Network Framework Research Articles

Trends in Global Agricultural Carbon Emission Research: A Bibliometric Analysis

As climate change intensifies and countries actively pursue carbon peaking and carbon neutrality targets, agriculture has emerged as a significant source of carbon emissions. A comprehensive analysis of global agricultural carbon emission research can enhance the agricultural environment and achieve a mutually beneficial outcome for environmental protection and economic development. Despite the evolution of research domains and methodologies, the global context remains closely connected to the current state of the discipline. Drawing on the Web of Science core collection, this paper develops a knowledge network framework, examines the current status and hotspots of agricultural carbon emissions, forecasts future development trends, and analyzes the findings using CiteSpace visualization software. The findings indicate that the number of papers on agricultural carbon emissions has been increasing annually, with minor fluctuations; time series analysis and sustainable development have emerged as the current focal points, and relevant institutions are collaborating increasingly closely. However, cooperation among scholars requires further enhancement. Countries such as China, the United States, and Germany are the primary nations for paper publication. The hotspot analysis reveals a high frequency of keywords such as greenhouse gas emissions and climate change, indicating that research on agricultural carbon emissions has matured and the emphasis has shifted from accounting to management. This paper develops a domain knowledge framework to assist readers in understanding agricultural carbon emission patterns and provide resources for further research. Follow-up studies should enhance both comprehensiveness and breadth, promote interdisciplinary cooperation, provide a scientific foundation for policymakers, and outline future research directions.

Automated estimation of offshore polymetallic nodule abundance based on seafloor imagery using deep learning

The burgeoning demand for critical metals used in high-tech and green technology industries has turned attention toward the vast resources of polymetallic nodules on the ocean floor. Traditional methods for estimating the abundance of these nodules, such as direct sampling or acoustic imagery are time and labour-intensive or often insufficient for large-scale or accurate assessment. This paper advocates for the automatization of polymetallic nodules detection and abundance estimation using deep learning algorithms applied to seabed photographs.We propose UNET convolutional neural network framework specifically trained to process the unique features of seabed imagery, which can reliably detect and estimate the abundance of polymetallic nodules based on thousands of seabed photographs in significantly reduced time (below 10 h for 30 thousand photographs). Our approach addresses the challenges of data preparation, variable image quality, coverage-abundance transition model and sediments presence.We indicated the utilization of this approach can substantially increase the efficiency and accuracy of resource estimation, dramatically reducing the time and cost currently required for manual assessment. Furthermore, we discuss the potential of this method to be integrated into large-scale systems for sustainable exploitation of these undersea resources.

Transformative Transparent Hybrid Deep Learning Framework for Accurate Cataract Detection

This paper presents a transformative explainable convolutional neural network (CNN) framework for cataract detection, utilizing a hybrid deep learning model combining Siamese networks with VGG16. By leveraging a learning rate scheduler and Grad-CAM (Gradient-weighted Class Activation Mapping) for explainability, the proposed model not only achieves high accuracy in identifying cataract-infected images but also provides interpretable visual explanations of its predictions. Performance evaluation metrics such as accuracy, precision, recall, and F1 score demonstrate the model’s robustness, with a perfect accuracy of 100%. Grad-CAM visualizations highlight the key image regions—primarily around the iris and pupil—that contribute most to the model’s decision-making, making the system more transparent for clinical use. Additionally, novel statistical analysis methods, including saliency map evaluation metrics like AUC (Area Under the Curve) and the Pointing Game, were employed to quantify the quality of the model’s explanations. These metrics enhance the interpretability of the model and support its practical applicability in medical image analysis. This approach advances the integration of deep learning with explainable AI, offering a robust, accurate, and interpretable solution for cataract detection with the potential for broader adoption in ocular disease diagnosis and medical decision support systems.

Rapid Prediction and Parameter Evaluation of Process-Induced Deformation in L-Shape Structures Based on Feature Selection and Artificial Neural Networks

The process-induced deformation (PID) during the manufacturing of thermosetting composite materials can significantly compromise manufacturing precision. This paper introduces an innovative method that combines a finite element analysis (FEA), feature classification algorithms, and an Artificial Neural Network (ANN) framework to rapidly predict the PID of a typical L-shaped structure. Initially, a comprehensive range of parameters that influence PID are compiled in this research, followed by the generation of a dataset through FEA considering viscoelastic constitutive models, validated by experimental results. Influential parameters are classified using Random Forest and LASSO regression methods, with each parameter rated according to its impact on PID, delineating their varying degrees of importance. Subsequently, through a hyperparameter analysis, an ANN framework is developed to rapidly predict the PID, while also refining the assessment of the parameters’ significance. This innovative approach achieves a computational time reduction of 98% with less than a 5% loss in accuracy, and highlights that under limited computational conditions, considering only a subset or all of the parameters—the peak temperature, corner angle, coefficient of chemical shrinkage, coefficient of thermal expansion, curing pressure, and E1—minimizes accuracy loss. The study demonstrates that machine learning algorithms can effectively address the challenge of predicting composite material PID, providing valuable insights for practical manufacturing applications.

OPTIMIZING AUTHENTICATION SECURITY IN INTELLIGENT SYSTEMS THROUGH VISUAL BIOMETRICS FOR ENHANCED EFFICIENCY

Context. The primary objective of this article is to explore aspects related to ensuring security and enhancing the efficiency of authentication processes in intelligent systems through the application of visual biometrics. The focus is on advancing and refining authentication systems by employing sophisticated biometric identification methods. Objective. A specialized intelligent system has been developed, utilizing a Siamese neural network to establish secure user authentication within the existing system. Beyond incorporating fundamental security measures such as hashing and secure storage of user credentials, the contemporary significance of implementing two-factor authentication is underscored. This approach significantly fortifies user data protection, thwarting most contemporary hacking methods and safeguarding against data breaches. The study acknowledges certain limitations in its approach, possibly affecting the generalizability of the findings. These limitations provide avenues for future research and exploration, contributing to the ongoing evolution of authentication methodologies in intelligent systems. Method. The two-factor authentication system integrates facial recognition technology, employing visual biometrics for heightened security compared to alternative two-factor authentication methods. Various implementations of the Siamese neural network, utilizing Contrastive loss function and Triplet loss function, were evaluated. Subsequently, a neural network employing the Triplet loss function was implemented and trained. Results. The article emphasizes the practical implications of the developed intelligent system, showcasing its effectiveness in minimizing the risk of unauthorized access to user accounts. The integration of contemporary authentication methodologies ensures a secure and robust user authentication process. Conclusions. The implementation of facial recognition technology in authentication processes has broader social implications. It contributes to a more secure digital environment by preventing unauthorized access, ultimately safeguarding user privacy and data. The study’s originality lies in its innovative approach to authentication, utilizing visual biometrics within a Siamese neural network framework. The developed intelligent system represents a valuable contribution to the field, offering an effective and contemporary solution to user authentication challenges.

EEG Data Augmentation Method for Identity Recognition Based on Spatial–Temporal Generating Adversarial Network

Traditional identity recognition methods are facing significant security challenges due to their vulnerability to leakage and forgery. Brainprint recognition, a novel biometric identification technology leveraging EEG signals, has emerged as a promising alternative owing to its advantages such as resistance to coercion, non-forgeability, and revocability. Nevertheless, the scarcity of high-quality electroencephalogram (EEG) data limits the performance of brainprint recognition systems, necessitating the use of shallow models that may not perform optimally in real-world scenarios. Data augmentation has been demonstrated as an effective solution to address this issue. However, EEG data encompass diverse features, including temporal, frequency, and spatial components, posing a crucial challenge in preserving these features during augmentation. This paper proposes an end-to-end EEG data augmentation method based on a spatial–temporal generative adversarial network (STGAN) framework. Within the discriminator, a temporal feature encoder and a spatial feature encoder were parallelly devised. These encoders effectively captured global dependencies across channels and time of EEG data, respectively, leveraging a self-attention mechanism. This approach enhances the data generation capabilities of the GAN, thereby improving the quality and diversity of the augmented EEG data. The identity recognition experiments were conducted on the BCI-IV2A dataset, and Fréchet inception distance (FID) was employed to evaluate data quality. The proposed method was validated across three deep learning models: EEGNET, ShallowConvNet, and DeepConvNet. Experimental results indicated that data generated by STGAN outperform DCGAN and RGAN in terms of data quality, and the identity recognition accuracies on the three networks were improved by 2.49%, 2.59% and 1.14%, respectively.

Accident causation analysis of waterway dangerous goods transport: An approach based on improved ISM and graph theory

This study presents a new method for exploring the causal mechanisms of waterway dangerous goods transport accidents. The proposed approach combines an improved Interpretive Structural Modeling (ISM) and graph theory to construct and analyze causal networks. This method has been refined to address challenges such as reliance on expert judgment in evaluating variable relationships and increased computational complexity as the number of variables grows. Firstly, an event representation model is established to discretize the accident into distinct events. Then, internal attribute influence mechanisms are defined within a network framework to identify event-attribute relationships. The reachability matrix of attribute relationships is calculated using the ISM process. Subsequently, a multi-layer causal network is constructed by integrating tiered results and graph theory, followed by topological and robustness analyses to clarify the causal mechanisms of internal attributes. Finally, the method is validated through a public accident case from the China Maritime Safety Administration, and the analysis results were corroborated with the accident investigation findings, providing comprehensive and in-depth theoretical explanation and support for the investigation outcomes.

A combined deep learning framework for mammalian m6A site prediction.

N6-methyladenosine (m6A) is the most prevalent chemical modification in eukaryotic mRNAs and plays key roles in diverse cellular processes. Precise localization of m6A sites is thus critical for characterizing the functional roles of m6A in various conditions and dissecting the mechanisms governing its deposition. Here, we design a combined framework of Transformer architecture and recurrent neural network, deepSRAMP, to identify m6A sites using sequence-based and genome-derived features. As a result, deepSRAMP achieves a notably enhanced performance compared to its predecessor, SRAMP, the most-used predictor in this field. Moreover, based on multiple benchmark datasets, deepSRAMP greatly outperforms other state-of-the-art m6A predictors, including WHISTLE and DeepPromise, with an average 16.1% and 18.3% increase in AUROC and a 43.9% and 46.4% increase in AUPRC. Finally, deepSRAMP can be successfully exploited on mammalian m6A epitranscriptome mapping under diverse cellular conditions and can potentially reveal differential m6A sites among transcript isoforms of individual genes.

Extracting fiber paths from the optimized lamination parameters of variable-stiffness laminated shells based on physic-informed neural network

This paper presents a novel approach for extracting fiber paths from the optimized lamination parameters (LPs) of variable stiffness laminated shells, utilizing the framework of physics-informed neural network (PINN). In this methodology, each fiber layer is associated with a specific stream function, which is approximated by an independent neural network. The stream function is governed by a partial differential equation (PDE) derived from the fiber orientation field in the parameter space. Moreover, the isocontours of the stream function are transformed into the actual fiber paths in the physical space. To account for manufacturing constraints, Riemannian geometry serves as a computational tool to determine the intrinsic distance between adjacent fiber paths and the geodesic curvature of the isocontours. By incorporating regularization terms into the loss function based on the physical relationships, the constrained optimization problem is converted into an unconstrained one, making it more suitable for neural network training. Meanwhile, a fiber path extraction (FPE) algorithm is used to minimize the loss function at randomly sampled points through gradient descent. The numerical results suggest that the extraction of fiber paths using PINN can achieve satisfactory levels of accuracy while effectively satisfying the imposed constraints.

A Data Augmentation Method and the Embedding Mechanism for Detection of Pulmonary Nodules on Small Samples

Abstract Lung Computed Tomography (CT) screening for pulmonary nodules provides an effective method for early diagnosis. The deep-learning-based computer-aided detection (CAD) system effectively identifies and precisely localizes suspicious pulmonary nodules in CT images, thereby significantly enhancing the accuracy and efficiency of CT diagnosis. In the medical field, the availability of medical data is limited, and research using small samples is of practical significance. By studying the data augmentation technology based on the generative model under the condition of small samples, and refining the model structure through the embedding mechanism, the accuracy and robustness of the deep learning model are explored. A 3D pixel-level statistical algorithm is proposed for the generation of pulmonary nodules. By combining simulated pulmonary nodules with healthy lung tissue, we can generate new samples of pulmonary nodules. The embedding mechanism is designed to enhance the comprehension of pixel meanings in pulmonary nodule samples by introducing latent variables. The results of the 3DVNET model with the augmentation method for pulmonary nodule detection under small sample conditions demonstrate that the proposed data augmentation method outperforms the method based on a generative adversarial network (GAN) framework, and the embedding mechanism for pulmonary nodules detection shows a significant improvement in accuracy. Conclusion: the proposed data augmentation method and embedding mechanism demonstrate significant potential in enhancing the accuracy and robustness of the model, thereby facilitating their application to various common imaging diagnostic tasks, and research using small samples is of practical significance.

A deep learning framework for solving the prediction and reconstruction problem of Bingham fluid flow field

As a typical non-Newtonian fluid, Bingham fluid is employed in a multitude of fields, including petroleum, construction, and the chemical industry. However, due to the intricate intrinsic properties of Bingham fluids and the necessity for precision and efficacy in specific engineering applications, the rapid and precise prediction and reconstruction of its flow field information has become a challenge and a focal point of contemporary research. In this paper, we introduce a novel deep-learning approach to address the two-dimensional laminar motion of Bingham fluids. The proposed Papanastasiou Regularization Physics-Informed Neural Network (PR-PINN) framework effectively predicts and reconstructs the flow field of Bingham fluids. Initially, the framework applies Papanastasiou regularization to the governing equations of Bingham fluids, enhancing the network's adaptability to solving the flow field problem by incorporating boundary conditions and an adaptive weight assignment strategy. We consider two scenarios: equal-diameter circular pipe flow and conical pipe flow. The PR-PINN network is utilized for flow field prediction and reconstruction. Our results show that PR-PINN achieves high accuracy in flow field prediction and can reconstruct velocity and pressure fields using limited measurement data. Based on these findings, we explore the impact of boundary constraints, the effect of large intrinsic parameters on prediction accuracy, and the influence of measurement points and boundary constraints on flow field reconstruction. In summary, the PR-PINN network exhibits satisfactory performance and significant potential for predicting and reconstructing Bingham fluid flow fields.

SpaInGNN: Enhanced clustering and integration of spatial transcriptomics based on refined graph neural networks

Recent developments in spatial transcriptomics (ST) technology have markedly enhanced the proposed capacity to comprehensively characterize gene expression patterns within tissue microenvironments while crucially preserving spatial context. However, the identification of spatial domains at the single-cell level remains a significant challenge in elucidating biological processes. To address this, SpaInGNN was developed, a sophisticated graph neural network (GNN) framework that accurately delineates spatial domains by integrating spatial location data, histological information, and gene expression profiles into low-dimensional latent embeddings. Additionally, to fully leverage spatial coordinate data, spatial integration using graph neural network (SpaInGNN) refines the graph constructed for spatial locations by incorporating both tissue image distance and Euclidean distance, following a pre-clustering of gene expression profiles. This refined graph is then embedded using a self-supervised GNN, which minimizes self-reconfiguration loss. By applying SpaInGNN to refined graphs across multiple consecutive tissue slices, this study mitigates the impact of batch effects in data analysis. The proposed method demonstrates substantial improvements in the accuracy of spatial domain recognition, providing a more faithful representation of the tissue organization in both mouse olfactory bulb and human lateral prefrontal cortex samples

Deep Learning for Fast and Reliable Initial Access in AI-Driven 6G mmWave Networks

We present DeepIA, a deep neural network (DNN) framework for fast and reliable initial access (IA) for artificial intelligence (AI)-driven 6G millimeter wave (mmWave) networks. DeepIA reduces the beam sweep time compared to a conventional exhaustive search-based IA process by utilizing only a subset of the available beams. DeepIA maps received signal strengths (RSSs) obtained from a subset of beams to the beam that is best oriented to the receiver. In both line of sight (LoS) and non-line of sight (NLoS) conditions, DeepIA reduces the IA time and outperforms the conventional IA&#x0027;s beam prediction accuracy. We show that DeepIA&#x0027;s accuracy saturates with the number of beams used, and also depends on the particular choice of the beams used. The choice of beams that are selected is consequential and improves accuracy by upto upto <inline-formula><tex-math notation="LaTeX">$35\%$</tex-math></inline-formula> and <inline-formula><tex-math notation="LaTeX">$70\%$</tex-math></inline-formula> in NLoS and LoS channels. We find that, averaging multiple RSS snapshots further reduces the number of beams needed and achieves more than <inline-formula><tex-math notation="LaTeX">$95\%$</tex-math></inline-formula> accuracy in both LoS and NLoS conditions. We introduce interference into our models to understand impact on performance. Finally, we evaluate the beam prediction time of DeepIA through embedded hardware implementation and show the improvement over the baseline approach.

A StarGAN and transformer-based hybrid classification-regression model for multi-institution VMAT patient-specific quality assurance.

The field of artificial intelligence (AI)-based patient-specific quality assurance (PSQA) for volumetric modulated arc therapy (VMAT) faces challenges in terms of developing general models across institutions due to the prevalence of multi-institution data collection and multivariate heterogeneity. Building a general model that is capable of handling diverse multi-institution data is critical for enabling large-scale integration and analysis. This study aims to develop a star generative adversarial network (StarGAN) and transformer-based hybrid classification-regression PSQA framework to address unification of heterogeneous data from different institutions. A StarGAN and transformer-based hybrid classification-regression model was developed as a general PSQA framework to predict gamma passing rates (GPRs) and classify quality assurance (QA) results as "Pass" or "Fail" at multiple institutions. A total of 1815 VMAT plans were collected from eight institutions to develop the general PSQA framework and perform clinical commissioning and implementation. Among them, 20 independent clinical plans from each of eight institutions, for a total of 160 plans, were used for the clinical commissioning, and 205 new clinical plans from eight institutions were used for clinical implementation. For the 3%/3, 3%/2, and 2%/2mm gamma criteria, the sensitivity of the proposed PSQA framework with pretraining was 90.13%, 92.03%, and 95.84%, respectively, while the specificity was 76.01%, 76.12%, and 85.34%, respectively. The mean absolute errors (MAEs) of the proposed PSQA framework with pretraining were 1.36%, 2.37%, and 3.96%, respectively, while the root-mean-square errors (RMSEs) were 2.31%, 3.89%, and 5.17%, respectively. The results demonstrated visible improvement at multiple institutions. For clinical commissioning, the deviations between the predicted and measured results were all within 3% for 3%/3 and 3%/2mm at eight institutions. For clinical implementation, all failure plans were correctly identified by the proposed PSQA framework. The general PSQA framework enables diverse clinical data sources to be handled to achieve enhanced model performance and generalizability, and provides a solution to the unification of heterogeneous data from different institutions to construct robust QA models. This approach can be clinically deployed for VMAT QA.

Physics-informed neural networks for weakly compressible flows using Galerkin–Boltzmann formulation

In this work, we study the Galerkin–Boltzmann formulation within a physics-informed neural network (PINN) framework to solve flow problems in weakly compressible regimes. The Galerkin–Boltzmann equations are discretized with second-order Hermite polynomials in microscopic velocity space, which leads to a first-order conservation law with six equations. Reducing the output dimension makes this equation system particularly well suited for PINNs compared with the widely used D2Q9 lattice Boltzmann velocity space discretizations. We created two distinct neural networks to overcome the scale disparity between the equilibrium and non-equilibrium states in collision terms of the equations. We test the accuracy and performance of the formulation with benchmark problems and solutions for forward and inverse problems with limited data. We compared our approach with the incompressible Navier–Stokes equation and the D2Q9 formulation. We show that the Galerkin–Boltzmann formulation results in similar L2 errors in velocity predictions in a comparable training time with the Navier–Stokes equation and lower training time than the D2Q9 formulation. We also solve forward and inverse problems for a flow over a square, try to capture an accurate boundary layer, and infer the relaxation time parameter using available data from a high-fidelity solver. Our findings show the potential of utilizing the Galerkin–Boltzmann formulation in PINN for weakly compressible flow problems.

Nonlinear Optimal Control Based on FBDEs and its Application to AGV.

This article focuses on solving a finite-horizon nonlinear optimal control problem by using the Pontryagin's maximum principle. In practical applications, linearization is a common approach for solving nonlinear dynamical systems. However, it is not universally applicable due to various reasons, such as instability and low accuracy. In contrast to linearization, the inherent challenge in directly solving the above nonlinear optimal control problem lies in addressing the highly coupled nonlinear forward and backward differential equations. In order to address this problem, an equivalent relationship is established between these equations and a new optimization problem. By exploiting the inherent relationship between supervised learning and an optimization problem from the view of a dynamical system, a deep neural network framework is constructed for describing the new optimization problem. Furthermore, a numerical algorithm for optimal control, which is very powerful for a large variety of nonlinear dynamical systems, is implemented by training a deep residual network. Finally, the effectiveness of the algorithm is demonstrated by solving a trajectory tracking control problem for automatic guided vehicle. The obtained results reveal that the proposed control scheme can achieve high-precision tracking.

Street tree segmentation method combining image semantic segmentation and point cloud clustering

Abstract As a common object in the park scene, the 3D information of street trees is crucial for digital cities, and extracting individual trees from point cloud data accurately and efficiently is a hotspot and a difficult point-in-point cloud processing. Aiming at the interference problem of complex non-tree objects and dynamic objects in the park environment, a tree point cloud segmentation method combining a deep learning network framework with a point cloud clustering algorithm is proposed in this paper. First, this paper applies the YOLOv8 to the semantic segmentation of camera images, and fuses image semantics with point cloud data, to build the semantic point cloud model. Then, preliminary extraction for street trees is performed using the semantic information of this point cloud model, and radius filtering is used to reduce the outliers. Finally, the individual tree segmentation is realized using an enhanced multi-level Euclidean clustering algorithm based on KD-Tree. Experimental results indicate that the proposed method performs well in extracting and segmenting the roadway trees, with a recall of 94.5%, a precision of 80.7%, and an F1-score of 87.0%.

Physics-informed spatio-temporal hybrid neural networks for predicting remaining useful life in aircraft engine

Aircraft engines have complex structures and various operating conditions, which leads to the health monitoring data of aircraft engines’ high coupling in the spatial domain and time invariance in the temporal domain. Existing methods for remaining useful life prediction of aircraft engines are deficient in handling spatial data and spatial–temporal data fusion. To address this problem, a novel method named physics-informed spatio-temporal hybrid neural networks (PI-STHNN) is proposed. In this study, a spatial domain data association graph for aircraft engines is constructed by utilizing a thermal cycle physical model as prior knowledge and combining it with the grey relational grade analysis method. Specifically, the proposed spatio-temporal hybrid neural network framework extracts the temporal features and spatial coupling features of the data in parallel. Then attention mechanism is employed to weigh and fuse all feature representations. Finally, the method is validated on the two aircraft engine datasets, the results show that PI-STHNN outperforms current state-of-the-art methods. Furthermore, our analysis sheds light on the advantages of incorporating physical information into graph neural network models and visually presents the attention weights to elucidate the contributions of time-domain and spatial-domain models within our hybrid approach.

Modeling and managing resilience and risk for interdependent networks

Catastrophic events have the potential to cause major disruptions to interdependent networks such as supply chains, critical infrastructures and other networks that are vital for the functioning of our society. Addressing the resilience and risk of compromised networks is challenging due to a variety of factors. First, these networks are becoming increasingly interdependent, such that network recovery is contingent upon recovery in connected networks. Additionally, interdependent networks may have multiple functions, system users, owners, and stakeholders. There is a need for data-informed decision-making models that address resilience and risk for these interdependent infrastructure networks. We address these issues by: 1) Modeling interdependencies among infrastructure networks using a multi-layer interdependent network framework, 2) Quantifying the relationship between network resilience and the inter-network connection structure, and 3) Supporting management and strategic decision-making for investment in inter-network connection structures, supporting risk mitigation needs and strategies. Our paper combines network optimization and network science methods to produce a unified framework to analyze resilience. We apply the methods of this paper to the interdependent infrastructure network of Puerto Rico following the 2017 Hurricane Maria. This paper supports decision-making for data-informed resilience management for interdependent infrastructure networks.

Physics-informed line graph neural network for power flow calculation.

Power flow calculation plays a significant role in the operation and planning of modern power systems. Traditional numerical calculation methods have good interpretability but high time complexity. They are unable to cope with increasing amounts of data in power systems; therefore, many machine learning based methods have been proposed for more efficient power flow calculation. Despite the good performance of these methods in terms of computation speed, they often overlook the importance of transmission lines and do not fully consider the physical mechanisms in the power systems, thereby weakening the prediction accuracy of power flow. Given the importance of the transmission lines as well as to comprehensively consider their mutual influence, we shift our focus from bus adjacency relationships to transmission line adjacency relationships and propose a physics-informed line graph neural network framework. This framework propagates information between buses and transmission lines by introducing the concepts of the incidence matrix and the line graph matrix. Based on the mechanics of the power flow equations, we further design a loss function by integrating physical information to ensure that the output results of the model satisfy the laws of physics and have better interpretability. Experimental results on different power grid datasets and different scenarios demonstrate the accuracy of our proposed model.