## 5 Conclusions  
In this paper, a corrosion rate prediction framework based on adaptive MTGNN multi-feature spatio-temporal correlation analysis is proposed for the corrosion rate prediction of pipeline walls, and the actual monitoring data of drainage pipeline in a city is used as an example to explore the prediction performance of the model under multivariate input and different prediction steps. The following conclusions are obtained:  
1. By introducing strongly correlated features in the node embedding of the input layer, the prediction performance of the model is substantially improved compared with the single feature input and all feature input. Adaptive MTGNN captures the synergistic temporal patterns among multiple features in an end-to-end manner and is able to more accurately reflect the changing trends of time series. This result demonstrates the superior ability of adaptive MTGNN in modeling complex cross-variate information and effectively utilizing auxiliary features.
2. The deep learning model based on adaptive MTGNN to construct spatio-temporal graphs can extract the neighborhood aggregated spatio-temporal information and adaptively learn the internal graph structure through graph convolution and temporal convolution without the need for prior knowledge of edges. The experimental results show that the model increases the extraction of spatial features compared with the traditional time series prediction methods, which can achieve higher prediction accuracy and provide a reference for similar pipeline internal corrosion prediction problems.
3. In this study, a \"chunked progressive\" training strategy is used to decompose the multi-step prediction task into progressive sub-intervals, which enables the model to perform well in short-term prediction. However, there is still room for improvement in long-term prediction accuracy. Future research can introduce attention mechanisms or Transformer architectures to dynamically allocate importance to different time steps, alleviating error accumulation.
4. The fixed-size dilated convolution kernels used in this paper may lack flexibility when dealing with a large amount of non-stationary corrosion fluctuation data, making it difficult to adaptively adjust to match heterogeneous temporal features in complex environments. Future work will explore dynamic adjustable convolution kernel mechanisms, optimizing kernel size selection by integrating data-driven and physical prior knowledge, while combining lightweight strategies to reduce computational costs,  
Figure 12: Comparison of various metrics for different models.  
thereby enhancing the model's generalization ability to nonlinear spatio-temporal dynamics and engineering applicability.  
M.S.: Investigation, Writing--original draft, Methodology, Visualization. S.Q.: Writing--review and editing, Conceptualization. All authors have read and agreed to the published version of the manuscript.  
This research was supported by the \"Shanghai Science and Technology Innovation Action Plan for Social Development Technology Research and Development Projects (21 DZ1204202)\".  
Not applicable.  
The data used in this research are available from the corresponding author on reasonable request.  
The authors want to thank the editor and anonymous reviewers for their valuable suggestions for improving this paper.  
The authors declare no conflicts of interest.