Graph Neural Controlled Differential Equation for Spatiotemporal Forecasting
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Current methods fail to effectively combine neural controlled differential equations (NCDE) for temporal and spatial processing in spatiotemporal graph data, limiting the accuracy of forecasting tasks such as traffic forecasting.
Innovation Solution
A spatiotemporal data processing apparatus and method that integrates a graph neural controlled differential equation (NCDE) framework, using preprocessing to generate continuous paths and combining graph convolution networks (GCN) with NCDE for both temporal and spatial processing, employing two NCDE modules with controlled differential equation functions to calculate hidden trajectories and forecast output layers.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If NCDE for temporal processing and GCN for spatial processing are used separately, then each processing task can be performed independently, but the accuracy of spatiotemporal graph data processing is limited
Solution Approach 1:
The patent merges NCDE for temporal processing with GCN for spatial processing into a unified spatiotemporal graph NCDE framework. The graph convolution operation is integrated as the controlled vector field in the NCDE, allowing simultaneous processing of both spatial and temporal dimensions through a single mathematical formulation rather than separate independent modules
Solution Approach 2:
The unified NCDE framework serves multiple functions: it performs both temporal evolution modeling and spatial graph convolution operations within a single mathematical structure. The controlled vector field can adaptively handle different types of operations (spatial mixing and temporal dynamics) based on the graph structure and input data, making the framework versatile for various spatiotemporal forecasting tasks
2Measurement precision
If a unified framework combining temporal and spatial NCDE is created, then forecasting accuracy is improved, but the computational complexity increases
Solution Approach 1:
The unified NCDE framework is segmented into distinct functional components: the graph convolution operation handles spatial relationships through the controlled vector field, while the NCDE integration handles temporal evolution. This segmentation allows each component to be optimized independently and facilitates efficient implementation through modular computation strategies
3Measurement precision
If continuous paths are generated for each node, then temporal processing accuracy is enhanced, but the preprocessing complexity increases
Solution Approach 1:
The system performs preliminary action by generating continuous paths for each node before the main NCDE processing. These continuous paths are pre-computed using the graph structure and historical data, transforming discrete time series into continuous trajectories that can be directly fed into the NCDE framework, thereby simplifying the subsequent temporal processing
Data Source
AI summary
There is provided a spatiotemporal data processing including a preprocessing unit that generates a continuous path for each node in time series data, and a main processing unit that combines a graph convolution network (GCN) with a neural controlled differential equation (NCDE) for the generated path to perform integration processing on temporal information and spatial information, and the main processing unit performs temporal processing and spatial processing on each node with two controlled differential equation (CDE) functions to calculate a last hidden vector and forecast an output layer.