Mapping Network-Coordinated Stacked Gated Recurrent Units for Turbulence Prediction

Accurately predicting fluid forces acting on the sur-face of a structure is crucial in engineering design.However,this task becomes particularly challenging in turbulent flow,due to the complex and irregular changes in the flow field.In this study,we propose a novel deep learning method,named mapping net-work-coordinated stacked gated recurrent units(MSU),for pre-dicting pressure on a circular cylinder from velocity data.Specifi-cally,our coordinated learning strategy is designed to extract the most critical velocity point for prediction,a process that has not been explored before.In our experiments,MSU extracts one point from a velocity field containing 121 points and utilizes this point to accurately predict 100 pressure points on the cylinder.This method significantly reduces the workload of data measure-ment in practical engineering applications.Our experimental results demonstrate that MSU predictions are highly similar to the real turbulent data in both spatio-temporal and individual aspects.Furthermore,the comparison results show that MSU predicts more precise results,even outperforming models that use all velocity field points.Compared with state-of-the-art methods,MSU has an average improvement of more than 45%in various indicators such as root mean square error(RMSE).Through comprehensive and authoritative physical verification,we estab-lished that MSU’s prediction results closely align with pressure field data obtained in real turbulence fields.This confirmation underscores the considerable potential of MSU for practical applications in real engineering scenarios.The code is available at https://github.com/zhangzm0128/MSU.

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.

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.

Anomaly-Based Intrusion DetectionModel Using Deep Learning for IoT Networks

The rapid growth of Internet of Things(IoT)devices has brought numerous benefits to the interconnected world.However,the ubiquitous nature of IoT networks exposes them to various security threats,including anomaly intrusion attacks.In addition,IoT devices generate a high volume of unstructured data.Traditional intrusion detection systems often struggle to cope with the unique characteristics of IoT networks,such as resource constraints and heterogeneous data sources.Given the unpredictable nature of network technologies and diverse intrusion methods,conventional machine-learning approaches seem to lack efficiency.Across numerous research domains,deep learning techniques have demonstrated their capability to precisely detect anomalies.This study designs and enhances a novel anomaly-based intrusion detection system(AIDS)for IoT networks.Firstly,a Sparse Autoencoder(SAE)is applied to reduce the high dimension and get a significant data representation by calculating the reconstructed error.Secondly,the Convolutional Neural Network(CNN)technique is employed to create a binary classification approach.The proposed SAE-CNN approach is validated using the Bot-IoT dataset.The proposed models exceed the performance of the existing deep learning approach in the literature with an accuracy of 99.9%,precision of 99.9%,recall of 100%,F1 of 99.9%,False Positive Rate(FPR)of 0.0003,and True Positive Rate(TPR)of 0.9992.In addition,alternative metrics,such as training and testing durations,indicated that SAE-CNN performs better.

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.

MDCN:Modified Dense Convolution Network Based Disease Classification in Mango Leaves

The most widely farmed fruit in the world is mango.Both the production and quality of the mangoes are hampered by many diseases.These diseases need to be effectively controlled and mitigated.Therefore,a quick and accurate diagnosis of the disorders is essential.Deep convolutional neural networks,renowned for their independence in feature extraction,have established their value in numerous detection and classification tasks.However,it requires large training datasets and several parameters that need careful adjustment.The proposed Modified Dense Convolutional Network(MDCN)provides a successful classification scheme for plant diseases affecting mango leaves.This model employs the strength of pre-trained networks and modifies them for the particular context of mango leaf diseases by incorporating transfer learning techniques.The data loader also builds mini-batches for training the models to reduce training time.Finally,optimization approaches help increase the overall model’s efficiency and lower computing costs.MDCN employed on the MangoLeafBD Dataset consists of a total of 4,000 images.Following the experimental results,the proposed system is compared with existing techniques and it is clear that the proposed algorithm surpasses the existing algorithms by achieving high performance and overall throughput.

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.

Predicting Traffic Flow Using Dynamic Spatial-Temporal Graph Convolution Networks

Traffic flow prediction plays a key role in the construction of intelligent transportation system.However,due to its complex spatio-temporal dependence and its uncertainty,the research becomes very challenging.Most of the existing studies are based on graph neural networks that model traffic flow graphs and try to use fixed graph structure to deal with the relationship between nodes.However,due to the time-varying spatial correlation of the traffic network,there is no fixed node relationship,and these methods cannot effectively integrate the temporal and spatial features.This paper proposes a novel temporal-spatial dynamic graph convolutional network(TSADGCN).The dynamic time warping algorithm(DTW)is introduced to calculate the similarity of traffic flow sequence among network nodes in the time dimension,and the spatiotemporal graph of traffic flow is constructed to capture the spatiotemporal characteristics and dependencies of traffic flow.By combining graph attention network and time attention network,a spatiotemporal convolution block is constructed to capture spatiotemporal characteristics of traffic data.Experiments on open data sets PEMSD4 and PEMSD8 show that TSADGCN has higher prediction accuracy than well-known traffic flow prediction algorithms.

Recommendation System Based on Perceptron and Graph Convolution Network

The relationship between users and items,which cannot be recovered by traditional techniques,can be extracted by the recommendation algorithm based on the graph convolution network.The current simple linear combination of these algorithms may not be sufficient to extract the complex structure of user interaction data.This paper presents a new approach to address such issues,utilizing the graph convolution network to extract association relations.The proposed approach mainly includes three modules:Embedding layer,forward propagation layer,and score prediction layer.The embedding layer models users and items according to their interaction information and generates initial feature vectors as input for the forward propagation layer.The forward propagation layer designs two parallel graph convolution networks with self-connections,which extract higher-order association relevance from users and items separately by multi-layer graph convolution.Furthermore,the forward propagation layer integrates the attention factor to assign different weights among the hop neighbors of the graph convolution network fusion,capturing more comprehensive association relevance between users and items as input for the score prediction layer.The score prediction layer introduces MLP(multi-layer perceptron)to conduct non-linear feature interaction between users and items,respectively.Finally,the prediction score of users to items is obtained.The recall rate and normalized discounted cumulative gain were used as evaluation indexes.The proposed approach effectively integrates higher-order information in user entries,and experimental analysis demonstrates its superiority over the existing algorithms.

AFSTGCN:Prediction for multivariate time series using an adaptive fused spatial-temporal graph convolutional network

The prediction for Multivariate Time Series(MTS)explores the interrelationships among variables at historical moments,extracts their relevant characteristics,and is widely used in finance,weather,complex industries and other fields.Furthermore,it is important to construct a digital twin system.However,existing methods do not take full advantage of the potential properties of variables,which results in poor predicted accuracy.In this paper,we propose the Adaptive Fused Spatial-Temporal Graph Convolutional Network(AFSTGCN).First,to address the problem of the unknown spatial-temporal structure,we construct the Adaptive Fused Spatial-Temporal Graph(AFSTG)layer.Specifically,we fuse the spatial-temporal graph based on the interrelationship of spatial graphs.Simultaneously,we construct the adaptive adjacency matrix of the spatial-temporal graph using node embedding methods.Subsequently,to overcome the insufficient extraction of disordered correlation features,we construct the Adaptive Fused Spatial-Temporal Graph Convolutional(AFSTGC)module.The module forces the reordering of disordered temporal,spatial and spatial-temporal dependencies into rule-like data.AFSTGCN dynamically and synchronously acquires potential temporal,spatial and spatial-temporal correlations,thereby fully extracting rich hierarchical feature information to enhance the predicted accuracy.Experiments on different types of MTS datasets demonstrate that the model achieves state-of-the-art single-step and multi-step performance compared with eight other deep learning models.

SGT-Net: A Transformer-Based Stratified Graph Convolutional Network for 3D Point Cloud Semantic Segmentation

In recent years,semantic segmentation on 3D point cloud data has attracted much attention.Unlike 2D images where pixels distribute regularly in the image domain,3D point clouds in non-Euclidean space are irregular and inherently sparse.Therefore,it is very difficult to extract long-range contexts and effectively aggregate local features for semantic segmentation in 3D point cloud space.Most current methods either focus on local feature aggregation or long-range context dependency,but fail to directly establish a global-local feature extractor to complete the point cloud semantic segmentation tasks.In this paper,we propose a Transformer-based stratified graph convolutional network(SGT-Net),which enlarges the effective receptive field and builds direct long-range dependency.Specifically,we first propose a novel dense-sparse sampling strategy that provides dense local vertices and sparse long-distance vertices for subsequent graph convolutional network(GCN).Secondly,we propose a multi-key self-attention mechanism based on the Transformer to further weight augmentation for crucial neighboring relationships and enlarge the effective receptive field.In addition,to further improve the efficiency of the network,we propose a similarity measurement module to determine whether the neighborhood near the center point is effective.We demonstrate the validity and superiority of our method on the S3DIS and ShapeNet datasets.Through ablation experiments and segmentation visualization,we verify that the SGT model can improve the performance of the point cloud semantic segmentation.

A novel complex-high-order graph convolutional network paradigm:ChyGCN

In recent years,there has been a growing interest in graph convolutional networks(GCN).However,existing GCN and variants are predominantly based on simple graph or hypergraph structures,which restricts their ability to handle complex data correlations in practical applications.These limitations stem from the difficulty in establishing multiple hierarchies and acquiring adaptive weights for each of them.To address this issue,this paper introduces the latest concept of complex hypergraphs and constructs a versatile high-order multi-level data correlation model.This model is realized by establishing a three-tier structure of complexes-hypergraphs-vertices.Specifically,we start by establishing hyperedge clusters on a foundational network,utilizing a second-order hypergraph structure to depict potential correlations.For this second-order structure,truncation methods are used to assess and generate a three-layer composite structure.During the construction of the composite structure,an adaptive learning strategy is implemented to merge correlations across different levels.We evaluate this model on several popular datasets and compare it with recent state-of-the-art methods.The comprehensive assessment results demonstrate that the proposed model surpasses the existing methods,particularly in modeling implicit data correlations(the classification accuracy of nodes on five public datasets Cora,Citeseer,Pubmed,Github Web ML,and Facebook are 86.1±0.33,79.2±0.35,83.1±0.46,83.8±0.23,and 80.1±0.37,respectively).This indicates that our approach possesses advantages in handling datasets with implicit multi-level structures.

Aspect-Guided Multi-Graph Convolutional Networks for Aspect-based Sentiment Analysis

The Aspect-Based Sentiment Analysis(ABSA)task is designed to judge the sentiment polarity of a particular aspect in a review.Recent studies have proved that GCN can capture syntactic and semantic features from dependency graphs generated by dependency trees and semantic graphs generated by Multi-headed self-attention(MHSA).However,these approaches do not highlight the sentiment information associated with aspect in the syntactic and semantic graphs.We propose the Aspect-Guided Multi-Graph Convolutional Networks(AGGCN)for Aspect-Based Sentiment Classification.Specifically,we reconstruct two kinds of graphs,changing the weight of the dependency graph by distance from aspect and improving the semantic graph by Aspect-guided MHSA.For interactive learning of syntax and semantics,we dynamically fuse syntactic and semantic diagrams to generate syntactic-semantic graphs to learn emotional features jointly.In addition,Multi-dropout is added to solve the overftting of AGGCN in training.The experimental results on extensive datasets show that our model AGGCN achieves particularly advanced results and validates the effectiveness of the model.

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.

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.

A novel multi-resolution network for the open-circuit faults diagnosis of automatic ramming drive system

The open-circuit fault is one of the most common faults of the automatic ramming drive system(ARDS),and it can be categorized into the open-phase faults of Permanent Magnet Synchronous Motor(PMSM)and the open-circuit faults of Voltage Source Inverter(VSI). The stator current serves as a common indicator for detecting open-circuit faults. Due to the identical changes of the stator current between the open-phase faults in the PMSM and failures of double switches within the same leg of the VSI, this paper utilizes the zero-sequence voltage component as an additional diagnostic criterion to differentiate them.Considering the variable conditions and substantial noise of the ARDS, a novel Multi-resolution Network(Mr Net) is proposed, which can extract multi-resolution perceptual information and enhance robustness to the noise. Meanwhile, a feature weighted layer is introduced to allocate higher weights to characteristics situated near the feature frequency. Both simulation and experiment results validate that the proposed fault diagnosis method can diagnose 25 types of open-circuit faults and achieve more than98.28% diagnostic accuracy. In addition, the experiment results also demonstrate that Mr Net has the capability of diagnosing the fault types accurately under the interference of noise signals(Laplace noise and Gaussian noise).

Intelligent geochemical interpretation of mass chromatograms:Based on convolution neural network

Gas chromatography-mass spectrometry(GC-MS)is an extremely important analytical technique that is widely used in organic geochemistry.It is the only approach to capture biomarker features of organic matter and provides the key evidence for oil-source correlation and thermal maturity determination.However,the conventional way of processing and interpreting the mass chromatogram is both timeconsuming and labor-intensive,which increases the research cost and restrains extensive applications of this method.To overcome this limitation,a correlation model is developed based on the convolution neural network(CNN)to link the mass chromatogram and biomarker features of samples from the Triassic Yanchang Formation,Ordos Basin,China.In this way,the mass chromatogram can be automatically interpreted.This research first performs dimensionality reduction for 15 biomarker parameters via the factor analysis and then quantifies the biomarker features using two indexes(i.e.MI and PMI)that represent the organic matter thermal maturity and parent material type,respectively.Subsequently,training,interpretation,and validation are performed multiple times using different CNN models to optimize the model structure and hyper-parameter setting,with the mass chromatogram used as the input and the obtained MI and PMI values for supervision(label).The optimized model presents high accuracy in automatically interpreting the mass chromatogram,with R2values typically above 0.85 and0.80 for the thermal maturity and parent material interpretation results,respectively.The significance of this research is twofold:(i)developing an efficient technique for geochemical research;(ii)more importantly,demonstrating the potential of artificial intelligence in organic geochemistry and providing vital references for future related studies.

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.

UNet Based onMulti-Object Segmentation and Convolution Neural Network for Object Recognition

The recent advancements in vision technology have had a significant impact on our ability to identify multiple objects and understand complex scenes.Various technologies,such as augmented reality-driven scene integration,robotic navigation,autonomous driving,and guided tour systems,heavily rely on this type of scene comprehension.This paper presents a novel segmentation approach based on the UNet network model,aimed at recognizing multiple objects within an image.The methodology begins with the acquisition and preprocessing of the image,followed by segmentation using the fine-tuned UNet architecture.Afterward,we use an annotation tool to accurately label the segmented regions.Upon labeling,significant features are extracted from these segmented objects,encompassing KAZE(Accelerated Segmentation and Extraction)features,energy-based edge detection,frequency-based,and blob characteristics.For the classification stage,a convolution neural network(CNN)is employed.This comprehensive methodology demonstrates a robust framework for achieving accurate and efficient recognition of multiple objects in images.The experimental results,which include complex object datasets like MSRC-v2 and PASCAL-VOC12,have been documented.After analyzing the experimental results,it was found that the PASCAL-VOC12 dataset achieved an accuracy rate of 95%,while the MSRC-v2 dataset achieved an accuracy of 89%.The evaluation performed on these diverse datasets highlights a notably impressive level of performance.

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.