这篇论文把已知图结构嵌入神经微分方程里做时间序列预测，效果比没加图信息的NCDE更好。在河流流量和交通流数据上都有提升，对图和时序结合感兴趣可以看看。
INDEQS是一种基于图的神经控制微分方程时间序列预测方法，在架构中分别应用先验有向图信息于内混合（隐藏状态混合）和外混合（向量场与控制信号混合）。该方法提供轻量级图约束变体和支持自适应图卷积的学习变体。在合成的有向图连续平流模拟数据集以及真实世界的河流水位和PeMS08交通流预测任务上，INDEQS的外信息融合变体在参数量相近时，平均绝对误差持续低于未利用先验的NCDE。连续解码器相比离散卷积解码器在准确性和时间灵活性上更优。
INDEQS: Informed Neural controlled Differential EQuationS
Neural Controlled Differential Equations (NCDE) provide a powerful continuous-time framework for forecasting time series, but standard graph-based extensions typically learn spatial structure purely from data, even in settings where a directed graph structure is known a priori. We introduce Informed Neural controlled Differential EQuationS (INDEQS), a graph-based NCDE forecasting method that incorporates prior knowledge of a directed graph at distinct architectural positions. INDEQS separates inner mixing of hidden states across graph nodes from outer mixing between vector field and control, and offers both a lightweight graph-constrained variant and a more expressive variant, learning additional graph connections from data via adaptive graph convolutions. To systematically study when graph informedness is beneficial in forecasting, we devise a continuous advection simulation on directed graphs, yielding synthetic spatio-temporal datasets with known ground-truth flow structure. We then evaluate INDEQS on two real-world tasks: river discharge forecasting on a hydrological network and traffic flow prediction on PeMS08. Across these synthetic and real-world benchmarks, outer informedness consistently improves mean absolute error over an uninformed NCDE with comparable parameter count, particularly on larger graphs, while inner informedness offers a more parameter-efficient alternative when strict adherence to a known adjacency is desired. A comparison of discrete convolutional and continuous-time decoders further shows that continuous decoders yield better accuracy and greater temporal flexibility on real-world tasks. An implementation of INDEQS and the advection simulation is available at https://github.com/Mitchi1/indeqs.