applies situational factor updates outside the model's scope through mechanical aggregation in odds space. This turns forecasting from a prose-based judgment into a structured process with explicit intermediate objects. Across multiple live forecasting benchmarks, AuditForecast improves forecasting accuracy and calibration relative to strong agentic baselines, surpasses market-implied references in several settings, and outperforms substantially more expensive deep-research agents while remaining Pareto-dominant in the cost--accuracy tradeoff. Beyond performance gains, AuditForecast produces an auditable forecasting report that makes forecast construction explicit and supports systematic post hoc analysis.

Yuanpu Cao, Yongkang Du, Yurui Chang +2

The Pennsylvania State University

Probabilistic Forecasting
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Sep 3, 2026

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.

Stephan Rasp, Boris Babenko, Dominic Masters +22

1Google DeepMind · 2Google Research · 3Google

Probabilistic ForecastingWeather Forecasting
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Sep 2, 2026

Improving global precipitation forecasts with an AI weather model trained on satellite observations

Precipitation forecasts shape decision-making across the global economy, particularly in sectors such as agriculture. However, unlike variables such as temperature, precipitation is highly intermittent and localized, making it difficult to forecast. While recent advances in AI weather prediction systems have enabled them to surpass physical models on globally averaged metrics, improvements in mean error rarely translate to actionable forecasts of severe flooding or dry crop fields. Furthermore, most of these models are trained and evaluated against a reanalysis data product, ERA5, which has well-known biases. Here we retrain AIFS, ECMWF's widely-used, open-source operational 0.25° probabilistic graph-transformer weather model, on satellite-based precipitation observations. Our model, Laxmi, improves global probabilistic accuracy by 19% and resolves systematic distributional biases in ERA5. Specifically, Laxmi reduces drizzle overprediction by 33% for amounts less than 3 mm per day. It also mitigates extreme rainfall underprediction, improving the global 95th percentile Brier skill score by 57%. Across a case study of 10 Indian tropical storms, Laxmi delivered the most accurate forecast of 150 mm event-total precipitation in 7 events, compared to 1 for AIFS and 2 for the leading physical model, IFS. Our results demonstrate that incorporating observation-based precipitation data directly into training can substantially improve forecasts.

Julian F. Schmitt, Bertrand Delorme, Robert C. King +4

X, The Moonshot Factory, Google LLC, Mountain View, CA, USA · Google, Google LLC, Mountain View, CA, USA · Environmental Science and Engineering, California Institute of Technology, Pasadena, CA, USA +1

Precipitation ForecastingProbabilistic ForecastingWeather Forecasting
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Sep 1, 2026

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.

Yufei Chen, Yiran Zhao, Xiaogang Xu +3

1Shandong University · 2Nanjing University of Aeronautics and Astronautics · School of Software Technology, Zhejiang University +2

Probabilistic Forecasting
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Aug 31, 2026

Uncertainty-Aware Trajectory Forecasting from Imperfect Tracking

Most trajectory forecasting models are trained on clean annotated histories, and are often evaluated under the same idealized assumption, although practical deployments rely on trajectories produced by imperfect multi-object trackers. The real-world observations exhibit localization jitter, missed or unstable detections, and data-association ambiguity, which are usually either ignored or removed through denoising. This paper instead treats tracking-derived reliability cues as an informative signal to be propagated to the predictor. We propose a plug-in uncertainty-aware formulation in which each observed state is encoded as an uncertain state representation, modeled by a Gaussian distribution whose covariance combines detection-level localization uncertainty and association-level ambiguity through the law of total variance. Existing backbones are adapted with minimal architectural changes: input trajectories are represented as Gaussian observations, and predicted trajectories are produced as Gaussian forecasts rather than deterministic coordinates. To train predictors that remain robust under structured observation noise, we combine temporally correlated Ornstein-Uhlenbeck perturbations with response-based knowledge distillation from a teacher trained on clean trajectories. Experiments on Oxford Town Centre and VIRAT using real tracker outputs, together with a complementary ETH/UCY pseudo-detection protocol, show that the proposed formulation improves displacement accuracy and the reliability-sharpness trade-off of probabilistic forecasts.

Stephane Da Silva Martins, Victor Petrovic, Emanuel Aldea +1

SATIE – CNRS UMR 8029, Université Paris-Saclay, France · ENS Paris-Saclay, Université Paris-Saclay, France

Probabilistic Trajectory PredictionProbabilistic ForecastingUncertainty PropagationTrajectory Prediction
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Aug 31, 2026

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.

Rodrigo Almeida, Noelia Otero, Jost Arndt +3

Applied Machine Learning Group, Fraunhofer Heinrich-Hertz Institute, 10587 Berlin, Germany · Department of Electrical Engineering and Computer Science, Technische Universität Berlin, 10587 Berlin, Germany · BIFOLD - Berlin Institute for the Foundations of Learning and Data, 10587 Berlin, Germany

Probabilistic ForecastingAleatoric UncertaintyUncertainty DecompositionEpistemic UncertaintyWeather Forecasting
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Aug 31, 2026

Foundation models for electricity price forecasting and battery arbitrage: Can they replace market-specific forecasting models?

Foundation models promise accurate forecasts with little or no task-specific training, but whether they can replace models designed specifically for electricity price forecasting remains unclear. We compare nine variants from five foundation model families, evaluated in zero-shot mode, with two state-of-the-art electricity price forecasting benchmarks in Germany, Poland, and Spain over 2021-2025. Their performance is assessed in terms of point and probabilistic forecasting accuracy, as well as economic value in battery energy storage arbitrage. Only the TabPFN models consistently and significantly outperform the benchmarks across all three markets and all statistical measures. However, this statistical dominance does not translate directly into economic dominance: TabPFN performs best under unlimited bids and riskier quantile-based strategies, whereas the Distributional Deep Neural Network benchmark is more profitable when risk tolerance is lower. Thus, foundation models cannot universally replace market-specific models, and their value depends on both model architecture and the decision problem.

Arkadiusz Lipiecki, Rafał Weron

Department of Computational Social Science, Wrocław University of Science and Technology, Poland · Department of Operations Research and Business Intelligence, Wrocław University of Science and Technology, Poland · Center for Research in Energy (CoRE), Aarhus University, 8000 Aarhus C, Denmark

Tabular Foundation ModelsElectricity Price ForecastingTime Series ForecastingProbabilistic ForecastingTime-Series Foundation Models
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Aug 31, 2026

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.

Dohyun Park, Changhoon Song, Tengyuan Chang +2

Department of Mathematical Sciences, Seoul National University, Seoul, Republic of Korea. · Research Institute of Mathematics, Seoul National University, Seoul,2026 Republic of Korea. · Department of Environmental Management, Seoul National University, Seoul, Republic of Korea.

Precipitation ForecastingProbabilistic ForecastingPrecipitation DownscalingConditional Diffusion ModelsPrecipitation NowcastingExtreme Weather Forecasting
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Aug 28, 2026

How Proper Scoring Rules Shape LLM Forecasting

This paper evaluates how reward function choice shapes the performance and behavior of LLM forecasters. We compare five proper scoring rules as training objectives for binary forecasts of resolved real-world events. Although the rules share the same theoretical incentive for truthful probability reporting, the resulting models differ in calibration, probability use, and estimated profiles of bias, information, and noise, with smaller differences in aggregate accuracy and discrimination. The Brier-trained model has the lowest observed Brier score and highest AUC-ROC, while the log-trained model has the highest observed log score and lowest calibration error. Models with similar aggregate performance also reach that performance through different combinations of bias, information, and noise. Proper scoring rules therefore need not behave interchangeably as training objectives. Reward choice may shape not only how well an LLM forecasts, but how its forecasting errors are structured.

Benjamin Turtel, Paul Wilczewski, Kris Skotheim +2

Lightning Rod Labs · Technology and Operations Management, INSEAD, Fontainebleau, France · Wharton School and School of Arts & Sciences, University of Pennsylvania

Probabilistic ForecastingProper Scoring RulesLanguage Model Calibration
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Aug 27, 2026

Climate Physics Dynamic Matching

Deep generative models such as flow matching and diffusion models have shown potential for learning complex dynamical systems, but typically act as black boxes that neglect underlying physical structure, while physics-based models governed by partial differential equations are often incomplete due to missing source terms, or uncertain parametrisations. We present Climate Physics Dynamic Matching (ClimPhyDM), a variational simulation-free dynamics informed framework for weather forecasting that combines an advection-type physics prior with data-driven components in a variational framework. % to capture the stochasticity and multi-modality of unresolved atmospheric dynamics. On the ERA5 benchmark at hourly (42-hour) and monthly (5-month) resolutions, ClimPhyDM outperforms ClimODE, and GB-DM, keeping the lower error at extended horizon, indicating improved temporal stability and resistance to error accumulation, while its simulation-free paradigm also enables training on a single modest 12 GB consumer GPU.

Gurjeet Sangra Singh, Frantzeska Lavda, Alexandros Kalousis

University of Geneva, Geneva, Switzerland · HES-SO Geneva, Geneva, Switzerland

Weather ForecastingPhysics-Informed Generative ModelingClimate ModelingEarth ScienceProbabilistic Forecasting
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Aug 27, 2026

SimCast-S2S: A Computationally Efficient Diffusion Model for Subseasonal Precipitation Forecasting

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 (VAEs), 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 aspects 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.

Hiep V. Dang, Antonios Mamalakis

Department of Environmental Sciences, University of Virginia, Charlottesville, VA 22903, United States · School of Data Science, Department of Environmental Sciences, University of Virginia, Charlottesville, VA 22903, United States

Precipitation ForecastingLatent Diffusion ModelsProbabilistic ForecastingConditional Diffusion ModelsWeather Forecasting
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Aug 25, 2026

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.

Chenghan Li, Qingxiang Liu, Yinliang Xu +1

Tsinghua Shenzhen International Graduate School, Tsinghua University, Shenzhen 518055, China · Intelligent Transportation Thrust, The Hong Kong University of Science and Technology (Guangzhou), Guangzhou 511458, China

Probabilistic ForecastingElectricity Load ForecastingElectric Vehicle ChargingConcept Drift
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Aug 23, 2026

Arbitrage-Aware Probabilistic Multi-Step Forecasting of Implied Volatility Surfaces: Joint Generation of Surface-Return Trajectories Using Latent Diffusion

Implied volatility surfaces summarise the option market and are central to many financial applications. Probabilistic forecasting of 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 surface representation, while diffusion captures the evolution. Evaluated on SPX surfaces, the framework generates realistic probabilistic multi-step scenarios. Its predictive mean also outperforms persistence beyond the shortest horizons.

Dominik Manuel Buchegger, Lukas Gonon

University of St.Gallen St.Gallen, Switzerland

Quantitative FinanceProbabilistic ForecastingMultivariate Time Series ForecastingConditional Diffusion ModelsLatent Diffusion Models
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Aug 23, 2026

Tracing the Unlabeled Storm: Cross-Variable Transfer in a Lagrangian Atmospheric JEPA Framework

Deep atmospheric convection governs South Asian monsoon variability, yet attempting to learn its latent world model directly from zero-inflated, heavy-tailed precipitation yields suboptimal predictive representations. Continuous atmospheric proxies, such as outgoing longwave radiation (OLR), express this convective organization far more coherently. We address this mismatch with cross-variable proxy learning: M-JEPA, a multiscale Monsoon Joint-Embedding Predictive Architecture, is pretrained on five continuous proxy fields over Lagrangian patches tracking moving convective systems---without rainfall supervision at any point. The resulting frozen representation is transferred to daily precipitation forecasts through a shared decoder trunk featuring parallel probabilistic and deterministic branches. Because rainfall is strictly unobserved during pretraining, downstream skill directly measures the predictive information captured in the latent rollout. A frozen-backbone probing framework with two controls (an identical architecture trained on rainfall alone, and a randomly initialized backbone) attributes the transfer specifically to proxy pretraining: direct rainfall training exhibits 36%36\% higher CRPS error (7.527.52 vs.\ 5.545.54,mm/day). Against the 51-member operational ECMWF ensemble, the transferred model attains a statistically resolved CRPS advantage (6.816.81 vs.\ 6.896.89,mm/day) and higher Brier skill (+0.05+0.05 vs.\ −0.04-0.04) using 15.415.4M parameters on a single consumer GPU, concentrated at heavy-rain thresholds and fine spatial scales, while the ensemble retains an advantage in neighborhood skill and deterministic references on point metrics. The result provides a competitive monsoon precipitation forecast grounded in intraseasonal dynamics and a diagnostic framework for evaluating transferred atmospheric representations.

K M Anirudh, S Sandeep, Hariprasad Kodamana

Centre for Atmospheric Sciences, IIT Delhi, New Delhi, India · Yardi School of Artificial Intelligence, IIT Delhi, New Delhi, India · Department of Chemical Engineering, IIT Delhi, New Delhi, India

Precipitation ForecastingSpatiotemporal ForecastingJoint-Embedding Predictive ArchitectureTransfer LearningProbabilistic Forecasting
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Aug 23, 2026

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.

Sebastian Pfister, Benjamin Holzschuh, Nils Thuerey

School of Computation, Information and Technology, Technical University of Munich, Germany.

Generative ModelingProbabilistic ForecastingFlow-Based Generative ModelingDiffusion SamplingDiffusion Model Distillation
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Aug 19, 2026

Tianmu-TC: Physics-constraints Generative Artificial Intelligence for Global Tropical Cyclone Forecasting

Tropical cyclones (TCs) pose severe risks from strong winds and heavy rainfall. However, forecasting their track and intensity remains challenging due to chaotic atmosphere and the rapid amplification of initial condition errors, leading to growing forecast uncertainty. While numerical weather prediction (NWP) and deep learning models have made progress, they remain computationally demanding and often fail under complex meteorological scenarios. Here, we present Tianmu-TC, a physics-constraints generative framework for global TC forecasting. Trained on Western North Pacific data, Tianmu-TC leverages physics-constraints to generate controllable outputs with reduced uncertainty thus improving forecast reliability. Experiments show Tianmu-TC outperforms deterministic and ensemble meteorological artificial intelligence models and authoritative NWP systems such as ECMWF in global ocean basins, with significantly lower computational cost. We further show Tianmu-TC performs well in challenging scenarios such as data sparsity, anomaly tracks, rapid intensification and weakening. These findings suggest physics-constraints generative AI offers a promising approach for reliable, efficient global TC forecasting.

Shiqi Zhang, Pan Mu, Cheng Huang +6

College of Computer Science and Technology, Zhejiang University of Technology, Hangzhou & 310023, China. · School of Control Science and Engineering, Shandong University, Jinan & 250061, China. · School of Computer Science and Engineering, Tianjin University of Technology, Tianjin & 300384, China. +1

Tropical Cyclone Intensity ForecastingWeather ForecastingPhysics-Informed Generative ModelingSpatiotemporal ForecastingProbabilistic Forecasting
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Aug 13, 2026

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 HH, 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 HH 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 HH 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.

Georgy Noarov, Aaron Roth

Probabilistic ForecastingWeak-to-Strong GeneralizationAdaptive Learning
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Aug 12, 2026

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 and surface descriptors. We ask instead whether Earth observation foundation models can provide transferable subgrid surface representations for probabilistic weather downscaling. We augment a convolutional conditional neural process (ConvCNP) 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 summarize annual surface conditions, they improve downscaling 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 relative to a topography-only ConvCNP baseline. A hand-crafted descriptor incorporating richer surface information than topography alone captures comparable persistent subgrid signal but yields far smaller predictive gains than the learned embedding representation. These improvements persist when forecasts from the Aurora AI model replace ERA5 reanalysis fields and when predicting at newly deployed weather station networks. To our knowledge, this is the first evidence that long-timescale Earth observation embeddings can support short-timescale weather downscaling where subgrid departures are systematically structured by persistent surface properties.

Pedro Sousa, Will Tebbutt, Sadiq Jaffer +3

Department of Computer Science, University of Cambridge · Department of Engineering, University of Cambridge

Probabilistic ForecastingWeather Forecasting
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Aug 11, 2026

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.

Kiran Madhusudhanan, Christian Klötergens, Lars Schmidt-Thieme +1

Institute of Computer Science University of Hildesheim Hildesheim, Germany

Long-Term Time Series ForecastingNormalizing FlowsResidual LearningProbabilistic ForecastingProbabilistic Time Series Forecasting
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Aug 10, 2026

Evaluating Generative Time-Series Models on Data with Point Masses

Many of the series that generative time-series models are benchmarked on place a large probability mass on a single value --- it does not rain, no ride is requested, no part is ordered. We report what happens when such data is evaluated carefully. First, the standard rolling-origin protocol can score a model on a window whose atom structure bears no resemblance to the dataset: on one benchmark the dataset is 42%42\% zeros and the evaluation windows are 13%13\%, on another 47%47\% against 5%5\%. This is not a cosmetic problem --- it reversed one of our own conclusions, turning the strongest occurrence model in our study into what looked like a cautionary tale. Second, we give a control in which CRPS is invariant by construction while the temporal coupling is destroyed, which measures exactly how much that coupling contributes to a chosen statistic. Third, benchmarking seven models on a matched protocol over five seeds, an autoregressive hurdle beats a conditional flow on five of six datasets, by up to a factor of 153153, while the flow's own occurrence statistics vary by up to 62%62\% across training seeds and every baseline is deterministic. Finally, the model ordering is not the same under five different occurrence statistics, and the two that do not share a construction agree with each other least.

Jian Xu

RIKEN iTHEMS, Wako, Japan · RIKEN Center for Advanced Intelligence Project (AIP), Tokyo, Japan

Time Series ForecastingTime Series GenerationForecasting BenchmarksProbabilistic ForecastingProbabilistic Time Series Forecasting
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Aug 9, 2026

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.

Lucas J. Howard, Elizabeth A. Barnes

Boston University, Faculty of Computing and Data Sciences

Time Series ForecastingProbabilistic ForecastingSpatiotemporal Forecasting
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Aug 8, 2026

Forecasting Without Full Identification: Reliability and Computational Cost in Clot-Growth Simulation

We forecast clot growth from sparse early measurements with incomplete biochemical information. Using 1,000 simulated trajectories, we compare inverse search, which weights candidate inputs by their agreement with early observations, with a direct multilayer perceptron (MLP) predicting future clot size. Inverse search is more accurate when tissue factor alone, or tissue factor and fibrinogen, are unknown. When all five inputs are unknown, direct prediction achieves 2.16% pooled relative L2L_2 forecast error, outperforming search with 8,192 candidates using a forward MLP (3.25%) or latent neural ordinary differential equation model (3.36%). A conditional error bound separates candidate disagreement, weight on poor early fits, surrogate error, and candidate coverage. Increasing randomized quasi-Monte Carlo candidate budgets from 512 to 32,768 reduces numerical variation. A covariance score ranks additional assays by expected forecast value while accounting for measurement noise. At 10% range-scaled assay noise, incorporating assay uncertainty reduces forecast error from about 5% to below 3% for both surrogates. An independent reaction cascade verifies candidate integration against tensor quadrature, with mean normalized forecast-integration error below 10−510^{-5} at 32,768 candidates. These results demonstrate accurate clot-growth forecasting without full biochemical identification and support selecting prediction strategies and additional measurements according to accuracy, reliability, and computational cost.

Lennon J. Shikhman, Lily DiPaulo, Ying Qian +1

School of Interactive Computing, Georgia Institute of Technology, Atlanta, GA 30332 · Department of Mathematics and Systems Engineering, Florida Institute of Technology, Melbourne, FL 32901 · School of Chemical, Materials and Biomedical Engineering, University of Georgia, Athens, GA 30605

Simulation-Based InferenceProbabilistic ForecastingClinical Prediction
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Aug 7, 2026

EpiFlow: A framework for improving the utility of wastewater signals for disease forecasting

Wastewater-based surveillance is an effective tool for disease monitoring and can provide early warning of outbreaks. Although wastewater viral loads (WVL) correlate with disease burden, their utility for improving real-time forecasting remains under investigation. During the early phases of an epidemic, many indicators can effectively monitor disease spread, but their reliability may decline because of reporting fatigue and low prevalence. Hospital burden can vary substantially even during low-prevalence periods, making accurate forecasting of burden indicators essential for minimizing disease impacts. In this paper, we present principled approaches for processing wastewater data, characterizing its relationship with burden indicators, and generating real-time forecasts. We assess the predictability of WVL using entropy measures. We analyze the relationship between WVL and burden indicators using causality tests that capture temporal dynamics and the leading-indicator behavior of WVL. We incorporate these insights into a time-varying forecasting model that accounts for the evolving relationship between the signals. We also evaluate the effects of delays in WVL reporting through simulations. We test the utility of our methods by forecasting COVID-19 hospital admissions across Virginia and its health regions during periods of varying disease prevalence. Incorporating WVL improves forecast accuracy relative to baseline models, particularly during critical epidemic phases, and results in a 20 percentage point improvement in forecast coverage. Our results demonstrate that WVL signals can improve infectious disease forecasting even under conditions of low prevalence or delayed reporting.

Aniruddha Adiga, Jingyuan Chou, Gursharn Kaur +8

Biocomplexity Institute, University of Virginia · Department of Computer Science, University of Virginia · Virginia Department of Health +3

Epidemic ForecastingProbabilistic ForecastingNon-Stationary Time Series Forecasting
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Aug 7, 2026

Dirichlet Follow-the-Leader Closes the Gap in Simultaneous Multiclass U-Calibration

Can one forecaster attain the optimal regret rate for every bounded proper loss and also adapt to every smooth proper loss? Recent work answered this up to a dimension gap. Its self-concordant perturbation gives roughly K5/4TK^{5/4}\sqrt{T} worst-case regret and incurs an additional βKlog⁡Kβ\sqrt{K}\log K for ββ-smooth losses. We close both gaps with a one-line forecaster. After observing class counts ct−1c_{t-1}, draw the next prediction from Dir⁡(ct−1)\operatorname{Dir}(c_{t-1}), on the face of classes seen so far. This is a fresh Bayesian bootstrap of the outcomes. The analysis rests on an exact identity: averaging any bounded proper loss under Dir⁡(α)\operatorname{Dir}(α) equals a discrete derivative of its Dirichlet-averaged Bayes risk. The identity makes the be-the-perturbed-leader term telescope to a nonpositive Jensen gap. A one-count likelihood ratio then bounds stability by the inverse square root of that class's count. The resulting single, horizon-free algorithm satisfies sup⁡ℓEReg⁡ℓ≤4STT≤4KT\sup_{\ell}\mathbb{E}\operatorname{Reg}_{\ell}\leq 4\sqrt{S_T T}\leq 4\sqrt{K T} and EReg⁡ℓ≤52β(1+log⁡T)\mathbb{E}\operatorname{Reg}_{\ell}\leq \frac{5}{2}β(1+\log T) for every ββ-smooth proper loss. Here STS_T is the number of observed classes. Known lower bounds show that both rates are optimal in their nontrivial regimes. The proof covers nondifferentiable losses and changes of the active simplex face.

Pahan Dewasurendra

Johns Hopkins University

Probabilistic ForecastingFollow-the-Regularized-LeaderModel CalibrationOnline Learning
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Aug 6, 2026

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.

Sam Levang, Fran Bartolic, Ty Dickinson +3

Salient

Time Series ForecastingProbabilistic ForecastingSpatiotemporal ForecastingTime Series TransformersWeather Forecasting
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