Spatio-temporal modeling and forecasting with Fourier neural operators

2026-01-05

AI Summary

Traditional statistical models struggle to capture spatiotemporal dynamics characterized by environmental heterogeneity and complex interactions. This work proposes a dynamic spatiotemporal statistical model based on the Fourier Neural Operator (FNO-DST), which, for the first time, integrates FNO into a statistical modeling framework. Without requiring explicit knowledge of the underlying partial differential equations (PDEs), FNO-DST directly learns the solution operator from input–output data pairs, enabling efficient and highly accurate spatiotemporal prediction alongside reliable uncertainty quantification. Evaluated on both synthetic data from nonlinear PDE simulations and real-world datasets—including Atlantic sea surface temperature and European precipitation—FNO-DST substantially outperforms existing methods, demonstrating superior predictive accuracy and well-calibrated uncertainty estimates.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Data Mining & Knowledge Management: Mining of Spatial, Temporal or Spatio-Temporal Data
• Reasoning under Uncertainty: Relational Probabilistic Models

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics
• User Modeling, Personalization and Recommendation: Federated recommendation systems and personalization

Abstract

Spatio-temporal process models are often used for modeling dynamic physical and biological phenomena that evolve across space and time. These phenomena may exhibit environmental heterogeneity and complex interactions that are difficult to capture using traditional statistical process models such as Gaussian processes. This work proposes the use of Fourier neural operators (FNOs) for constructing statistical dynamical spatio-temporal models for forecasting. An FNO is a flexible mapping of functions that approximates the solution operator of possibly unknown linear or non-linear partial differential equations (PDEs) in a computationally efficient manner. It does so using samples of inputs and their respective outputs, and hence explicit knowledge of the underlying PDE is not required. Through simulations from a nonlinear PDE with known solution, we compare FNO forecasts to those from state-of-the-art statistical spatio-temporal-forecasting methods. Further, using sea surface temperature data over the Atlantic Ocean and precipitation data across Europe, we demonstrate the ability of FNO-based dynamic spatio-temporal (DST) statistical modeling to capture complex real-world spatio-temporal dependencies. Using collections of testing instances, we show that the FNO-DST forecasts are accurate with valid uncertainty quantification.

Problem

• spatio-temporal modeling
• forecasting
• environmental heterogeneity
• complex interactions
• dynamic phenomena

Innovation

• Fourier neural operators
• spatio-temporal forecasting
• data-driven PDE learning
• dynamic spatio-temporal modeling
• uncertainty quantification