prediction

This work proposes a machine learning–oriented paradigm for weather forecasting that reimagines the traditionally complex and closed operational systems to meet the demands of efficiency, openness, and collaboration in the era of artificial intelligence. By integrating agent-driven software engineering, open compressed data formats, shared validation workflows, interactive computing environments, and generative AI techniques, the framework systematically transforms model development, data utilization, computational management, and service delivery. Designed to equip meteorological and climate centers with future-ready infrastructure, it establishes robust data governance mechanisms, quality assurance protocols, and pathways for workforce skill transformation. The approach maintains scientific rigor while substantially enhancing the accessibility, efficiency, and interactivity of forecasting services.

This work addresses the limitation of existing safety-critical systems, which typically evaluate only predictive accuracy while lacking rigorous validation of the overall calibration of predicted probability distributions. To bridge this gap, the authors propose a modular calibration testing framework that decouples the calibration process into four interchangeable components: data model, scoring rule, hypothesis formulation, and statistical test procedure. Built upon formal statistical hypothesis testing, the framework provides a single accept/reject decision for the entire predictive distribution. Crucially, it rejects only overly confident predictions while tolerating reasonable deviations, thereby balancing practicality with flexibility. Empirical evaluations on weather forecasting and robotic pose estimation tasks demonstrate that the framework effectively supports reliable deployment in safety-critical applications.

Probabilistic forecasting in dynamical systems remains challenging due to missing data and observational noise, which hinder reliable uncertainty quantification. Method: We propose an end-to-end learning framework integrating stochastic differential equation (SDE) modeling, Bayesian inference, and variational approximation—introducing stochastic interpolation to probabilistic forecasting for the first time, enabling distributional (rather than point) predictions of future states. Our approach explicitly encodes physical priors from dynamical systems theory, ensuring both theoretical interpretability and robustness to incomplete and noisy observations. Results: Evaluated on multiple benchmarks including WeatherBench, our method improves prediction interval coverage and calibration by over 25% compared to deterministic baselines. It establishes a novel paradigm for long-horizon uncertainty quantification in meteorological and physics-informed modeling.

This paper addresses the degradation of probabilistic forecast calibration in dynamic data streams caused by distributional shift, feedback loops, and adversarial perturbations. We propose the first general online calibration framework grounded in Blackwell approachability—a theoretically rigorous foundation for sequential decision-making under uncertainty. Our method provides strong calibration guarantees in compact output spaces (e.g., classification and bounded regression) and enables lossless post-hoc recalibration of arbitrary pre-trained predictors. Technically, it unifies insights from Blackwell approachability theory, online optimization, and gradient-based updates, and introduces task-specific efficient algorithms for both classification and regression. Empirical evaluation demonstrates substantial improvements in calibration quality for energy system forecasting, with marked gains in robustness and practical utility for downstream decision-making tasks.

This paper addresses two-stage stochastic optimization problems with contextual information. Method: We propose a novel “single-scenario optimal solving” paradigm: under fixed recourse matrices and linear second-stage costs, we theoretically establish for the first time that such problems reduce to point-estimate optimization over a single scenario. We develop a joint learning-and-optimization framework featuring a decision-optimal structured loss function, which trains a parametric forecasting model to produce point predictions explicitly tailored to optimal decisions. Contribution/Results: On synthetic inventory control and real-world bike-sharing dispatch tasks, our approach reduces decision cost by 12–23% compared to conventional “predict-then-optimize” pipelines and distributional forecasting baselines, while cutting computational overhead by an order of magnitude—significantly enhancing end-to-end decision-making efficacy.

This study addresses the limitation of existing forecasting systems that rely predominantly on point predictions and thus fail to adequately characterize uncertainty for informed decision-making. To overcome this, the authors propose a hybrid framework that extends point forecasts from classical models—such as Theta, exponential smoothing, and ARIMA—into probabilistic forecasts by integrating error post-processing with model-specific, horizon-dependent uncertainty scaling. The approach calibrates forecast errors using historical simulation, conformal prediction, quantile regression, and GARCH-based methods, and systematically evaluates in-sample versus out-of-sample calibration performance. Empirical results on the M4 dataset demonstrate an average 4.6% reduction in Continuous Ranked Probability Score (CRPS). In-sample calibration consistently outperforms out-of-sample calibration, particularly over longer forecast horizons, thereby validating the effectiveness and practical utility of the proposed framework.

This study addresses the persistent challenges of inadequate statistical coverage and inaccurate uncertainty quantification in existing AI-based weather forecasting models, particularly during extreme events. It introduces, for the first time, an online conformal prediction framework that makes no distributional assumptions to post-process outputs from three leading global probabilistic AI models—GenCast, NeuralGCM, and AIFS-ENS. The proposed method significantly improves the statistical coverage accuracy of temperature and precipitation forecasts, including extreme events, without compromising other probabilistic performance metrics. By providing mathematically rigorous uncertainty guarantees, this approach enables reliably calibrated AI-driven weather predictions.

This study addresses the challenge of uncertainty quantification in aggregated time series forecasting, particularly for annual totals and year-over-year growth rates. It proposes a simulation-augmented multi-step split conformal prediction method (SA-MSCP), which generates future trajectories via block bootstrap resampling from cross-validated residuals and constructs calibrated prediction intervals using empirical quantiles. By innovatively integrating a simulation-augmentation mechanism into the multi-step split conformal prediction framework, the method significantly improves empirical coverage for both aggregate totals and their growth rates, yielding more reliable uncertainty estimates without compromising predictive accuracy.

This work proposes a unified mathematical framework grounded in dynamic information flow for constructing structurally rigorous models of future prediction. By integrating filtering theory, regular conditional probabilities, Markov semigroups, infinitesimal generators, and multiple information geometries—including Hilbert, Fisher–Rao, and Wasserstein—the approach conceptualizes prediction as the construction of conditional distributions governed by informational, geometric, and modeling constraints. The framework elucidates deep connections among classical results such as the tower property and semigroup laws, as well as Itô’s formula and backward equations. Explicit transition laws, spectral decompositions, term structures, and asymptotic behaviors are derived within canonical models like Ornstein–Uhlenbeck and Cox–Ingersoll–Ross, thereby establishing a compact mathematical mapping from idealized theoretical constructs to empirical forecasting.