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Supercritical CO₂ (SC–CO₂) fracturing is a potential technology that creates a complex fracturing fracture network to improve reservoir permeability. SC–CO₂-driven intersections of the fracturing fracture network are influenced by some key factors, including the disturbances generated form natural fractures, adjacent multi-wells and adjacent fractures, which increase the challenges in evaluation, control and optimization of the SC–CO₂ fracturing fracture networks. If the evaluation of the fracture network is not accurate and effective, the risk of oil and gas development will increase due to the microseismicity induced by multi-well SC–CO₂ fracturing, which makes it challenging to control the on-site engineering practices.

The numerical models considering the thermal-hydro-mechanical coupling effect in multi-well SC–CO₂ fracturing were established, and the typical cases considering naturally fracture and multi-wells were proposed to investigate the intersections and connections of fracturing fracture network, shear stress shadows and induced microseismic events. The quantitative results from the typical cases, such as fracture length, volume, fluid rate, pore pressure and the maximum and accumulated magnitudes of induced microseismic events, were derived.

In naturally fractured reservoirs, SC–CO₂ fracturing fractures will deflect and propagate along the natural fractures, eventually intersect and connect with fractures from other wells. The quantitative results indicate that SC–CO₂ fracturing in naturally fractured reservoirs produces larger fractures than the slick water as fracturing fluid, due to the ability of SC–CO₂ to connect macroscopic and microscopic fractures. Compared with slick water fracturing, SC–CO₂ fracturing can increase the length of fractures, but it will not increase microseismic events; therefore, SC–CO₂ fracturing can improve fracturing efficiency and increase productivity, but it may not simultaneously lead to additional microseismic events.

The results of this study on the multi-well SC–CO₂ fracturing may provide references for the fracturing design of deep oil and gas resource extraction, and provide some beneficial supports for the induced microseismic event disasters, promoting the next step of engineering application of multi-well SC–CO₂ fracturing.

Community detection is a key factor in analyzing the structural features of complex networks. However, traditional dynamic community detection methods often fail to effectively solve the problems of deep network information loss and computational complexity in hyperbolic space. To address this challenge, a hyperbolic space-based dynamic graph neural network community detection model (HSDCDM) is proposed.

HSDCDM first projects the node features into the hyperbolic space and then utilizes the hyperbolic graph convolution module on the Poincaré and Lorentz models to realize feature fusion and information transfer. In addition, the parallel optimized temporal memory module ensures fast and accurate capture of time domain information over extended periods. Finally, the community clustering module divides the community structure by combining the node characteristics of the space domain and the time domain. To evaluate the performance of HSDCDM, experiments are conducted on both artificial and real datasets.

Experimental results on complex networks demonstrate that HSDCDM significantly enhances the quality of community detection in hierarchical networks. It shows an average improvement of 7.29% in NMI and a 9.07% increase in ARI across datasets compared to traditional methods. For complex networks with non-Euclidean geometric structures, the HSDCDM model incorporating hyperbolic geometry can better handle the discontinuity of the metric space, provides a more compact embedding that preserves the data structure, and offers advantages over methods based on Euclidean geometry methods.

This model aggregates the potential information of nodes in space through manifold-preserving distribution mapping and hyperbolic graph topology modules. Moreover, it optimizes the Simple Recurrent Unit (SRU) on the hyperbolic space Lorentz model to effectively extract time series data in hyperbolic space, thereby enhancing computing efficiency by eliminating the reliance on tangent space.

As intelligent technology advances, practical applications often involve data with multiple labels. Therefore, multi-label feature selection methods have attracted much attention to extract valuable information. However, current methods tend to lack interpretability when evaluating the relationship between different types of variables without considering the potential causal relationship.

To address the above problems, we propose an ensemble causal feature selection method based on mutual information and group fusion strategy (CMIFS) for multi-label data. First, the causal relationship between labels and features is analyzed by local causal structure learning, respectively, to obtain a causal feature set. Second, we eliminate false positive features from the obtained feature set using mutual information to improve the feature subset reliability. Eventually, we employ a group fusion strategy to fuse the obtained feature subsets from multiple data sub-space to enhance the stability of the results.

Experimental comparisons are performed on six datasets to validate that our proposal can enhance the interpretation and robustness of the model compared with other methods in different metrics. Furthermore, the statistical analyses further validate the effectiveness of our approach.

The present study makes a noteworthy contribution to proposing a causal feature selection approach based on mutual information to obtain an approximate optimal feature subset for multi-label data. Additionally, our proposal adopts the group fusion strategy to guarantee the robustness of the obtained feature subset.