The reconstruction of physical fields from sparse measurements is pivotal in both scientific research and engineering applications. Traditional methods are increasingly supplemented by deep learning models due to their efficacy in extracting features from data. However, except for the low accuracy on complex physical systems, these models often fail to comply with essential physical constraints, such as governing equations and boundary conditions. To overcome this limitation, we introduce a novel data-driven field reconstruction framework, termed the Physics-aligned Schr\"{o}dinger Bridge (PalSB). This framework leverages a diffusion bridge mechanism that is specifically tailored to align with physical constraints. The PalSB approach incorporates a dual-stage training process designed to address both local reconstruction mapping and global physical principles. Additionally, a boundary-aware sampling technique is implemented to ensure adherence to physical boundary conditions. We demonstrate the effectiveness of PalSB through its application to three complex nonlinear systems: cylinder flow from Particle Image Velocimetry experiments, two-dimensional turbulence, and a reaction-diffusion system. The results reveal that PalSB not only achieves higher accuracy but also exhibits enhanced compliance with physical constraints compared to existing methods. This highlights PalSB's capability to generate high-quality representations of intricate physical interactions, showcasing its potential for advancing field reconstruction techniques. The source code can be found at https://github.com/lzy12301/PalSB.

Recently the research of traffic flow prediction with deep learning framework has be largely developed, whereas most current methods are still faced with the following shortcomings. For spatial feature extraction, studies have shown that both local and non-local correlations exist on traffic networks. Considering the temporal dependencies, short-term impending and longer periodic components are two most critical patterns of traffic data, which further provide different information for the prediction task. Furthermore, multi-source heterogeneous external data, which naturally holds semantic gap with traffic data, also have impact on traffic flow. To solve the above problems, this paper proposes an AutoMSNet (Multi-Source Spatio-Temporal Network via Automatic neural architecture search). The AutoMSNet is composed of an encoder-decoder structure. The encoder takes neighboring data as inputs, while the decoder captures long-term periodic patterns. Thus, different functions of two temporal features are simultaneously extracted. Moreover, a neural architecture search space is designed for spatial feature extraction. Through architecture search technique, graph convolutions with different receptive fields are automatically selected and combined to form an optimal module structure. Therefore, both local and non-local spatial features can be adaptively captured. Besides, a meta learning feature fusion strategy is proposed to integrate external data, which can alleviate the semantic gap between different data sources. Extensive experiments on three real-world traffic datasets evaluate the superiority of the proposed model.

Predicting urban traffic flow is a challenging task, due to the complicated spatio-temporal dependencies on traffic networks. Urban traffic flow usually has both short-term neighboring and long-term periodic temporal dependencies. It is also noticed that the spatial correlations over different traffic nodes are both local and non-local. What’s more, the traffic flow is affected by various external factors. To capture the non-local spatial correlations, we propose a Dilated Attentional Graph Convolution (DAGC). The DAGC utilizes a dilated graph convolution kernel to expand the nodes’ receptive field and exploit multi-order neighborhood. Technically, the lower-order neighborhood corresponds to local spatial dependencies, while the higher-order neighborhood corresponds to non-local spatial dependencies between nodes. Based on DAGC, a Multi-Source Spatio-Temporal Network (MS-Net) is designed, which suffices to integrate long-range historical traffic data as well as multi-modal external information. MS-Net consists of four components: a spatial feature extraction module, a temporal feature fusion module, an external factors embedding module, and a multi-source data fusion module. Extensive experiments on three real traffic datasets demonstrates that the proposed model performs well on both the public transportation networks, road networks, and can handle large-scale traffic networks in particular the Beijing bus network which has more than 4,000 traffic nodes.

Traffic flow prediction is a challenging task while most existing works are faced with two main problems in extracting complicated intrinsic and extrinsic features. In terms of intrinsic features, current methods don't fully exploit different functions of short-term neighboring and long-term periodic temporal patterns. As for extrinsic features, recent works mainly employ hand-crafted fusion strategies to integrate external factors but remain generalization issues. To solve these problems, we propose a meta-learning based multi-source spatio-temporal network (Meta-MSNet). The Meta-MSNet is designed with an encoder-decoder structure. The encoder captures neighboring temporal dependencies while the decoder extracts periodic features. Furthermore, two meta-learning based fusion modules are designed to integrate multi-source external data both on temporal and spatial dimensions. Experiments on three real-world traffic datasets have verified the superiority of the proposed model.

Predicting traffic flow on traffic networks is a very challenging task, due to the complicated and dynamic spatial-temporal dependencies between different nodes on the network. The traffic flow renders two types of temporal dependencies, including short-term neighboring and long-term periodic dependencies. What's more, the spatial correlations over different nodes are both local and non-local. To capture the global dynamic spatial-temporal correlations, we propose a Global Spatial-Temporal Network (GSTNet), which consists of several layers of spatial-temporal blocks. Each block contains a multi-resolution temporal module and a global correlated spatial module in sequence, which can simultaneously extract the dynamic temporal dependencies and the global spatial correlations. Extensive experiments on the real world datasets verify the effectiveness and superiority of the proposed method on both the public transportation network and the road network.