Spatio-temporal probabilistic forecast using MMAF-guided learning

2026-03-16

AI Summary

This work addresses the challenge of simultaneously achieving calibration and capturing structural dependencies in probabilistic forecasting of spatiotemporal raster data. We propose a novel approach based on Gaussian-weighted random feedforward neural networks, integrated within an MMAF-guided learning framework. By incorporating the theory of Ornstein-Uhlenbeck processes into low-dimensional embedding design, our method explicitly models spatiotemporal dependencies and causal structures without requiring complex architectures. The resulting model enables well-calibrated multi-step probabilistic forecasts and demonstrates strong performance across multiple time scales on both synthetic and real-world datasets, matching or even surpassing state-of-the-art convolutional and diffusion-based models.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Relational Probabilistic Models
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

We employ stochastic feed-forward neural networks with Gaussian-distributed weights to determine a probabilistic forecast for spatio-temporal raster datasets. The networks are trained using MMAF-guided learning, a generalized Bayesian methodology in which the observed data are preprocessed using an embedding designed to produce a low-dimensional representation that captures their dependence and causal structure. The design of the embedding is theory-guided by the assumption that a spatio-temporal Ornstein-Uhlenbeck process with finite second-order moments generates the observed data. The trained networks, in inference mode, are then used to generate ensemble forecasts by applying different initial conditions at different horizons. Experiments conducted on both synthetic and real data demonstrate that our forecasts remain calibrated across multiple time horizons. Moreover, we show that on such data, simple feed-forward architectures can achieve performance comparable to, and in some cases better than, convolutional or diffusion deep learning architectures used in probabilistic forecasting tasks.

Problem

• spatio-temporal forecasting
• probabilistic forecast
• raster datasets
• forecast calibration
• ensemble forecasting

Innovation

• MMAF-guided learning
• stochastic feed-forward neural networks
• spatio-temporal probabilistic forecasting
• Ornstein-Uhlenbeck process
• ensemble forecasting