Core Concepts
Incorporating domain-specific differential equations into graph convolutional networks can improve robustness to mismatched training and test data patterns compared to domain-agnostic deep learning models.
Abstract
The paper proposes a methodology to incorporate domain-specific differential equations into graph convolutional networks (GCNs) to improve their robustness to mismatched training and test data patterns.
Key highlights:
Existing deep learning models for spatiotemporal forecasting, such as graph neural networks, perform poorly when the test data exhibits different patterns compared to the training data. This challenge is known as domain generalization.
The authors hypothesize that incorporating domain-specific differential equations that capture the underlying dynamics can make the GCN models more robust to such domain mismatches.
The authors theoretically derive conditions where GCNs incorporating domain differential equations have lower generalization discrepancy compared to domain-agnostic models.
Two novel domain-informed GCN models are developed: Reaction-Diffusion Graph Convolutional Network (RDGCN) for traffic speed prediction, and Susceptible-Infectious-Recovered Graph Convolutional Network (SIRGCN) for infectious disease prediction.
Experimental results on real-world datasets demonstrate that the proposed domain-informed GCN models outperform state-of-the-art deep learning baselines in scenarios with mismatched training and test data.
Stats
The paper uses the following real-world datasets:
Metra-la: 207 vertices, 233 edges, 5-minute resolution, 122 days
Pems-bay: 281 vertices, 315 edges, 5-minute resolution, 151 days
Seattle-loop: 323 vertices, 660 edges, 5-minute resolution, 365 days
Japan-Prefectures: 47 vertices, 133 edges, weekly resolution, 347 weeks
US-States: 49 vertices, 152 edges, weekly resolution, 834 weeks
Quotes
"Ensuring both accuracy and robustness in time series prediction is critical to many applications, ranging from urban planning to pandemic management."
"When sufficient training data where all spatiotemporal patterns are well-represented, existing deep-learning models can make reasonably accurate predictions. However, existing methods fail when the training data are drawn from different circumstances (e.g., traffic patterns on regular days) compared to test data (e.g., traffic patterns after a natural disaster)."