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.

Apr 29, 2026

FutureWorld: A Live Reinforcement Learning Environment for Predictive Agents with Real-World Outcome Rewards

Live future prediction refers to the task of making predictions about real-world events before they unfold. This task is increasingly studied using large language model-based agent systems, and it is important for building agents that can continually learn from the real world. It can provide a large number of prediction questions grounded in diverse real-world events, while preventing answer leakage. To leverage the advantages of future prediction, we present FutureWorld, a live agentic reinforcement learning environment that closes the training loop between prediction, outcome realization, and parameter updates. Specifically, we modify and extend verl-tool, resulting in a new framework that we call verl-tool-future. Unlike standard reinforcement learning training frameworks that rely on immediate rewards, verl-tool-future stores prediction-time rollouts, backfills rewards after real-world outcomes become available, and then replays the completed trajectories for policy update. Across three open-source agents, successive FutureWorld training rounds lead to consistent improvements in prediction accuracy, probabilistic scoring, and calibration, demonstrating that delayed real-world outcome feedback can serve as an effective reinforcement learning signal.

Zhixin Han, Yanzhi Zhang, Chuyang Wei +11

College of Software, Nankai University · Zhongguancun Academy, Beijing, China · Academy of Mathematics and Systems Science, Chinese Academy of Sciences +3

Agentic RLReinforcement LearningProbabilistic ForecastingRL for LLM AgentsDelayed RL
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Apr 29, 2026

Recipes for Calibration Checks in Safety-Critical Applications

Safety-critical prediction systems, such as autonomous vehicles, weather forecasters, and medical monitors, commonly rely on probabilistic forecasters. These forecasters make predictions about possible future outcomes, and their quality and robustness needs to be validated and certified. Often, only accuracy -- the mean of the predictions -- is evaluated against true outcomes. However, for safety-critical scenarios and decision making under uncertainty, the full distributional properties of the forecasts should be checked: do the observed prediction errors actually follow the forecasted probability distributions? To this end, we introduce a framework for calibration checks: statistical tests that validate distributional properties of forecasts when measured over many samples. In order to support ease-of-use in real-world operations, these checks produce a single accept/reject decision for data collected from a forecaster. This contrasts typical calibration calculations which produce one or multiple continuous calibration scores and require expertise to implement in a validation workflow. We further support operationalization by introducing modifications to calibration testing that (a) reject only overconfident predictions, allowing for pessimistic or cautious predictions in safety-critical settings, and (b) tolerate small, operationally acceptable deviations even for large numbers of validation samples. We organize the calibration checking process into a modular pipeline comprising four steps: (i) the data model, (ii) the chosen metric, (iii) the hypothesis formulation, and (iv) the testing procedure. Each step consists of independently swappable components, thereby supporting a large variety of possible use-cases and trade-offs. We demonstrate the applicability of the framework on two complementary example problems, weather forecasting and robot pose estimation.

Romeo Valentin

Department of Aeronautics and Astronautics Stanford University Stanford, CA 94305, USA

Probabilistic ForecastingUncertainty Calibration
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Apr 28, 2026

Evaluating Strategic Reasoning in Forecasting Agents

Forecasting benchmarks produce accuracy leaderboards but little insight into why some forecasters are more accurate than others. We introduce Bench to the Future 2 (BTF-2), 1,417 pastcasting questions with a frozen 15M-document research corpus in which agents reproducibly research and forecast offline, producing full reasoning traces. BTF-2 detects accuracy differences of 0.004 Brier score, and can distinguish differential agent strengths in research vs. judgment. We build a forecaster 0.011 Brier more accurate than any single frontier agent, and use it to evaluate agent strategic reasoning without hindsight bias. We find the better forecaster differs primarily in its pre-mortem analysis of its blind spots and consideration of black swans. Expert human forecasters found the dominant strategic reasoning failures of frontier agents are in assessing political and business leaders' incentives, judging their likelihood to follow through on stated plans, and modeling institutional processes.

Tom Liptay, Dan Schwarz, Rafael Poyiadzi +2

FutureSearch

LLM Agent EvaluationForecasting BenchmarksProbabilistic Forecasting
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Apr 28, 2026

Conditional Flow Matching for Probabilistic Downscaling of Maximum 3-day Snowfall in Alaska

Precipitation in complex terrain is governed by orographic processes operating at scales of a few kilometers, yet climate models typically run at resolutions of 50--100km where this topographic detail is absent. Dynamical downscaling with high-resolution regional models such as WRF can resolve these processes, but the computational cost -- months of wall-clock time per scenario -- precludes the large ensembles needed for uncertainty quantification. We present WxFlow, a conditional generative model based on flow matching that learns to map coarse-resolution climate model output and high-resolution topography to calibrated probabilistic ensembles of fine-scale precipitation fields. Applied to 4km WRF simulations of maximum 3-day snowfall over southeast Alaska, WxFlow achieves 87.8% improvement in spectral fidelity and dramatically lower Continuous Ranked Probability Scores relative to conventional lapse-rate-corrected bicubic downscaling, while generating 50-member ensembles in seconds on a laptop. Ensemble spread is spatially coherent and governed by topography, reflecting physically plausible uncertainty structure. All code is available at https://github.com/glide-ism/wrf-flow.

Douglas Brinkerhoff, Elizabeth Fischer

Department of Computer Science, University of Montana · International Arctic Research Center, University of Alaska

Uncertainty QuantificationClimate ScienceProbabilistic ForecastingPrecipitation DownscalingClimate ModelingClimate Downscaling
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Apr 27, 2026

Prior-Agnostic Robust Forecast Aggregation

Robust forecast aggregation combines the predictions of multiple information sources to perform well in the worst case across all possible information structures. Previous work largely focuses on settings with a known binary state space, where the state is either 0 or 1. We study prior-agnostic robust forecast aggregation in which the aggregator observes only experts' reports, yet is ignorant of both the underlying joint information structure and the full prior, including the underlying state space. Unlike the standard model that fixes the binary state space {0, 1}, we allow the (binary) unknown state values to be arbitrary numbers in [0, 1], so the same reported probability may correspond to very different realized outcome frequencies across environments. Our main contribution is a simple, explicit, closed-form log-odds aggregator that linearly pools forecasts in logit space, together with (nearly-)tight minimax-regret guarantees across three knowledge regimes. We first show that under conditionally independent (CI) signals, robust aggregation with an unknown state space is strictly harder than in the known-state setting by establishing a larger lower bound, and our aggregation rule can achieve a worst-case regret of 0.0255. Along the way, we also characterize tight regret bounds for Blackwell-ordered structures and for general information structures. In the classical setting with known state space {0,1}, our aggregator achieves regret strictly below 0.0226 for CI structures. To the best of our knowledge, this is the first explicit closed-form aggregator that achieves a regret upper bound strictly less than 0.0226. Finally, we extend the model where the aggregator additionally knows each expert's marginal forecast distribution; in this setting, with the CI structures, we show that a generalized log-odds rule achieves regret of 0.0228, complementing with a lower bound of 0.0225.

Zhi Chen, Cheng Peng, Wei Tang

Chinese University of Hong Kong

Minimax RegretProbabilistic ForecastingRegret Minimization
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Apr 21, 2026

Calibrating Scientific Foundation Models with Inference-Time Stochastic Attention

Transformer-based scientific foundation models are increasingly deployed in high-stakes settings, but current architectures give deterministic outputs and provide limited support for calibrated predictive uncertainty. We propose Stochastic Attention, a sample average lightweight inference-time modification that randomizes attention by replacing softmax weights with normalized multinomial samples controlled by a single concentration parameter, and produces predictive ensembles without retraining. To set this parameter, we introduce a calibration objective that matches the stochastic attention output with the target, yielding an efficient univariate post-hoc tuning problem. We evaluate this mechanism on scientific foundation models for weather and time-series forecasting, as well as several regression tasks. Across benchmarks against uncertainty-aware baselines, we find that Sample Average Stochastic Attention achieves the strongest native calibration and the sharpest prediction intervals at comparable calibration, with adaptation costs nearly three orders of magnitude lower than the next-best baseline.

Akash Yadav, Taiwo A. Adebiyi, Ruda Zhang

University of Houston

Post-Hoc CalibrationProbabilistic ForecastingTime-Series Foundation ModelsUncertainty Calibration
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Apr 20, 2026

Agentic Forecasting with Structured Linguistic Beliefs

We propose the Bayesian Linguistic Forecaster (BLF), which is a search-based ReAct style agent for (binary) forecasting that augments its context with a linguistic 'belief state', consisting of a probability estimate and a structured natural-language evidence summary. (The belief update is 'Bayesian-inspired' rather than exact Bayesian inference, although we do include a comparison to a more explicit Bayesian approach using LLM-elicited likelihood surrogates.) On 400 historical ForecastBench question-date instances, BLF has the highest overall Brier Index among the compared external agents, and is the only compared method to significantly outperform a crowd+empirical-prior baseline in terms of overall performance. Our backtesting framework combines date-aware search tools, leakage auditing, and paired comparisons for variance control to provide a rigorous empirical framework for comparing agentic forecasting systems.

Kevin Murphy

Department of Computer Science University of British Columbia Vancouver, BC, Canada

Forecasting BenchmarksProbabilistic ForecastingLLM-Based Time Series Forecasting
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Apr 20, 2026

Forecasting Ionospheric Irregularities on GNSS Lines of Sight Using Dynamic Graphs with Ephemeris Conditioning

Most data-driven ionospheric forecasting models operate on gridded products, which do not preserve the time-varying sampling structure of satellite-based sensing. We instead model the ionosphere as a dynamic graph over ionospheric pierce points (IPPs), with connectivity that evolves as satellite positions change. Because satellite trajectories are predictable, the graph topology over the forecast horizon can be constructed in advance. We exploit this property to condition forecasts on the future graph structure, which we term ephemeris conditioning. This enables prediction on lines of sight that appear only in the forecast horizon. We evaluate our framework on multi-GNSS (Global Navigation Satellite System) data from a co-located receiver pair in Singapore spanning January 2023 through April 2025. The task is to forecast Rate of TEC Index (ROTI)-defined irregularities at 5-minute cadence up to 2 hours ahead as binary probabilistic classification per node. The resulting model, IonoDGNN, achieves a Brier Skill Score (BSS) of 0.49 and a precision-recall area under the curve (PR-AUC) of 0.75, improving over persistence by 35% in BSS and 52% in PR-AUC, with larger gains at longer lead times. Ablations confirm that graph structure and ephemeris conditioning each contribute meaningfully, with conditioning proving essential for satellites that rise during the forecast horizon (receiver operating characteristic AUC: 0.95 vs.\ 0.52 without). Under simulated coverage dropout, the model retains predictive skill on affected nodes through spatial message passing from observed neighbors. These results suggest that dynamic graph forecasting on evolving lines of sight is a viable alternative to grid-based representations for ionospheric irregularity forecasting. The model and evaluation code will be released upon publication.

Mert Can Turkmen, Eng Leong Tan, Yee Hui Lee

Nanyang Technological University Singapore

Probabilistic ForecastingDynamic Graph LearningSpatiotemporal ForecastingSpatiotemporal GNNs
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Apr 20, 2026

Earth System Foundation Model (ESFM): A unified framework for heterogeneous data integration and forecasting

Foundation models (FMs) for the Earth system learn statistical relationships between physical variables across massive datasets to enable versatile downstream applications through finetuning, separating them from task-specific weather models. Here, we introduce Earth System Foundation Model (ESFM), a fully open model building on the 3D Swin UNet backbone of the pioneering Aurora model. ESFM introduces extensions that increase functionality and foster adoption in climate sciences. First, the encoding scheme and training protocols have been extended to handle diverse datasets, including those containing missing values across all spatio-temporal dimensions such as satellite data, as well as station data, all under one backbone. Axial attention is introduced to capture inter-variable dependencies. As a result ESFM skillfully predicts variables in regions or on pressure levels where no data is present at the initial time, while preserving inter-variable relationships, for example between temperature, pressure, and humidity. Individual variable tokenization enables different sets of variables to be shuffled during training and simplifies the process of building extensions for new downstream tasks. Adaptive layer norm-based ensembles allow for a simple yet effective way to transform deterministic ESFM to a probabilistic FM. We present findings using dense gridded data (ERA5, CMIP6), regionally masked dense data, sparse gridded MODIS satellite data, and station data. Results demonstrate competitive or superior performance relative to state-of-the-art benchmarks. Case studies of Super Typhoon Doksuri (2023) and 2024 sudden stratospheric warming events show accurate positional and magnitude estimations of extreme weather. ESFM retains the strengths of previous foundation models, such as long-term stability, but facilitates application to a variety of downstream tasks.

Firat Ozdemir, Yun Cheng, Salman Mohebi +11

Swiss Data Science Center (SDSC), ETH Zurich & EPFL, Zurich & Lausanne, Switzerland · ETH AI Center, ETH Zurich, Zurich, Switzerland · ETH Zurich, Zurich, Switzerland +1

Geospatial Foundation ModelsClimate ScienceProbabilistic ForecastingClimate ModelingSpatiotemporal ForecastingWeather Forecasting
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Apr 19, 2026

Human-AI Collaboration for Estimating Scientific Replicability

Determining whether published scientific findings can successfully be replicated is a long-standing challenge in the empirical sciences. Existing approaches for replicability assessment typically rely either on human judgment, i.e., creative assembly of human experts, or on machine learning models trained on paper content metadata. While both approaches have demonstrated value, each also has important limitations. Human forecasts can be influenced by cognitive biases and narrow exposure to the research literature, while automated assessments often struggle to capture contextual cues and subtle signals of credibility. In this paper, we examine a hybrid approach. Specifically, we introduce a hybrid prediction market in which algorithmic agents trade alongside human participants to jointly estimate the likelihood that a published scientific finding will be corroborated via the outcome of a controlled replication study. Agents are trained on outcomes from hundreds of prior replication studies while human participants contribute domain knowledge through real-time trading. We evaluate this hybrid approach through multiple live experiments involving participants from different academic disciplines and compare its performance to artificial-only and human-only baselines. Our results show that, except for a few cases, hybrid markets match or outperform artificial prediction markets, producing more accurate and reliable replication forecasts.

Tatiana Chakravorti, Robert Fraleigh, Timothy Fritton +7

The Pennsylvania State University · Rutgers University

Probabilistic ForecastingScientific ReproducibilityHuman-AI CollaborationPrediction Markets
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Apr 19, 2026

Forecast Sports Outcomes under Efficient Market Hypothesis: Theoretical and Experimental Analysis of Odds-Only and Generalised Linear Models

Converting betting odds into accurate outcome probabilities is a fundamental challenge in order to use betting odds as a benchmark for sports forecasting and market efficiency analysis. In this study, we propose two methods to overcome the limitations of existing conversion methods. Firstly, we propose an odds-only method to convert betting odds to probabilities without using historical data for model fitting. While existing odds-only methods, such as Multiplicative, Shin, and Power exist, they do not adjust for biases or relationships we found in our betting odds dataset, which consists of 90014 football matches across five different bookmakers. To overcome these limitations, our proposed Odds-Only-Equal-Profitability-Confidence (OO-EPC) method aligns with the bookmakers' pricing objectives of having equal confidence in profitability for each outcome. We provide empirical evidence from our betting odds dataset that, for the majority of bookmakers, our proposed OO-EPC method outperforms the existing odds-only methods. Beyond controlled experiments, we applied the OO-EPC method under real-world uncertainty by using it for six iterations of an annual basketball outcome forecasting competition. Secondly, we propose a generalised linear model that utilises historical data for model fitting and then converts betting odds to probabilities. Existing generalised linear models attempt to capture relationships that the Efficient Market Hypothesis already captures. To overcome this shortcoming, our proposed Favourite-Longshot-Bias-Adjusted Generalised Linear Model (FL-GLM) fits just one parameter to capture the favourite-longshot bias, providing a more interpretable alternative. We provide empirical evidence from historical football matches where, for all bookmakers, our proposed FL-GLM outperforms the existing multinomial and logistic generalised linear models.

Kaito Goto, Naoya Takeishi, Takehisa Yairi

Research Center for Advanced Science and Technology, The University of Tokyo, Japan

Probabilistic ForecastingGeneralized Linear ModelsSports Outcome Prediction
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Apr 17, 2026

Enhancing AI and Dynamical Subseasonal Forecasts with Probabilistic Bias Correction

Decision-makers rely on weather forecasts to plant crops, manage wildfires, allocate water and energy, and prepare for weather extremes. Today, such forecasts enjoy unprecedented accuracy out to two weeks thanks to steady advances in physics-based dynamical models and data-driven artificial intelligence (AI) models. However, model skill drops precipitously at subseasonal timescales (2 - 6 weeks ahead), due to compounding errors, systemic model biases, and the chaotic nature of the atmosphere. To counter this degradation, we introduce probabilistic bias correction (PBC), a machine learning framework that substantially reduces systematic error by learning to correct historical probabilistic forecasts. When applied to the leading dynamical and AI models from the European Centre for Medium-Range Weather Forecasts (ECMWF), PBC doubles the modest subseasonal skill of the AI Forecasting System and improves the skill of the operationally-debiased dynamical model for 91% of pressure, 92% of temperature, and 98% of precipitation targets. We designed PBC for operational deployment, and, in ECMWF's 2025 real-time forecasting competition, its global forecasts placed first for all weather variables and lead times, outperforming the dynamical models from six operational forecasting centers, an international dynamical multi-model ensemble, ECMWF's AI Forecasting System, and the forecasting systems of 34 teams worldwide. These probabilistic skill gains translate into more accurate prediction of extreme events and have the potential to improve agricultural planning, energy management, and disaster preparedness in vulnerable communities.

Hannah Guan, Soukayna Mouatadid, Paulo Orenstein +10

Harvard College, Cambridge, MA, USA. · University of Toronto, Toronto, ON, Canada. · Instituto de Matemática Pura e Aplicada, Rio de Janeiro, RJ, Brazil. +6

Probabilistic ForecastingWeather Forecasting
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Apr 16, 2026

Assessing the Performance-Efficiency Trade-off of Foundation Models in Probabilistic Electricity Price Forecasting

Large-scale renewable energy deployment introduces pronounced volatility into the electricity system, turning grid operation into a complex stochastic optimization problem. Accurate electricity price forecasting (EPF) is essential not only to support operational decisions, such as optimal bidding strategies and balancing power preparation, but also to reduce economic risk and improve market efficiency. Probabilistic forecasts are particularly valuable because they quantify uncertainty stemming from renewable intermittency, market coupling, and regulatory changes, enabling market participants to make informed decisions that minimize losses and optimize expected revenues. However, it remains an open question which models to employ to produce accurate forecasts. Should these be task-specific machine learning (ML) models or Time Series Foundation Models (TSFMs)? In this work, we compare four models for day-ahead probabilistic EPF (PEPF) in European bidding zones: a deterministic NHITS backbone with Quantile-Regression Averaging (NHITS+QRA) and a conditional Normalizing-Flow forecaster (NF) are compared with two TSFMs, namely Moirai and ChronosX. On the one hand, we find that TSFMs outperform task-specific deep learning models trained from scratch in terms of CRPS, Energy Score, and predictive interval calibration across market conditions. On the other hand, we find that well-configured task-specific models, particularly NHITS combined with QRA, achieve performance very close to TSFMs, and in some scenarios, such as when supplied with additional informative feature groups or adapted via few-shot learning from other European markets, they can even surpass TSFMs. Overall, our findings show that while TSFMs offer expressive modeling capabilities, conventional models remain highly competitive, emphasizing the need to weigh computational expense against marginal performance improvements in PEPF.

Jan Niklas Lettner, Hadeer El Ashhab, Veit Hagenmeyer +1

Karlsruhe Institute of Technology · Karlsruhe, Germany

Electricity Price ForecastingTime Series ForecastingProbabilistic ForecastingTime-Series Foundation ModelsProbabilistic Time Series ForecastingPower Systems
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Apr 14, 2026

CycloneMAE: A Scalable Multi-Task Learning Model for Global Tropical Cyclone Probabilistic Forecasting

Tropical cyclones (TCs) rank among the most destructive natural hazards, yet their forecasting faces fundamental trade-offs: numerical weather prediction (NWP) models are computationally prohibitive and struggle to leverage historical data, while existing deep learning (DL)-based intelligent models are variable-specific and deterministic, which fail to generalize across different forecasting variables. Here we present CycloneMAE, a scalable multi-task forecasting model that learns transferable TC representations from multi-modal data using a TC structure-aware masked autoencoder. By coupling a discrete probabilistic gridding mechanism with a pre-train/fine-tune paradigm, CycloneMAE simultaneously delivers deterministic forecasts and probability distributions. Evaluated across five global ocean basins, CycloneMAE outperforms leading NWP systems in pressure and wind forecasting up to 120 hours and in track forecasting up to 24 hours. Attribution analysis via integrated gradients reveals physically interpretable learning dynamics: short-term forecasts rely predominantly on the internal core convective structure from satellite imagery, whereas longer-term forecasts progressively shift attention to external environmental factors. Our framework establishes a scalable, probabilistic, and interpretable pathway for operational TC forecasting.

Renlong Hang, Zihao Xu, Jiuwei Zhao +3

School of Computer Science, School of Software, Nanjing University of Information Science and Technology, Nanjing, 210044, China. · School of Atmospheric Sciences, Nanjing University of Information Science and Technology, Nanjing, 210044, China. · Shanghai Typhoon Institute, China Meteorological Administration, Shanghai, 200030, China. +1

Tropical Cyclone Intensity ForecastingWeather ForecastingProbabilistic ForecastingMulti-Task LearningMasked AutoencodersExplainable Time Series Forecasting
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Apr 11, 2026

Ontological Trajectory Forecasting via Finite Semigroup Iteration and Lie Algebra Approximation in Geopolitical Knowledge Graphs

We present EL-DRUIN, an ontological reasoning system for geopolitical intelligence analysis that combines formal ontology, finite semigroup algebra, and Lie algebra approximation to forecast long-run relationship trajectories. Current LLM-based political analysis systems operate as summarisation engines, producing outputs bounded by textual pattern matching. EL-DRUIN departs from this paradigm by modelling geopolitical relationships as states in a finite set of named Dynamic Patterns, composing patterns via a semigroup operation whose structure constants are defined by an explicit composition table, and embedding each pattern as a vector in an 8-dimensional semantic Lie algebra space. Forward simulation iterates this semigroup operation, yielding reachable pattern sets at each discrete timestep; convergence to idempotent absorbing states (fixed points of the composition) constitutes the predicted long-run attractor. Bayesian posterior weights combine ontology-derived confidence priors with a Lie similarity term measuring the cosine similarity between the vector sum of composing patterns and the target pattern vector, providing interpretable, calibrated probabilities that are not self-reported by a language model. Bifurcation points -- steps at which two candidate attractors have near-equal posterior mass -- are detected and exposed to downstream analysis. We demonstrate the framework on six geopolitical scenarios including US-China technology decoupling and the Taiwan Strait military coercion trajectory. The architecture is publicly available as an open-source system with a Streamlit frontend exposing full computation traces, Bayesian posterior breakdowns, and 8D ontological state vectors.

Qihang Wu

Department of Industrial and Systems Engineering, The Hong Kong Polytechnic University

Ontology-Based ReasoningProbabilistic ForecastingKnowledge Graphs
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Apr 10, 2026

U-Cast: A Surprisingly Simple and Efficient Frontier Probabilistic AI Weather Forecaster

AI-based weather forecasting now rivals traditional physics-based ensembles, but state-of-the-art (SOTA) models rely on specialized architectures and massive computational budgets, creating a high barrier to entry. We demonstrate that such complexity is unnecessary for frontier performance. We introduce \ours, a probabilistic forecaster built on a standard U-Net backbone trained with a simple recipe: deterministic pre-training on Mean Absolute Error followed by short probabilistic fine-tuning on the Continuous Ranked Probability Score (CRPS) using Monte Carlo Dropout for stochasticity. As a result, our model matches or exceeds the probabilistic skill of GenCast and IFS ENS at 1.5∘1.5^\circ resolution while reducing training compute by over 10×10\times compared to leading CRPS-based models and inference latency by over 10×10\times compared to diffusion-based models. U-Cast trains in under 12 H200 GPU-days and generates a 15-day ensemble forecast in 3 seconds. These results suggest that scalable, general-purpose architectures paired with efficient training curricula can match complex domain-specific designs at a fraction of the cost, opening the training of frontier probabilistic weather models to the broader community.

Salva Rühling Cachay, Duncan Watson-Parris, Rose Yu

UC San Diego

Monte Carlo DropoutWeather ForecastingProbabilistic Forecasting
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Apr 9, 2026

Accurate and Reliable Uncertainty Estimates for Deterministic Predictions Extensions to Under and Overpredictions

Computational models support high-stakes decisions across engineering and science, and practitioners increasingly seek probabilistic predictions to quantify uncertainty in such models. Existing approaches generate predictions either by sampling input parameter distributions or by augmenting deterministic outputs with uncertainty representations, including distribution-free and distributional methods. However, sampling-based methods are often computationally prohibitive for real-time applications, and many existing uncertainty representations either ignore input dependence or rely on restrictive Gaussian assumptions that fail to capture asymmetry and heavy-tailed behavior. Therefore, we extend the ACCurate and Reliable Uncertainty Estimate (ACCRUE) framework to learn input-dependent, non-Gaussian uncertainty distributions, specifically two-piece Gaussian and asymmetric Laplace forms, using a neural network trained with a loss function that balances predictive accuracy and reliability. Through synthetic and real-world experiments, we show that the proposed approach captures an input-dependent uncertainty structure and improves probabilistic forecasts relative to existing methods, while maintaining flexibility to model skewed and non-Gaussian errors.

Rileigh Bandy, Enrico Camporeale, Andong Hu +2

Optimization and Uncertainty Quantification Department, Sandia National Laboratories, Albuquerque, NM · School of Physical and Chemical Sciences, Queen Mary University of London, London, UK and Space Weather Technology, Research and Education Center, University of Colorado, Boulder, CO · Space Weather Technology, Research and Education Center, University of Colorado, Boulder, CO +2

Distributional RegressionUncertainty QuantificationProbabilistic ForecastingUncertainty CalibrationConditional Distribution Estimation
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Apr 7, 2026

The Oracle's Fingerprint: Correlated AI Forecasting Errors and the Limits of Bias Transmission

When large language models (LLMs) are consulted as forecasting tools, the independence of individual errors -- the foundation of collective intelligence -- may collapse. We test three conditions necessary for this "epistemic monoculture" to emerge. In Study 1, we show that GPT-4o, Claude, and Gemini exhibit highly correlated forecasting errors on 568 resolved binary prediction questions (mean pairwise error correlation r = 0.77, p < 0.001; r = 0.78 excluding likely-leaked questions), despite being developed independently by different organizations. In Study 2, we test whether this correlated bias has propagated into human crowd forecasts, using a within-question design that tracks community prediction shifts across the ChatGPT launch boundary (November 2022). We find that community forecasts move in the direction predicted by LLMs (r = 0.20, p = 0.007), but this shift is fully explained by rational updating toward ground truth. In Study 3, we examine whether the category-level pattern of human forecasting errors increasingly resembles the LLM bias fingerprint. We find the opposite: pre-ChatGPT human biases already strongly resembled the LLM pattern (r = 0.87), while post-ChatGPT the resemblance weakened (r = -0.28). Together, these findings reveal an epistemic monoculture that is built but not yet activated: three nominally independent AI systems share the same failure modes, amplifying precisely the biases humans already hold.

Theodor Spiro

Correlated Errors in Language ModelsLLM ReliabilityLanguage Model Bias EvaluationProbabilistic Forecasting
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Apr 6, 2026

(Sparse) Attention to the Details: Preserving Spectral Fidelity in ML-based Weather Forecasting Models

We introduce Mosaic, a probabilistic weather forecasting model that addresses three failure modes of spectral degradation in ML-based weather prediction: spectral damping (statistical), high-frequency aliasing (architectural), and residual high-frequency leakage (parametric). Mosaic generates ensemble members through learned functional perturbations and operates on native-resolution grids via mesh-aligned block-sparse attention, a hardware-aligned mechanism that captures long-range dependencies at linear cost by sharing keys and values across spatially adjacent queries. At 1.5° resolution with 214M parameters, Mosaic matches or outperforms models trained on 6×\times finer resolution on key variables and achieves state-of-the-art results among 1.5° models, producing well-calibrated ensembles whose individual members exhibit near-perfect spectral alignment across all resolved frequencies. A 24-member, 10-day forecast takes under 12s on a single H100~GPU. Code is available at https://github.com/maxxxzdn/mosaic.

Maksim Zhdanov, Ana Lucic, Max Welling +1

AMLab · University of Amsterdam · CuspAI

Weather ForecastingProbabilistic ForecastingSpectral BiasBlock-Sparse Attention
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Apr 5, 2026

TimeSeek: Temporal Reliability of Agentic Forecasters

We introduce TimeSeek, a benchmark for studying how the reliability of agentic LLM forecasters changes over a prediction market's lifecycle. We evaluate 10 frontier models on 150 CFTC-regulated Kalshi binary markets at five temporal checkpoints, with and without web search, for 15,000 forecasts total. Models are most competitive early in a market's life and on high-uncertainty markets, but much less competitive near resolution and on strong-consensus markets. Web search improves pooled Brier Skill Score (BSS) for every model overall, yet hurts in 12% of model-checkpoint pairs, indicating that retrieval is helpful on average but not uniformly so. Simple two-model ensembles reduce error without surpassing the market overall. These descriptive results motivate time-aware evaluation and selective-deference policies rather than a single market snapshot or a uniform tool-use setting.

Hamza Mostafa, Om Shastri, Dennis Lee

The Wharton School, University of Pennsylvania

LLM Agent ReliabilityForecasting BenchmarksProbabilistic ForecastingPrediction Markets
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Apr 4, 2026

PolySwarm: A Multi-Agent Large Language Model Framework for Prediction Market Trading and Latency Arbitrage

This paper presents PolySwarm, a novel multi-agent large language model (LLM) framework designed for real-time prediction market trading and latency arbitrage on decentralized platforms such as Polymarket. PolySwarm deploys a swarm of 50 diverse LLM personas that concurrently evaluate binary outcome markets, aggregating individual probability estimates through confidence-weighted Bayesian combination of swarm consensus with market-implied probabilities, and applying quarter-Kelly position sizing for risk-controlled execution. The system incorporates an information-theoretic market analysis engine using Kullback-Leibler (KL) divergence and Jensen-Shannon (JS) divergence to detect cross-market inefficiencies and negation pair mispricings. A latency arbitrage module exploits stale Polymarket prices by deriving CEX-implied probabilities from a log-normal pricing model and executing trades within the human reaction-time window. We provide a full architectural description, implementation details, and evaluation methodology using Brier scores, calibration analysis, and log-loss metrics benchmarked against human superforecaster performance. We further discuss open challenges including hallucination in agent pools, computational cost at scale, regulatory exposure, and feedback-loop risk, and outline five priority directions for future research. Experimental results demonstrate that swarm aggregation consistently outperforms single-model baselines in probability calibration on Polymarket prediction tasks.

Rajat M. Barot, Arjun S. Borkhatariya

Department of Computer Science, State University of New York, Binghamton, Binghamton, NY, USA. · Department of Software Engineering, Arizona State University, Tempe, AZ, USA.

Algorithmic TradingPrediction MarketsMulti-Agent LLMsProbabilistic Forecasting
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Apr 3, 2026

Transfer Learning for Loan Recovery Prediction under Distribution Shifts with Heterogeneous Feature Spaces

Accurate forecasting of recovery rates (RR) is central to credit risk management and regulatory capital determination. In many loan portfolios, however, RR modeling is constrained by data scarcity arising from infrequent default events. Transfer learning (TL) offers a promising avenue to mitigate this challenge by exploiting information from related but richer source domains, yet its effectiveness critically depends on the presence and strength of distributional shifts, and on potential heterogeneity between source and target feature spaces. This paper introduces FT-MDN-Transformer, a mixture-density tabular Transformer architecture specifically designed for TL in RR forecasting across heterogeneous feature sets. The model produces both loan-level point estimates and portfolio-level predictive distributions, thereby supporting a wide range of practical RR forecasting applications. We evaluate the proposed approach in a controlled Monte Carlo simulation that facilitates systematic variation of covariate, conditional, and label shifts, as well as in a real-world transfer setting using the Global Credit Data (GCD) loan dataset as source and a novel bonds dataset as target. Our results show that FT-MDN-Transformer outperforms baseline models when target-domain data are limited, with particularly pronounced gains under covariate and conditional shifts, while label shift remains challenging. We also observe its probabilistic forecasts to closely track empirical recovery distributions, providing richer information than conventional point-prediction metrics alone. Overall, the findings highlight the potential of distribution-aware TL architectures to improve RR forecasting in data-scarce credit portfolios and offer practical insights for risk managers operating under heterogeneous data environments.

Christopher Gerling, Hanqiu Peng, Ying Chen +1

Humboldt-Universität zu Berlin, Unter den Linden 6, 10099 Berlin, Germany · National University of Singapore, 10 Lower Kent Ridge Road, Singapore 119076, Singapore

Cross-Domain Transfer LearningDomain AdaptationTransformerProbabilistic ForecastingCovariate Shift
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Apr 1, 2026

Forecasting Supply Chain Disruptions with Foresight Learning

Anticipating supply chain disruptions before they materialize is a core challenge for firms and policymakers alike. A key difficulty is learning to reason reliably about infrequent, high-impact events from noisy and unstructured inputs - a setting where general-purpose models struggle without task-specific adaptation. We introduce an end-to-end framework that trains LLMs to produce calibrated probabilistic forecasts using realized disruption outcomes as supervision. The resulting model substantially outperforms strong baselines - including GPT-5 - on accuracy, calibration, and precision. We also show that training induces more structured and reliable probabilistic reasoning without explicit prompting. These results suggest a general pathway for training domain-specific forecasting models that produce decision-ready signals. To support transparency we open-source the evaluation dataset used in this study. Dataset: https://huggingface.co/datasets/LightningRodLabs/supply-chain-predictions

Benjamin Turtel, Paul Wilczewski, Kris Skotheim

Lightning Rod Labs

Probabilistic ForecastingSupply Chain ManagementLLM Post-TrainingLLM-Based Time Series ForecastingTime Series Forecasting
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Apr 1, 2026

Super-Resolving Coarse-Resolution Weather Forecasts With Flow Matching

Machine learning-based weather forecasting models now surpass state-of-the-art numerical weather prediction systems, but training and operating these models at high spatial resolution remains computationally expensive. We present a modular framework that decouples forecasting from spatial resolution by applying learned generative super-resolution as a post-processing step to coarse-resolution forecast trajectories. We formulate super-resolution as a stochastic inverse problem, using a residual formulation to preserve large-scale structure while reconstructing unresolved variability. The model is trained with flow matching exclusively on reanalysis data and is applied to global medium-range forecasts. We evaluate (i) design consistency by re-coarsening super-resolved forecasts and comparing them to the original coarse trajectories, and (ii) high-resolution forecast quality using standard ensemble verification metrics and spectral diagnostics. Results show that super-resolution preserves large-scale structure and variance after re-coarsening, introduces physically consistent small-scale variability, and achieves competitive probabilistic forecast skill at 0.25° resolution relative to an operational ensemble baseline, while requiring only a modest additional training cost compared with end-to-end high-resolution forecasting.

Aymeric Delefosse, Anastase Charantonis, Dominique Béréziat

Inria, ARCHES, Paris, France · Sorbonne Université, CNRS, LIP6, Paris, France

Weather ForecastingProbabilistic Forecasting
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Mar 30, 2026

Downscaling weather forecasts from Low- to High-Resolution with Diffusion Models

We introduce a probabilistic diffusion-based method for global atmospheric downscaling implemented within the Anemoi framework. The approach transforms low-resolution ensemble forecasts into high-resolution ensembles by learning the conditional distribution of finer-scale residuals, defined as the difference between the high-resolution fields and the interpolated low-resolution inputs. The system is trained on reforecast pairs from ECMWF IFS, using coarse fields at 100 km to reconstruct fine-scale variability at 30 km resolution. The bulk of the training focuses on recovering small-scale structures, while fine-tuning in high-noise regimes enables the generation of extremes. Evaluation against the medium-range IFS ensemble target shows that the model increases probabilistic skill (FCRPS) for surface variables, reproduces target power spectra at small scales, captures physically consistent multivariate relationships such as wind-pressure coupling, and generates extreme values consistent with those of the target ensemble in tropical cyclones.

Joffrey Dumont Le Brazidec, Simon Lang, Martin Leutbecher +9

European Centre for Medium-Range Weather Forecasts (ECMWF)

Weather ForecastingProbabilistic ForecastingDiffusion Models
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Mar 27, 2026

Probabilistic Forecasting of Localized Wildfire Spread Based on Conditional Flow Matching

This study presents a probabilistic surrogate model for localized wildfire spread based on a conditional flow matching algorithm. The approach models fire progression as a stochastic process by learning the conditional distribution of fire arrival times given the current fire state along with environmental and atmospheric inputs. Model inputs include current burned area, near-surface wind components, temperature, relative humidity, terrain height, and fuel category information, all defined on a high-resolution spatial grid. The outputs are samples of arrival time within a three-hour time window, conditioned on the input variables. Training data are generated from coupled atmosphere-wildfire spread simulations using WRF-SFIRE, paired with weather fields from the North American Mesoscale model. The proposed framework enables efficient generation of ensembles of arrival times and explicitly represents uncertainty arising from incomplete knowledge of the fire-atmosphere system and unresolved variables. The model supports localized prediction over subdomains, reducing computational cost relative to physics-based simulators while retaining sensitivity to key drivers of fire spread. Model performance is evaluated against WRF-SFIRE simulations for both single-step (3-hour) and recursive multi-step (24-hour) forecasts. Results demonstrate that the method captures variability in fire evolution and produces accurate ensemble predictions. The framework provides a scalable approach for probabilistic wildfire forecasting and offers a pathway for integrating machine learning models with operational fire prediction systems and data assimilation.

Bryan Shaddy, Haitong Qin, Brianna Binder +4

Department of Aerospace and Mechanical Engineering, University of Southern California · Department of Mathematics, University of Southern California · Cooperative Institute for Research in the Atmosphere, Colorado State University +1

Wildfire ForecastingProbabilistic ForecastingSurrogate Modeling
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Mar 27, 2026

Characterization and forecasting of national-scale solar power ramp events

The rapid growth of solar energy is reshaping power system operations and increasing the complexity of grid management. As photovoltaic (PV) capacity expands, short-term fluctuations in PV generation introduce substantial operational uncertainty. At the same time, solar power ramp events intensify risks of grid instability and unplanned outages due to sudden large power fluctuations. Accurate identification, forecasting and mitigation of solar ramp events are therefore critical to maintaining grid stability. In this study, we analyze two years of PV power production from 6434 PV stations at 15-minute resolution. We develop quantitative metrics to define solar ramp events and systematically characterize their occurrence, frequency, and magnitude at a national scale. Furthermore, we examine the meteorological drivers of ramp events, highlighting the role of mesoscale cloud systems. In particular, we observe that ramp-up events are typically associated with cloud dissipation during the morning, while ramp-down events commonly occur when cloud cover increases in the afternoon. Additionally, we adopt a recently developed spatiotemporal forecasting framework to evaluate both deterministic and probabilistic PV power forecasts derived from deep learning and physics-based models, including SolarSTEPS, SHADECast, IrradianceNet, and IFS-ENS. The results show that SHADECast is the most reliable model, achieving a CRPS 10.8% lower than that of SolarSTEPS at a two-hour lead time. Nonetheless, state-of-the-art nowcasting models struggle to capture ramp dynamics, with forecast RMSE increasing by up to 50% compared to normal operating conditions. Overall, these results emphasize the need for improved high-resolution spatiotemporal modelling to enhance ramp prediction skill and support the reliable integration of large-scale solar generation into power systems.

Luca Lanzilao, Angela Meyer

School of Engineering and Computer Science, Bern University of Applied Sciences, Quellgasse 21, Biel, 2501, Bern, Switzerland · Department of Geosciences and Remote Sensing, TU Delft, Stevinweg 1, Delft, 2628 CN, South-Holland, The Netherlands

Solar Power ForecastingPower SystemsProbabilistic ForecastingSpatiotemporal Forecasting
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Mar 24, 2026

Artificial General Intelligence Forecasting and Scenario Analysis: State of the Field, Methodological Gaps, and Strategic Implications

In this report, we review the current state of methodologies to forecast the arrival of artificial general intelligence, assess their reliability, and analyze the implications for strategy and policy. We synthesize diverse forecasting approaches, document significant limitations in existing methods, and propose a research agenda for developing more-robust forecasting infrastructure. The report does not endorse a specific forecast or scenario but rather provides a framework for interpreting forecasts under conditions of deep uncertainty. We experimented with an iterative approach to human and artificial intelligence collaboration for this report. The primary drafting of the text was performed by large language models (GPT 5.1, Gemini 3 Pro, and Claude 4.5 Opus), with human researchers providing direction, peer review, fact-checking, and revision.

Gopal P. Sarma, Sunny D. Bhatt, Michael Jacob +1

Artificial General IntelligenceProbabilistic Forecasting
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Mar 20, 2026

Enhancing AI-Based Tropical Cyclone Track and Intensity Forecasting via Systematic Bias Correction

Tropical cyclones (TCs) pose severe threats to life, infrastructure, and economies in tropical and subtropical regions, underscoring the critical need for accurate and timely forecasts of both track and intensity. Recent advances in AI-based weather forecasting have shown promise in improving TC track forecasts. However, these systems are typically trained on coarse-resolution reanalysis data (e.g., ERA5 at 0.25 degree), which constrains predicted TC positions to a fixed grid and introduces significant discretization errors. Moreover, intensity forecasting remains limited especially for strong TCs by the smoothing effect of coarse meteorological fields and the use of regression losses that bias predictions toward conditional means. To address these limitations, we propose BaguanCyclone, a novel, unified framework that integrates two key innovations: (1) a probabilistic center refinement module that models the continuous spatial distribution of TC centers, enabling finer track precision; and (2) a region-aware intensity forecasting module that leverages high-resolution internal representations within dynamically defined sub-grid zones around the TC core to better capture localized extremes. Evaluated on the global IBTrACS dataset across six major TC basins, our system consistently outperforms both operational numerical weather prediction (NWP) models and most AI-based baselines, delivering a substantial enhancement in forecast accuracy. Remarkably, BaguanCyclone excels in navigating meteorological complexities, consistently delivering accurate forecasts for re-intensification, sweeping arcs, twin cyclones, and meandering events. Our code is available at https://github.com/DAMO-DI-ML/Baguan-cyclone.

Peisong Niu, Haifan Zhang, Yang Zhao +6

DAMO Academy, Alibaba Group Bellevue, USA

Tropical Cyclone Intensity ForecastingWeather ForecastingProbabilistic Forecasting
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Mar 20, 2026

Data-driven ensemble prediction of the global ocean

Data-driven models have advanced deterministic ocean forecasting, but extending machine learning to probabilistic global ocean prediction remains an open challenge. Here we introduce FuXi-ONS, the first machine-learning ensemble forecasting system for the global ocean, providing 5-day forecasts on a global 1° grid up to 365 days for sea-surface temperature, sea-surface height, subsurface temperature, salinity and ocean currents. Rather than relying on repeated integration of computationally expensive numerical models, FuXi-ONS learns physically structured perturbations and incorporates an atmospheric encoding module to stabilize long-range forecasts. Evaluated against GLORYS12 reanalysis, FuXi-ONS improves both ensemble-mean skill and probabilistic forecast quality relative to deterministic and noise-perturbed baselines, and shows competitive performance against established seasonal forecast references for SST and Niño3.4 variability, while running orders of magnitude faster than conventional ensemble systems. These results provide a strong example of machine learning advancing a core problem in ocean science, and establish a practical path toward efficient probabilistic ocean forecasting and climate risk assessment.

Qiusheng Huang, Xiaohui Zhong, Anboyu Guo +3

Artificial Intelligence Innovation and Incubation Institute, Fudan University, Shanghai, China. · Shanghai Innovation Institute, Shanghai, China. · Shanghai Academy of Artificial Intelligence for Science, Shanghai, China. +2

Probabilistic ForecastingSpatiotemporal ForecastingClimate ScienceEnsemble Learning
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