Power Quality Disturbance Identification Basing on Adaptive Kalman Filter andMulti-Scale Channel Attention Fusion Convolutional Network

In light of the prevailing issue that the existing convolutional neural network(CNN)power quality disturbance identification method can only extract single-scale features,which leads to a lack of feature information and weak anti-noise performance,a new approach for identifying power quality disturbances based on an adaptive Kalman filter(KF)and multi-scale channel attention(MS-CAM)fused convolutional neural network is suggested.Single and composite-disruption signals are generated through simulation.The adaptive maximum likelihood Kalman filter is employed for noise reduction in the initial disturbance signal,and subsequent integration of multi-scale features into the conventional CNN architecture is conducted.The multi-scale features of the signal are captured by convolution kernels of different sizes so that the model can obtain diverse feature expressions.The attention mechanism(ATT)is introduced to adaptively allocate the extracted features,and the features are fused and selected to obtain the new main features.The Softmax classifier is employed for the classification of power quality disturbances.Finally,by comparing the recognition accuracy of the convolutional neural network(CNN),the model using the attention mechanism,the bidirectional long-term and short-term memory network(MS-Bi-LSTM),and the multi-scale convolutional neural network(MSCNN)with the attention mechanism with the proposed method.The simulation results demonstrate that the proposed method is higher than CNN,MS-Bi-LSTM,and MSCNN,and the overall recognition rate exceeds 99%,and the proposed method has significant classification accuracy and robust classification performance.This achievement provides a new perspective for further exploration in the field of power quality disturbance classification.

A Lightweight Convolutional Neural Network with Hierarchical Multi-Scale Feature Fusion for Image Classification

Convolutional neural networks (CNNs) are widely used in image classification tasks, but their increasing model size and computation make them challenging to implement on embedded systems with constrained hardware resources. To address this issue, the MobileNetV1 network was developed, which employs depthwise convolution to reduce network complexity. MobileNetV1 employs a stride of 2 in several convolutional layers to decrease the spatial resolution of feature maps, thereby lowering computational costs. However, this stride setting can lead to a loss of spatial information, particularly affecting the detection and representation of smaller objects or finer details in images. To maintain the trade-off between complexity and model performance, a lightweight convolutional neural network with hierarchical multi-scale feature fusion based on the MobileNetV1 network is proposed. The network consists of two main subnetworks. The first subnetwork uses a depthwise dilated separable convolution (DDSC) layer to learn imaging features with fewer parameters, which results in a lightweight and computationally inexpensive network. Furthermore, depthwise dilated convolution in DDSC layer effectively expands the field of view of filters, allowing them to incorporate a larger context. The second subnetwork is a hierarchical multi-scale feature fusion (HMFF) module that uses parallel multi-resolution branches architecture to process the input feature map in order to extract the multi-scale feature information of the input image. Experimental results on the CIFAR-10, Malaria, and KvasirV1 datasets demonstrate that the proposed method is efficient, reducing the network parameters and computational cost by 65.02% and 39.78%, respectively, while maintaining the network performance compared to the MobileNetV1 baseline.

Multi-scale physics-informed neural networks for solving high Reynolds number boundary layer flows based on matched asymptotic expansions

Multi-scale system remains a classical scientific problem in fluid dynamics,biology,etc.In the present study,a scheme of multi-scale Physics-informed neural networks is proposed to solve the boundary layer flow at high Reynolds numbers without any data.The flow is divided into several regions with different scales based on Prandtl's boundary theory.Different regions are solved with governing equations in different scales.The method of matched asymptotic expansions is used to make the flow field continuously.A flow on a semi infinite flat plate at a high Reynolds number is considered a multi-scale problem because the boundary layer scale is much smaller than the outer flow scale.The results are compared with the reference numerical solutions,which show that the msPINNs can solve the multi-scale problem of the boundary layer in high Reynolds number flows.This scheme can be developed for more multi-scale problems in the future.

Resilience Augmentation in Unmanned Weapon Systems via Multi-Layer Attention Graph Convolutional Neural Networks

The collective Unmanned Weapon System-of-Systems(UWSOS)network represents a fundamental element in modern warfare,characterized by a diverse array of unmanned combat platforms interconnected through hetero-geneous network architectures.Despite its strategic importance,the UWSOS network is highly susceptible to hostile infiltrations,which significantly impede its battlefield recovery capabilities.Existing methods to enhance network resilience predominantly focus on basic graph relationships,neglecting the crucial higher-order dependencies among nodes necessary for capturing multi-hop meta-paths within the UWSOS.To address these limitations,we propose the Enhanced-Resilience Multi-Layer Attention Graph Convolutional Network(E-MAGCN),designed to augment the adaptability of UWSOS.Our approach employs BERT for extracting semantic insights from nodes and edges,thereby refining feature representations by leveraging various node and edge categories.Additionally,E-MAGCN integrates a regularization-based multi-layer attention mechanism and a semantic node fusion algo-rithm within the Graph Convolutional Network(GCN)framework.Through extensive simulation experiments,our model demonstrates an enhancement in resilience performance ranging from 1.2% to 7% over existing algorithms.

State-of-health estimation for fast-charging lithium-ion batteries based on a short charge curve using graph convolutional and long short-term memory networks

A fast-charging policy is widely employed to alleviate the inconvenience caused by the extended charging time of electric vehicles. However, fast charging exacerbates battery degradation and shortens battery lifespan. In addition, there is still a lack of tailored health estimations for fast-charging batteries;most existing methods are applicable at lower charging rates. This paper proposes a novel method for estimating the health of lithium-ion batteries, which is tailored for multi-stage constant current-constant voltage fast-charging policies. Initially, short charging segments are extracted by monitoring current switches,followed by deriving voltage sequences using interpolation techniques. Subsequently, a graph generation layer is used to transform the voltage sequence into graphical data. Furthermore, the integration of a graph convolution network with a long short-term memory network enables the extraction of information related to inter-node message transmission, capturing the key local and temporal features during the battery degradation process. Finally, this method is confirmed by utilizing aging data from 185 cells and 81 distinct fast-charging policies. The 4-minute charging duration achieves a balance between high accuracy in estimating battery state of health and low data requirements, with mean absolute errors and root mean square errors of 0.34% and 0.66%, respectively.

A Pooling Method Developed for Use in Convolutional Neural Networks

In convolutional neural networks,pooling methods are used to reduce both the size of the data and the number of parameters after the convolution of the models.These methods reduce the computational amount of convolutional neural networks,making the neural network more efficient.Maximum pooling,average pooling,and minimum pooling methods are generally used in convolutional neural networks.However,these pooling methods are not suitable for all datasets used in neural network applications.In this study,a new pooling approach to the literature is proposed to increase the efficiency and success rates of convolutional neural networks.This method,which we call MAM(Maximum Average Minimum)pooling,is more interactive than other traditional maximum pooling,average pooling,and minimum pooling methods and reduces data loss by calculating the more appropriate pixel value.The proposed MAM pooling method increases the performance of the neural network by calculating the optimal value during the training of convolutional neural networks.To determine the success accuracy of the proposed MAM pooling method and compare it with other traditional pooling methods,training was carried out on the LeNet-5 model using CIFAR-10,CIFAR-100,and MNIST datasets.According to the results obtained,the proposed MAM pooling method performed better than the maximum pooling,average pooling,and minimum pooling methods in all pool sizes on three different datasets.

Prediction of Porous Media Fluid Flow with Spatial Heterogeneity Using Criss-Cross Physics-Informed Convolutional Neural Networks

Recent advances in deep neural networks have shed new light on physics,engineering,and scientific computing.Reconciling the data-centered viewpoint with physical simulation is one of the research hotspots.The physicsinformedneural network(PINN)is currently the most general framework,which is more popular due to theconvenience of constructing NNs and excellent generalization ability.The automatic differentiation(AD)-basedPINN model is suitable for the homogeneous scientific problem;however,it is unclear how AD can enforce fluxcontinuity across boundaries between cells of different properties where spatial heterogeneity is represented bygrid cells with different physical properties.In this work,we propose a criss-cross physics-informed convolutionalneural network(CC-PINN)learning architecture,aiming to learn the solution of parametric PDEs with spatialheterogeneity of physical properties.To achieve the seamless enforcement of flux continuity and integration ofphysicalmeaning into CNN,a predefined 2D convolutional layer is proposed to accurately express transmissibilitybetween adjacent cells.The efficacy of the proposedmethodwas evaluated through predictions of several petroleumreservoir problems with spatial heterogeneity and compared against state-of-the-art(PINN)through numericalanalysis as a benchmark,which demonstrated the superiority of the proposed method over the PINN.

Multi-Material Topology Optimization of 2D Structures Using Convolutional Neural Networks

In recent years,there has been significant research on the application of deep learning(DL)in topology optimization(TO)to accelerate structural design.However,these methods have primarily focused on solving binary TO problems,and effective solutions for multi-material topology optimization(MMTO)which requires a lot of computing resources are still lacking.Therefore,this paper proposes the framework of multiphase topology optimization using deep learning to accelerate MMTO design.The framework employs convolutional neural network(CNN)to construct a surrogate model for solving MMTO,and the obtained surrogate model can rapidly generate multi-material structure topologies in negligible time without any iterations.The performance evaluation results show that the proposed method not only outputs multi-material topologies with clear material boundary but also reduces the calculation cost with high prediction accuracy.Additionally,in order to find a more reasonable modeling method for MMTO,this paper studies the characteristics of surrogate modeling as regression task and classification task.Through the training of 297 models,our findings show that the regression task yields slightly better results than the classification task in most cases.Furthermore,The results indicate that the prediction accuracy is primarily influenced by factors such as the TO problem,material category,and data scale.Conversely,factors such as the domain size and the material property have minimal impact on the accuracy.

Downscaling Seasonal Precipitation Forecasts over East Africa with Deep Convolutional Neural Networks

This study assesses the suitability of convolutional neural networks(CNNs) for downscaling precipitation over East Africa in the context of seasonal forecasting. To achieve this, we design a set of experiments that compare different CNN configurations and deployed the best-performing architecture to downscale one-month lead seasonal forecasts of June–July–August–September(JJAS) precipitation from the Nanjing University of Information Science and Technology Climate Forecast System version 1.0(NUIST-CFS1.0) for 1982–2020. We also perform hyper-parameter optimization and introduce predictors over a larger area to include information about the main large-scale circulations that drive precipitation over the East Africa region, which improves the downscaling results. Finally, we validate the raw model and downscaled forecasts in terms of both deterministic and probabilistic verification metrics, as well as their ability to reproduce the observed precipitation extreme and spell indicator indices. The results show that the CNN-based downscaling consistently improves the raw model forecasts, with lower bias and more accurate representations of the observed mean and extreme precipitation spatial patterns. Besides, CNN-based downscaling yields a much more accurate forecast of extreme and spell indicators and reduces the significant relative biases exhibited by the raw model predictions. Moreover, our results show that CNN-based downscaling yields better skill scores than the raw model forecasts over most portions of East Africa. The results demonstrate the potential usefulness of CNN in downscaling seasonal precipitation predictions over East Africa,particularly in providing improved forecast products which are essential for end users.

Multi-Label Image Classification Based on Object Detection and Dynamic Graph Convolutional Networks

Multi-label image classification is recognized as an important task within the field of computer vision,a discipline that has experienced a significant escalation in research endeavors in recent years.The widespread adoption of convolutional neural networks(CNNs)has catalyzed the remarkable success of architectures such as ResNet-101 within the domain of image classification.However,inmulti-label image classification tasks,it is crucial to consider the correlation between labels.In order to improve the accuracy and performance of multi-label classification and fully combine visual and semantic features,many existing studies use graph convolutional networks(GCN)for modeling.Object detection and multi-label image classification exhibit a degree of conceptual overlap;however,the integration of these two tasks within a unified framework has been relatively underexplored in the existing literature.In this paper,we come up with Object-GCN framework,a model combining object detection network YOLOv5 and graph convolutional network,and we carry out a thorough experimental analysis using a range of well-established public datasets.The designed framework Object-GCN achieves significantly better performance than existing studies in public datasets COCO2014,VOC2007,VOC2012.The final results achieved are 86.9%,96.7%,and 96.3%mean Average Precision(mAP)across the three datasets.

Detection of Oscillations in Process Control Loops From Visual Image Space Using Deep Convolutional Networks

Oscillation detection has been a hot research topic in industries due to the high incidence of oscillation loops and their negative impact on plant profitability.Although numerous automatic detection techniques have been proposed,most of them can only address part of the practical difficulties.An oscillation is heuristically defined as a visually apparent periodic variation.However,manual visual inspection is labor-intensive and prone to missed detection.Convolutional neural networks(CNNs),inspired by animal visual systems,have been raised with powerful feature extraction capabilities.In this work,an exploration of the typical CNN models for visual oscillation detection is performed.Specifically,we tested MobileNet-V1,ShuffleNet-V2,Efficient Net-B0,and GhostNet models,and found that such a visual framework is well-suited for oscillation detection.The feasibility and validity of this framework are verified utilizing extensive numerical and industrial cases.Compared with state-of-theart oscillation detectors,the suggested framework is more straightforward and more robust to noise and mean-nonstationarity.In addition,this framework generalizes well and is capable of handling features that are not present in the training data,such as multiple oscillations and outliers.

Prediction of Geopolymer Concrete Compressive Strength Using Convolutional Neural Networks

Geopolymer concrete emerges as a promising avenue for sustainable development and offers an effective solution to environmental problems.Its attributes as a non-toxic,low-carbon,and economical substitute for conventional cement concrete,coupled with its elevated compressive strength and reduced shrinkage properties,position it as a pivotal material for diverse applications spanning from architectural structures to transportation infrastructure.In this context,this study sets out the task of using machine learning(ML)algorithms to increase the accuracy and interpretability of predicting the compressive strength of geopolymer concrete in the civil engineering field.To achieve this goal,a new approach using convolutional neural networks(CNNs)has been adopted.This study focuses on creating a comprehensive dataset consisting of compositional and strength parameters of 162 geopolymer concrete mixes,all containing Class F fly ash.The selection of optimal input parameters is guided by two distinct criteria.The first criterion leverages insights garnered from previous research on the influence of individual features on compressive strength.The second criterion scrutinizes the impact of these features within the model’s predictive framework.Key to enhancing the CNN model’s performance is the meticulous determination of the optimal hyperparameters.Through a systematic trial-and-error process,the study ascertains the ideal number of epochs for data division and the optimal value of k for k-fold cross-validation—a technique vital to the model’s robustness.The model’s predictive prowess is rigorously assessed via a suite of performance metrics and comprehensive score analyses.Furthermore,the model’s adaptability is gauged by integrating a secondary dataset into its predictive framework,facilitating a comparative evaluation against conventional prediction methods.To unravel the intricacies of the CNN model’s learning trajectory,a loss plot is deployed to elucidate its learning rate.The study culminates in compelling findings that underscore the CNN model’s accurate prediction of geopolymer concrete compressive strength.To maximize the dataset’s potential,the application of bivariate plots unveils nuanced trends and interactions among variables,fortifying the consistency with earlier research.Evidenced by promising prediction accuracy,the study’s outcomes hold significant promise in guiding the development of innovative geopolymer concrete formulations,thereby reinforcing its role as an eco-conscious and robust construction material.The findings prove that the CNN model accurately estimated geopolymer concrete’s compressive strength.The results show that the prediction accuracy is promising and can be used for the development of new geopolymer concrete mixes.The outcomes not only underscore the significance of leveraging technology for sustainable construction practices but also pave the way for innovation and efficiency in the field of civil engineering.

Graph Convolutional Networks Embedding Textual Structure Information for Relation Extraction

Deep neural network-based relational extraction research has made significant progress in recent years,andit provides data support for many natural language processing downstream tasks such as building knowledgegraph,sentiment analysis and question-answering systems.However,previous studies ignored much unusedstructural information in sentences that could enhance the performance of the relation extraction task.Moreover,most existing dependency-based models utilize self-attention to distinguish the importance of context,whichhardly deals withmultiple-structure information.To efficiently leverage multiple structure information,this paperproposes a dynamic structure attention mechanism model based on textual structure information,which deeplyintegrates word embedding,named entity recognition labels,part of speech,dependency tree and dependency typeinto a graph convolutional network.Specifically,our model extracts text features of different structures from theinput sentence.Textual Structure information Graph Convolutional Networks employs the dynamic structureattention mechanism to learn multi-structure attention,effectively distinguishing important contextual features invarious structural information.In addition,multi-structure weights are carefully designed as amergingmechanismin the different structure attention to dynamically adjust the final attention.This paper combines these featuresand trains a graph convolutional network for relation extraction.We experiment on supervised relation extractiondatasets including SemEval 2010 Task 8,TACRED,TACREV,and Re-TACED,the result significantly outperformsthe previous.

Intrusion Detection System for Smart Industrial Environments with Ensemble Feature Selection and Deep Convolutional Neural Networks

Smart Industrial environments use the Industrial Internet of Things(IIoT)for their routine operations and transform their industrial operations with intelligent and driven approaches.However,IIoT devices are vulnerable to cyber threats and exploits due to their connectivity with the internet.Traditional signature-based IDS are effective in detecting known attacks,but they are unable to detect unknown emerging attacks.Therefore,there is the need for an IDS which can learn from data and detect new threats.Ensemble Machine Learning(ML)and individual Deep Learning(DL)based IDS have been developed,and these individual models achieved low accuracy;however,their performance can be improved with the ensemble stacking technique.In this paper,we have proposed a Deep Stacked Neural Network(DSNN)based IDS,which consists of two stacked Convolutional Neural Network(CNN)models as base learners and Extreme Gradient Boosting(XGB)as the meta learner.The proposed DSNN model was trained and evaluated with the next-generation dataset,TON_IoT.Several pre-processing techniques were applied to prepare a dataset for the model,including ensemble feature selection and the SMOTE technique.Accuracy,precision,recall,F1-score,and false positive rates were used to evaluate the performance of the proposed ensemble model.Our experimental results showed that the accuracy for binary classification is 99.61%,which is better than in the baseline individual DL and ML models.In addition,the model proposed for IDS has been compared with similar models.The proposed DSNN achieved better performance metrics than the other models.The proposed DSNN model will be used to develop enhanced IDS for threat mitigation in smart industrial environments.

Lightweight Multi-scale Convolutional Neural Network for Rice Leaf Disease Recognition

In the field of agricultural information,the identification and prediction of rice leaf disease have always been the focus of research,and deep learning(DL)technology is currently a hot research topic in the field of pattern recognition.The research and development of high-efficiency,highquality and low-cost automatic identification methods for rice diseases that can replace humans is an important means of dealing with the current situation from a technical perspective.This paper mainly focuses on the problem of huge parameters of the Convolutional Neural Network(CNN)model and proposes a recognitionmodel that combines amulti-scale convolution module with a neural network model based on Visual Geometry Group(VGG).The accuracy and loss of the training set and the test set are used to evaluate the performance of the model.The test accuracy of this model is 97.1%that has increased 5.87%over VGG.Furthermore,the memory requirement is 26.1M,only 1.6%of the VGG.Experiment results show that this model performs better in terms of accuracy,recognition speed and memory size.

Development of a convolutional neural network based geomechanical upscaling technique for heterogeneous geological reservoir

Geomechanical assessment using coupled reservoir-geomechanical simulation is becoming increasingly important for analyzing the potential geomechanical risks in subsurface geological developments.However,a robust and efficient geomechanical upscaling technique for heterogeneous geological reservoirs is lacking to advance the applications of three-dimensional(3D)reservoir-scale geomechanical simulation considering detailed geological heterogeneities.Here,we develop convolutional neural network(CNN)proxies that reproduce the anisotropic nonlinear geomechanical response caused by lithological heterogeneity,and compute upscaled geomechanical properties from CNN proxies.The CNN proxies are trained using a large dataset of randomly generated spatially correlated sand-shale realizations as inputs and simulation results of their macroscopic geomechanical response as outputs.The trained CNN models can provide the upscaled shear strength(R^(2)>0.949),stress-strain behavior(R^(2)>0.925),and volumetric strain changes(R^(2)>0.958)that highly agree with the numerical simulation results while saving over two orders of magnitude of computational time.This is a major advantage in computing the upscaled geomechanical properties directly from geological realizations without the need to perform local numerical simulations to obtain the geomechanical response.The proposed CNN proxybased upscaling technique has the ability to(1)bridge the gap between the fine-scale geocellular models considering geological uncertainties and computationally efficient geomechanical models used to assess the geomechanical risks of large-scale subsurface development,and(2)improve the efficiency of numerical upscaling techniques that rely on local numerical simulations,leading to significantly increased computational time for uncertainty quantification using numerous geological realizations.

Customized Convolutional Neural Network for Accurate Detection of Deep Fake Images in Video Collections

The motivation for this study is that the quality of deep fakes is constantly improving,which leads to the need to develop new methods for their detection.The proposed Customized Convolutional Neural Network method involves extracting structured data from video frames using facial landmark detection,which is then used as input to the CNN.The customized Convolutional Neural Network method is the date augmented-based CNN model to generate‘fake data’or‘fake images’.This study was carried out using Python and its libraries.We used 242 films from the dataset gathered by the Deep Fake Detection Challenge,of which 199 were made up and the remaining 53 were real.Ten seconds were allotted for each video.There were 318 videos used in all,199 of which were fake and 119 of which were real.Our proposedmethod achieved a testing accuracy of 91.47%,loss of 0.342,and AUC score of 0.92,outperforming two alternative approaches,CNN and MLP-CNN.Furthermore,our method succeeded in greater accuracy than contemporary models such as XceptionNet,Meso-4,EfficientNet-BO,MesoInception-4,VGG-16,and DST-Net.The novelty of this investigation is the development of a new Convolutional Neural Network(CNN)learning model that can accurately detect deep fake face photos.

An End-To-End Hyperbolic Deep Graph Convolutional Neural Network Framework

Graph Convolutional Neural Networks(GCNs)have been widely used in various fields due to their powerful capabilities in processing graph-structured data.However,GCNs encounter significant challenges when applied to scale-free graphs with power-law distributions,resulting in substantial distortions.Moreover,most of the existing GCN models are shallow structures,which restricts their ability to capture dependencies among distant nodes and more refined high-order node features in scale-free graphs with hierarchical structures.To more broadly and precisely apply GCNs to real-world graphs exhibiting scale-free or hierarchical structures and utilize multi-level aggregation of GCNs for capturing high-level information in local representations,we propose the Hyperbolic Deep Graph Convolutional Neural Network(HDGCNN),an end-to-end deep graph representation learning framework that can map scale-free graphs from Euclidean space to hyperbolic space.In HDGCNN,we define the fundamental operations of deep graph convolutional neural networks in hyperbolic space.Additionally,we introduce a hyperbolic feature transformation method based on identity mapping and a dense connection scheme based on a novel non-local message passing framework.In addition,we present a neighborhood aggregation method that combines initial structural featureswith hyperbolic attention coefficients.Through the above methods,HDGCNN effectively leverages both the structural features and node features of graph data,enabling enhanced exploration of non-local structural features and more refined node features in scale-free or hierarchical graphs.Experimental results demonstrate that HDGCNN achieves remarkable performance improvements over state-ofthe-art GCNs in node classification and link prediction tasks,even when utilizing low-dimensional embedding representations.Furthermore,when compared to shallow hyperbolic graph convolutional neural network models,HDGCNN exhibits notable advantages and performance enhancements.

TSCND:Temporal Subsequence-Based Convolutional Network with Difference for Time Series Forecasting

Time series forecasting plays an important role in various fields, such as energy, finance, transport, and weather. Temporal convolutional networks (TCNs) based on dilated causal convolution have been widely used in time series forecasting. However, two problems weaken the performance of TCNs. One is that in dilated casual convolution, causal convolution leads to the receptive fields of outputs being concentrated in the earlier part of the input sequence, whereas the recent input information will be severely lost. The other is that the distribution shift problem in time series has not been adequately solved. To address the first problem, we propose a subsequence-based dilated convolution method (SDC). By using multiple convolutional filters to convolve elements of neighboring subsequences, the method extracts temporal features from a growing receptive field via a growing subsequence rather than a single element. Ultimately, the receptive field of each output element can cover the whole input sequence. To address the second problem, we propose a difference and compensation method (DCM). The method reduces the discrepancies between and within the input sequences by difference operations and then compensates the outputs for the information lost due to difference operations. Based on SDC and DCM, we further construct a temporal subsequence-based convolutional network with difference (TSCND) for time series forecasting. The experimental results show that TSCND can reduce prediction mean squared error by 7.3% and save runtime, compared with state-of-the-art models and vanilla TCN.

Weighted Forwarding in Graph Convolution Networks for Recommendation Information Systems

Recommendation Information Systems(RIS)are pivotal in helping users in swiftly locating desired content from the vast amount of information available on the Internet.Graph Convolution Network(GCN)algorithms have been employed to implement the RIS efficiently.However,the GCN algorithm faces limitations in terms of performance enhancement owing to the due to the embedding value-vanishing problem that occurs during the learning process.To address this issue,we propose a Weighted Forwarding method using the GCN(WF-GCN)algorithm.The proposed method involves multiplying the embedding results with different weights for each hop layer during graph learning.By applying the WF-GCN algorithm,which adjusts weights for each hop layer before forwarding to the next,nodes with many neighbors achieve higher embedding values.This approach facilitates the learning of more hop layers within the GCN framework.The efficacy of the WF-GCN was demonstrated through its application to various datasets.In the MovieLens dataset,the implementation of WF-GCN in LightGCN resulted in significant performance improvements,with recall and NDCG increasing by up to+163.64%and+132.04%,respectively.Similarly,in the Last.FM dataset,LightGCN using WF-GCN enhanced with WF-GCN showed substantial improvements,with the recall and NDCG metrics rising by up to+174.40%and+169.95%,respectively.Furthermore,the application of WF-GCN to Self-supervised Graph Learning(SGL)and Simple Graph Contrastive Learning(SimGCL)also demonstrated notable enhancements in both recall and NDCG across these datasets.