[2603.25370] A Distribution-to-Distribution Neural Probabilistic Forecasting Framework for Dynamical Systems

Statistics > Machine Learning arXiv:2603.25370 (stat) [Submitted on 26 Mar 2026] Title:A Distribution-to-Distribution Neural Probabilistic Forecasting Framework for Dynamical Systems Authors:Tianlin Yang, Hailiang Du, Louis Aslett View a PDF of the paper titled A Distribution-to-Distribution Neural Probabilistic Forecasting Framework for Dynamical Systems, by Tianlin Yang and 2 other authors View PDF HTML (experimental) Abstract:Probabilistic forecasting provides a principled framework for uncertainty quantification in dynamical systems by representing predictions as probability distributions rather than deterministic trajectories. However, existing forecasting approaches, whether physics-based or neural-network-based, remain fundamentally trajectory-oriented: predictive distributions are usually accessed through ensembles or sampling, rather than evolved directly as dynamical objects. A distribution-to-distribution (D2D) neural probabilistic forecasting framework is developed to operate directly on predictive distributions. The framework introduces a distributional encoding and decoding structure around a replaceable neural forecasting module, using kernel mean embeddings to represent input distributions and mixture density networks to parameterise output predictive distributions. This design enables recursive propagation of predictive uncertainty within a unified end-to-end neural architecture, with model training and evaluation carried out directly in terms of probabili...