## 1 Introduction  
In the petroleum industry, porosity [1] is a critical parameter for reservoir evaluation, as it measures the void spaces within rocks and is often correlated with reservoir quality [2]. Traditional methods of porosity measurement, such as core sampling and rock physical analysis, are costly and time-consuming. Additionally, incomplete logging data, due to the economic and physical limitations of tools, as well as the complex nonlinear relationships between geological factors and logging parameters, pose significant challenges. Empirical equations often fail in different regions, prompting a shift towards nonlinear multivariate regression and models incorporating geological and mechanical properties [3]. However, the heterogeneous variations and nonlinear correlations of subsurface structures often result in unsatisfactory predictions. Machine learning algorithms have become an essential tool for predicting reservoir parameters, effectively addressing the nonlinear challenges faced by traditional methods [4]. These approaches enhance the accuracy and efficiency of porosity prediction by integrating logging data with geological information and optimizing exploration and development strategies in the petroleum industry. Distinguished from conventional techniques [5] that depend on expert analysis of log data, machine learning, notably deep learning, autonomously extracts features from data, adjusts to a range of geological settings, and demonstrates enhanced adaptability [6]. Among the widely recognized deep learning approaches are convolutional neural networks (CNNs) [7; 8], recurrent neural networks (RNNs) [9; 10], long short-term memory (LSTM) networks [11], and gated recurrent units (GRUs) [12] and their variants [13; 14; 15]. For example, [PERSON] et al. [16] innovatively developed a multi-layer LSTM (MLSTM) method based on the traditional LSTM model for porosity prediction, which was tested on three wells in southern China. The results showed that MLSTM method exhibited superior robustness and accuracy in deep sequence prediction compared to GRUs and RNNs. Different network models exhibit unique effectiveness when processing various types of data. RNNs and LSTM have the capability to retain previous information. At the same time, CNNs can automatically extract features that help capture relationships between variables, thereby enhancing predictive performance. However, a single model is typically only able to capture specific types of features, such as sequential or spatial characteristics. Research has shown that uncovering the correlations between deep sequences and features in logging curves can improve the accuracy of predictions [17]. Although CNNs excel at processing images and data with strong spatial correlations, they fall short in capturing the potential spatial correlations between different logging curves [18]. Graph neural networks (GNNs), on the other hand, can effectively handle non-Euclidean data by uncovering hidden spatial dependencies through local connectivity and permutation invariance [19]. GNNs have been thoroughly validated for capturing sequence and feature correlations, yet their primary applications are still concentrated in specific domains such as traffic flow and offshore wind speed prediction [20; 21; 22; 23; 24]. To reveal correlations within logging data, an increasing number of studies are employing undirected graphs, where the graph vertices represent data vectors and the edges represent the similarities or affinities of logging data. Graph convolutional networks (GCNs) excel at handling undirected graphs by incorporating their underlying topological structure [25]. GCNs estimate porosity through the use of multiple sequential spectral graph convolutions. In each stage, the model carries out a dual process: initially, it consolidates analogous data points according to an established graph topology, followed by a transformation that elevates the data into an expanded dimensional realm, thereby enriching the feature set.