Learning Spatiotemporal Dynamical Systems from Point Process Observations

2024-06-01

AI Summary

Existing neural network methods struggle to model the underlying continuous spatiotemporal dynamics of point process data arising from random, irregular spatiotemporal sampling in sensor networks (e.g., crowdsourced earthquake reports or pollution monitoring). Method: This paper introduces the first unified framework integrating Neural Ordinary Differential Equations (Neural ODEs), Neural Point Processes (NPPs), Implicit Neural Representations (INRs), and amortized variational inference to jointly learn both the continuous system dynamics and the generative mechanism of discrete, asynchronous observations. Contribution/Results: The proposed method achieves significant improvements in predictive accuracy and computational efficiency across multiple real-world spatiotemporal point process datasets. It offers inherent interpretability—by explicitly disentangling latent continuous dynamics from observation generation—and supports real-time deployment. By seamlessly handling sparse, irregular, and asynchronous sampling, it establishes a novel paradigm for modeling complex dynamic systems under challenging observational conditions.

Technology Category

• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Reasoning under Uncertainty: Relational Probabilistic Models
• Machine Learning: Time-Series/Data Streams

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Data management and stream processing for Web, mobile and wireless applications
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Spatiotemporal dynamics models are fundamental for various domains, from heat propagation in materials to oceanic and atmospheric flows. However, currently available neural network-based spatiotemporal modeling approaches fall short when faced with data that is collected randomly over time and space, as is often the case with sensor networks in real-world applications like crowdsourced earthquake detection or pollution monitoring. In response, we developed a new method that can effectively learn spatiotemporal dynamics from such point process observations. Our model integrates techniques from neural differential equations, neural point processes, implicit neural representations and amortized variational inference to model both the dynamics of the system and the probabilistic locations and timings of observations. It outperforms existing methods on challenging spatiotemporal datasets by offering substantial improvements in predictive accuracy and computational efficiency, making it a useful tool for modeling and understanding complex dynamical systems observed under realistic, unconstrained conditions.

Problem

• Learning spatiotemporal dynamics from random observations
• Improving predictive accuracy in complex systems
• Enhancing computational efficiency in real-world applications

Innovation

• Neural differential equations integration
• Neural point processes utilization
• Amortized variational inference application