Probabilistic Forecasting for Dynamical Systems with Missing or Imperfect Data

2025-03-15

AI Summary

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.

Technology Category

Reasoning under Uncertainty: Probabilistic ProgrammingMachine Learning: Calibration & Uncertainty QuantificationIntelligent Robots: State Estimation

Application Category

Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for rankingGraph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphsUser Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization

Abstract

The modeling of dynamical systems is essential in many fields, but applying machine learning techniques is often challenging due to incomplete or noisy data. This study introduces a variant of stochastic interpolation (SI) for probabilistic forecasting, estimating future states as distributions rather than single-point predictions. We explore its mathematical foundations and demonstrate its effectiveness on various dynamical systems, including the challenging WeatherBench dataset.

Problem

• Addresses forecasting in dynamical systems with incomplete data
• Introduces stochastic interpolation for probabilistic state estimation
• Validates method on complex datasets like WeatherBench

Innovation

• Stochastic interpolation for probabilistic forecasting
• Estimates future states as distributions
• Effective on noisy, incomplete dynamical systems