Neural Dynamics on Complex Networks
arXiv:1908.06491 · doi:10.1145/3292500.3330842
Abstract
Learning continuous-time dynamics on complex networks is crucial for understanding, predicting and controlling complex systems in science and engineering. However, this task is very challenging due to the combinatorial complexities in the structures of high dimensional systems, their elusive continuous-time nonlinear dynamics, and their structural-dynamic dependencies. To address these challenges, we propose to combine Ordinary Differential Equation Systems (ODEs) and Graph Neural Networks (GNNs) to learn continuous-time dynamics on complex networks in a data-driven manner. We model differential equation systems by GNNs. Instead of mapping through a discrete number of neural layers in the forward process, we integrate GNN layers over continuous time numerically, leading to capturing continuous-time dynamics on graphs. Our model can be interpreted as a Continuous-time GNN model or a Graph Neural ODEs model. Our model can be utilized for continuous-time network dynamics prediction, structured sequence prediction (a regularly-sampled case), and node semi-supervised classification tasks (a one-snapshot case) in a unified framework. We validate our model by extensive experiments in the above three scenarios. The promising experimental results demonstrate our model's capability of jointly capturing the structure and dynamics of complex systems in a unified framework.
arXiv commentDepartment of Population Health Sciences, Weill Cornell Medicine, Cornell University; [email protected], [email protected]
References in corpus (17)
- Adam: A Method for Stochastic Optimization
- Emergence of scaling in random networks
- Power laws, Pareto distributions and Zipf's law
- The origin of bursts and heavy tails in human dynamics
- A Critical Review of Recurrent Neural Networks for Sequence Learning
- Simplifying Graph Convolutional Networks
- Control Principles of Complex Networks
- Deep Hidden Physics Models: Deep Learning of Nonlinear Partial Differential Equations
- Human Dynamics: The Correspondence Patterns of Darwin and Einstein
- On the Frequency of Severe Terrorist Events
- Data Driven Governing Equations Approximation Using Deep Neural Networks
- Attention-based Graph Neural Network for Semi-supervised Learning
- Beyond Finite Layer Neural Networks: Bridging Deep Architectures and Numerical Differential Equations
- Evolutionary forces in language change
- Unfolding large-scale online collaborative human dynamics
- Learning Deep Hidden Nonlinear Dynamics from Aggregate Data
- Neural Dynamics on Complex Networks