Incorporating Domain Differential Equations into Graph Convolutional
  Networks to Lower Generalization Discrepancy
Yue Sun Chao Chen Yuesheng Xu Sihong Xie Rick S. Blum Parv Venkitasubramaniam
Ensuring both accuracy and robustness in time series prediction is critical
to many applications, ranging from urban planning to pandemic management. With
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). Such challenges
are usually classified under domain generalization. In this work, we show that
one way to address this challenge in the context of spatiotemporal prediction
is by incorporating domain differential equations into Graph Convolutional
Networks (GCNs). We theoretically derive conditions where GCNs incorporating
such domain differential equations are robust to mismatched training and
testing data compared to baseline domain agnostic models. To support our
theory, we propose two domain-differential-equation-informed networks called
Reaction-Diffusion Graph Convolutional Network (RDGCN), which incorporates
differential equations for traffic speed evolution, and
Susceptible-Infectious-Recovered Graph Convolutional Network (SIRGCN), which
incorporates a disease propagation model. Both RDGCN and SIRGCN are based on
reliable and interpretable domain differential equations that allow the models
to generalize to unseen patterns. We experimentally show that RDGCN and SIRGCN
are more robust with mismatched testing data than the state-of-the-art deep
learning methods.