Neural Dynamics on Complex Networks
Neural Dynamics on Complex Networks
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DOI：
10.1145/3394486.3403132
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发表时间：
2019-08
期刊：
影响因子：
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通讯作者：
Chengxi Zang;Fei Wang
中科院分区：
文献类型：
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作者：
Chengxi Zang;Fei Wang
学习复杂网络的连续时间动力学对于理解、预测和控制科学和工程中的复杂系统至关重要。然而，由于高维系统结构的组合复杂性、难以捉摸的连续时间非线性动力学及其结构动态依赖性，这项任务非常具有挑战性。为了应对这些挑战，我们建议结合常微分方程系统（ODE）和图神经网络（GNN），以数据驱动的方式学习复杂网络上的连续时间动态。我们通过 GNN 对微分方程系统进行建模。我们不是在前向过程中通过离散数量的神经层进行映射，而是在连续时间上对 GNN 层进行数字积分，从而捕获图上的连续时间动态。我们的模型可以解释为连续时间 GNN 模型或图神经 ODE 模型。我们的模型可用于统一框架中的连续时间网络动态预测、结构化序列预测（定期采样的情况）和节点半监督分类任务（单快照情况）。我们通过在上述三种场景中进行大量实验来验证我们的模型。有希望的实验结果证明了我们的模型能够在统一的框架中共同捕获复杂系统的结构和动态。
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.