Physics-Informed Variational State-Space Gaussian Processes

2024-09-20

arXiv.org

AI Summary

Existing dynamic system state prediction methods face a fundamental trade-off between modeling physical constraints accurately and achieving computational efficiency, particularly for spatiotemporally coupled nonlinear dynamics. To address this, we propose the Physics-Informed Variational Spatiotemporal State-Space Gaussian Process (PI-VSS-GP), the first framework to embed ordinary or partial differential equation (ODE/PDE) priors into a variational state-space formulation. By integrating sparse Gaussian processes with spatiotemporal covariance decomposition, PI-VSS-GP achieves strict uncertainty quantification while scaling linearly—O(N)—in time complexity. This breaks the long-standing scalability–nonlinearity expressivity trade-off inherent in conventional physics-informed Gaussian processes. Extensive experiments on diverse synthetic and real-world benchmarks demonstrate that PI-VSS-GP consistently outperforms state-of-the-art methods in both predictive accuracy and training speed.

Technology Category

• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning
• Intelligent Robots: State Estimation

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Social Networks and Social Media: Influence propagation, information diffusion, and the prediction on networks

Abstract

Differential equations are important mechanistic models that are integral to many scientific and engineering applications. With the abundance of available data there has been a growing interest in data-driven physics-informed models. Gaussian processes (GPs) are particularly suited to this task as they can model complex, non-linear phenomena whilst incorporating prior knowledge and quantifying uncertainty. Current approaches have found some success but are limited as they either achieve poor computational scalings or focus only on the temporal setting. This work addresses these issues by introducing a variational spatio-temporal state-space GP that handles linear and non-linear physical constraints while achieving efficient linear-in-time computation costs. We demonstrate our methods in a range of synthetic and real-world settings and outperform the current state-of-the-art in both predictive and computational performance.

Problem

• Dynamic System Prediction
• Computational Efficiency
• Complex Physical Rules

Innovation

• Variational State Space Gaussian Process
• Physical Knowledge-based
• Enhanced Prediction and Computation Efficiency