Graph Neural Network （GNN） is increasingly applied to complex fluid system predictions due to the superior capability in handling structured grids and strong combinatorial generalization. However， from a Lagrangian mesh-free perspective， GNN has unpredictable output variations when processing fluid particle information subjected to translation， rotation， or reflection transformations. To address this problem， an Equivariant Graph Neural Network-based Simulator （EGNS） method was proposed. Geometric vectors were first converted into relative equivariants. Then， equivariant message passing was employed at each step to ensure equivariance of entire neural network， maintaining consistency of spatial transformations between output and input equivariants. Finally， the optimized EGNS model was obtained by training in particle trajectories simulated with the Smoothed Particle Hydrodynamics （SPH） method. Experimental results on public fluid simulation datasets demonstrate that EGNS has superior predictive performance compared with Graph Neural Network-based Simulator （GNS）； specifically， EGNS achieves better accuracy in predicting fluid particle movement， velocity， and typical details， decreasing Mean Squared Error （MSE） in predicting particle positions by about 16%.

To obtain more accurate molecular toxicity prediction results， a molecular toxicity prediction model based on meta Graph Isomorphism Network （GIN） was proposed， namely Meta-MTP. Firstly， graph isomorphism neural network was used to obtain molecular characterization by using atoms as nodes， bonds as edges， and molecules as graph structures. The pre-trained model was used to initialize the GIN to obtain better parameters. A feedforward Transformer incorporating layer-wise attention and local enhancement was introduced. Atom type prediction and bond prediction were used as auxiliary tasks to extract more internal molecular information. The model was trained through a meta learning dual-level optimization strategy. Finally， the model was trained using Tox21 and SIDER datasets. Experimental results on Tox21 and SIDER datasets show that Meta-MTP has good molecular toxicity prediction ability. When the number of samples is 10， compared to FSGNNTR （Few-Shot Graph Neural Network-TRansformer） model in all tasks， the Area Under the ROC Curve （AUC） of Meta-MTP is improved by 1.4% and 5.4% respectively. Compared to three traditional graph neural network models， Graph Isomorphism Network （GIN）， Graph Convolutional Network （GCN）， and Graph Sample and AGgrEgate （GraphSAGE）， the AUC of Meta-MTP improves by 18.3%-23.7% and 7.3%-22.2% respectively.

Air quality data， as a typical spatio-temporal data， exhibits complex multi-scale intrinsic characteristics and has abrupt change problem. Concerning the problem that existing air quality prediction methods perform poorly when dealing with air quality prediction tasks containing large amount of abrupt change， a Multi-Granularity abrupt Change Fitting Network （MACFN） for air quality prediction was proposed. Firstly， multi-granularity feature extraction was first performed on the input data according to the periodicity of air quality data in time. Then， a graph convolution network and a temporal convolution network were used to extract the spatial correlation and temporal dependence of the air quality data， respectively. Finally， to reduce the prediction error， an abrupt change fitting network was designed to adaptively learn the abrupt change part of the data. The proposed network was experimentally evaluated on three real air quality datasets， and the Root Mean Square Error （RMSE） decreased by about 11.6%， 6.3%， and 2.2% respectively， when compared to the Multi-Scale Spatial Temporal Network （MSSTN）. The experimental results show that MACFN can efficiently capture complex spatio-temporal relationships and performs better in the task of predicting air quality that is prone to abrupt change with a large magnitude of variability.

Deep learning methods are widely used in bearing fault diagnosis， but in actual engineering applications， real service fault data during bearing service are not easily collected and lack of data labels， which is difficult to train adequately. Focused on the difficulty of bearing service fault diagnosis， a transfer learning model based on Graph Convolutional Network （GCN） in bearing service fault diagnosis was proposed. In the model， the fault knowledge was learned from artificially simulated damage fault data with sufficient data and transferred to real service faults， so as to improve the diagnostic accuracy of service faults. Specifically， the original vibration signals of artificially simulated damage fault data and service fault data were converted into the time-frequency maps with both time and frequency information through wavelet transform， and the obtained maps were input into graph convolutional layers for learning， so as to effectively extract the fault feature representations in the source and target domains. Then the Wasserstein distance between the data distributions of source domain and target domain was calculated to measure the difference between two data distributions， and a fault diagnosis model that can diagnose bearing service faults was constructed by minimizing the difference in data distribution. A variety of different tasks were designed for experiments with different bearing failure data sets and different operating conditions. Experimental results show that the proposed model has the ability to diagnose bearing service faults and also can be transferred from one working condition to another， and perform fault diagnosis between different component types and different working conditions.

The multi-hop transmission of multimedia emergency communication system based on Wireless Mesh Network (WMN) in underground mine have two problems: low basis bandwidth and high multi-hop transmission attenuation. This paper aimed to improve the multi-hop transmission performance for the system. In this paper, a trunk line network structure of multimedia emergency communication system based on WMN in under-ground mine was proposed. The authors established its transmission model, and then had a research on the main factors that affected the transmission performance. The multi-radio node structure of multi-hop mesh backbone network based on 802.11n was proposed and solved the two problems of multi-hop transmission. The experimental results show that it has more than 165Mbps basis bandwidth, and under the limited 60Mbps environment, the bandwidth attenuation of per hop is less than 1%, basically satisfying the application requirements of multimedia transmission in underground mine.