In recent years, Neural Differential Equations (NDEs) [1, 2] have emerged as a powerful bridge between dynamical systems and deep learning, finding applications in both supervised learning and generative modeling. In graph representation learning, controlled differential equations (CDEs) have been leveraged to simultaneously capture the evolution of node features and graph topology [3, 4], with promising applications such as traffic forecasting [4]. Building on our recent work where we successfully integrated permutation equivariance into Graph Neural CDEs for undirected, homogeneous graphs, this thesis aims to extend the framework to additional graph modalities—specifically, directed and heterogeneous graphs. Such an extension is expected to address real-world challenges in fields like clinical sciences or climate modeling, where interactions are inherently directional and multimodal.
[1] P Kidger. On neural differential equations. PhD thesis, University of Oxford, 2021.
[2] R. T. Q. Chen et al. Neural ordinary differential equations. Advances in Neural Information Processing Systems, 2018
[3] T. Qin and B. Walker et al. Learning dynamic graph embeddings with neural controlled differential equations. Preprint, 2023
[4] J. Choi et al. Graph Neural Controlled Differential Equations for Traffic Forecasting. AAAI, 2022