Probabilistic Forecasting

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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

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

Stochastically Perturbed Weights: Ensembles from Deterministic Machine-Learning Weather Models
Sep 8, 2026Simon Adamov, Oliver Fuhrer, Reto Knutti +1Uncertainty Quantification Ensemble Learning
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
Forecasting the Winner of a Live Tennis Match
Sep 7, 2026Charles Xie, Aneesh MuppidiProbabilistic Forecasting Sports Outcome Prediction
Natick High School 15 West Street, Natick, Massachusetts 01760, USA · University of Oxford Oxford, United Kingdom
Statistical versus machine learning-based spatial interpolation of post-processed ensemble weather forecasts
Sep 7, 2026Mária LakatosEnsemble Learning Probabilistic Forecasting
Faculty of Informatics, University of Debrecen, Hungary
Inferring Urban Mobility Interactions from Aggregated Dynamics
Sep 7, 2026Yi Wang, Jing Li, Jinliang Deng +5Traffic Flow Estimation Probabilistic Forecasting
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
The Corroboration Illusion: When More News Makes LLM Forecasts Less True
Sep 5, 2026Yuan Lu, Yukuan ZhangLLM Security Data Poisoning Attacks
Peking university Beijing, China · University of Central Florida Orlando, FL, USA
From Narrative to Auditable Forecasts: A Structured Scaffold for Agentic Forecasting
Sep 5, 2026Yuanpu Cao, Yongkang Du, Yurui Chang +2Probabilistic Forecasting
The Pennsylvania State University
WeatherNext 3: Increasing resolution and performance of global weather models with raw observations
Sep 3, 2026Stephan Rasp, Boris Babenko, Dominic Masters +22Probabilistic Forecasting Weather Forecasting
1Google DeepMind · 2Google Research · 3Google
Improving global precipitation forecasts with an AI weather model trained on satellite observations
Sep 2, 2026Julian F. Schmitt, Bertrand Delorme, Robert C. King +4Precipitation Forecasting Probabilistic Forecasting
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
LEAP: Likelihood Elicitation and Aggregation for LLM-based Probabilistic Forecasting
Sep 1, 2026Yufei Chen, Yiran Zhao, Xiaogang Xu +3Probabilistic Forecasting
1Shandong University · 2Nanjing University of Aeronautics and Astronautics · School of Software Technology, Zhejiang University +2
Uncertainty-Aware Trajectory Forecasting from Imperfect Tracking
Aug 31, 2026Stephane Da Silva Martins, Victor Petrovic, Emanuel Aldea +1Probabilistic Trajectory Prediction Probabilistic Forecasting
SATIE – CNRS UMR 8029, Université Paris-Saclay, France · ENS Paris-Saclay, Université Paris-Saclay, France
Uncertainty-Aware End-to-End AI Weather Forecasting: Disentangling Observation and Model Contributions
Aug 31, 2026Rodrigo Almeida, Noelia Otero, Jost Arndt +3Probabilistic Forecasting Aleatoric Uncertainty
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
Foundation models for electricity price forecasting and battery arbitrage: Can they replace market-specific forecasting models?
Aug 31, 2026Arkadiusz Lipiecki, Rafał WeronTabular Foundation Models Electricity Price Forecasting
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
Diffusion-Based Refinement for Kilometer-Scale Probabilistic Precipitation Nowcasting
Aug 31, 2026Dohyun Park, Changhoon Song, Tengyuan Chang +2Precipitation Forecasting Probabilistic Forecasting
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.
How Proper Scoring Rules Shape LLM Forecasting
Aug 28, 2026Benjamin Turtel, Paul Wilczewski, Kris Skotheim +2Probabilistic Forecasting Proper Scoring Rules
Lightning Rod Labs · Technology and Operations Management, INSEAD, Fontainebleau, France · Wharton School and School of Arts & Sciences, University of Pennsylvania
Climate Physics Dynamic Matching
Aug 27, 2026Gurjeet Sangra Singh, Frantzeska Lavda, Alexandros KalousisWeather Forecasting Physics-Informed Generative Modeling
University of Geneva, Geneva, Switzerland · HES-SO Geneva, Geneva, Switzerland
SimCast-S2S: A Computationally Efficient Diffusion Model for Subseasonal Precipitation Forecasting
Aug 27, 2026Hiep V. Dang, Antonios MamalakisPrecipitation Forecasting Latent Diffusion Models
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
A Behavior-Guided Online Probabilistic Forecasting Method for Electric vehicle Charging Loads
Aug 25, 2026Chenghan Li, Qingxiang Liu, Yinliang Xu +1Probabilistic Forecasting Electricity Load Forecasting
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
Arbitrage-Aware Probabilistic Multi-Step Forecasting of Implied Volatility Surfaces: Joint Generation of Surface-Return Trajectories Using Latent Diffusion
Aug 23, 2026Dominik Manuel Buchegger, Lukas GononQuantitative Finance Probabilistic Forecasting
University of St.Gallen St.Gallen, Switzerland
Tracing the Unlabeled Storm: Cross-Variable Transfer in a Lagrangian Atmospheric JEPA Framework
Aug 23, 2026K M Anirudh, S Sandeep, Hariprasad KodamanaPrecipitation Forecasting Spatiotemporal Forecasting
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
StocBench: A Benchmark for Generative Modeling of Stochastic Dynamics
Aug 23, 2026Sebastian Pfister, Benjamin Holzschuh, Nils ThuereyGenerative Modeling Probabilistic Forecasting
School of Computation, Information and Technology, Technical University of Munich, Germany.
Tianmu-TC: Physics-constraints Generative Artificial Intelligence for Global Tropical Cyclone Forecasting
Aug 19, 2026Shiqi Zhang, Pan Mu, Cheng Huang +6Tropical Cyclone Intensity Forecasting Weather Forecasting
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
Defensive Boosting for Online Probabilistic Forecasting
Aug 13, 2026Georgy Noarov, Aaron RothProbabilistic Forecasting Weak-to-Strong Generalization
Earth observation embeddings are effective sub-grid descriptors for probabilistic weather downscaling
Aug 12, 2026Pedro Sousa, Will Tebbutt, Sadiq Jaffer +3Probabilistic Forecasting Weather Forecasting
Department of Computer Science, University of Cambridge · Department of Engineering, University of Cambridge
Two-stage Odd Residual Flows for Mean-Preserving Probabilistic Time Series Forecasting
Aug 11, 2026Kiran Madhusudhanan, Christian Klötergens, Lars Schmidt-Thieme +1Long-Term Time Series Forecasting Normalizing Flows
Institute of Computer Science University of Hildesheim Hildesheim, Germany
Evaluating Generative Time-Series Models on Data with Point Masses
Aug 10, 2026Jian XuTime Series Forecasting Time Series Generation
RIKEN iTHEMS, Wako, Japan · RIKEN Center for Advanced Intelligence Project (AIP), Tokyo, Japan
Do AI Forecast Ensembles Sample the Correct Conditional Distribution?
Aug 9, 2026Lucas J. Howard, Elizabeth A. BarnesTime Series Forecasting Probabilistic Forecasting
Boston University, Faculty of Computing and Data Sciences
Forecasting Without Full Identification: Reliability and Computational Cost in Clot-Growth Simulation
Aug 8, 2026Lennon J. Shikhman, Lily DiPaulo, Ying Qian +1Simulation-Based Inference Probabilistic Forecasting
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
EpiFlow: A framework for improving the utility of wastewater signals for disease forecasting
Aug 7, 2026Aniruddha Adiga, Jingyuan Chou, Gursharn Kaur +8Epidemic Forecasting Probabilistic Forecasting
Biocomplexity Institute, University of Virginia · Department of Computer Science, University of Virginia · Virginia Department of Health +3
Dirichlet Follow-the-Leader Closes the Gap in Simultaneous Multiclass U-Calibration
Aug 7, 2026Pahan DewasurendraProbabilistic Forecasting Follow-the-Regularized-Leader
Johns Hopkins University
Timestep-Conditioned Transformers for Global Weather Forecasting
Aug 6, 2026Sam Levang, Fran Bartolic, Ty Dickinson +3Time Series Forecasting Probabilistic Forecasting
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Stochastically Perturbed Weights: Ensembles from Deterministic Machine-Learning Weather Models

Simon Adamov, Oliver Fuhrer, Reto Knutti, Sebastian Schemm

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 Quantification Ensemble Learning Probabilistic Forecasting Weather Forecasting

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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.