We propose new hybrid Lagrange neural networks called LaNets to predict the numerical solutions of partial differential equations.That is,we embed Lagrange interpolation and small sample learning into deep neural netw...We propose new hybrid Lagrange neural networks called LaNets to predict the numerical solutions of partial differential equations.That is,we embed Lagrange interpolation and small sample learning into deep neural network frameworks.Concretely,we first perform Lagrange interpolation in front of the deep feedforward neural network.The Lagrange basis function has a neat structure and a strong expression ability,which is suitable to be a preprocessing tool for pre-fitting and feature extraction.Second,we introduce small sample learning into training,which is beneficial to guide themodel to be corrected quickly.Taking advantages of the theoretical support of traditional numerical method and the efficient allocation of modern machine learning,LaNets achieve higher predictive accuracy compared to the state-of-the-artwork.The stability and accuracy of the proposed algorithmare demonstrated through a series of classical numerical examples,including one-dimensional Burgers equation,onedimensional carburizing diffusion equations,two-dimensional Helmholtz equation and two-dimensional Burgers equation.Experimental results validate the robustness,effectiveness and flexibility of the proposed algorithm.展开更多
Scene segmentation is widely used in autonomous driving for environmental perception.Semantic scene segmentation has gained considerable attention owing to its rich semantic information.It assigns labels to the pixels...Scene segmentation is widely used in autonomous driving for environmental perception.Semantic scene segmentation has gained considerable attention owing to its rich semantic information.It assigns labels to the pixels in an image,thereby enabling automatic image labeling.Current approaches are based mainly on convolutional neural networks(CNN),however,they rely on numerous labels.Therefore,the use of a small amount of labeled data to achieve semantic segmentation has become increasingly important.In this study,we developed a domain adaptation framework based on optimal transport(OT)and an attention mechanism to address this issue.Specifically,we first generated the output space via a CNN owing to its superior of feature representation.Second,we utilized OT to achieve a more robust alignment of the source and target domains in the output space,where the OT plan defined a well attention mechanism to improve the adaptation of the model.In particular,the OT reduced the number of network parameters and made the network more interpretable.Third,to better describe the multiscale properties of the features,we constructed a multiscale segmentation network to perform domain adaptation.Finally,to verify the performance of the proposed method,we conducted an experiment to compare the proposed method with three benchmark and four SOTA methods using three scene datasets.The mean intersection-over-union(mIOU)was significantly improved,and visualization results under multiple domain adaptation scenarios also show that the proposed method performed better than semantic segmentation methods.展开更多
Fast and accurate MRI reconstruction is a key concern in modern clinical practice.Recently,numerous Deep-Learning methods have been proposed for MRI reconstruction,however,they usually fail to reconstruct sharp detail...Fast and accurate MRI reconstruction is a key concern in modern clinical practice.Recently,numerous Deep-Learning methods have been proposed for MRI reconstruction,however,they usually fail to reconstruct sharp details from the subsampled k-space data.To solve this problem,we propose a lightweight and accurate Edge Attention MRI Reconstruction Network(EAMRI)to reconstruct images with edge guidance.Specifically,we design an efficient Edge Prediction Network to directly predict accurate edges from the blurred image.Meanwhile,we propose a novel Edge Attention Module(EAM)to guide the image reconstruction utilizing the extracted edge priors,as inspired by the popular self-attention mechanism.EAM first projects the input image and edges into Q_(image),K_(edge),and V_(image),respectively.Then EAM pairs the Q_(image)with K_(edge)along the channel dimension,such that 1)it can search globally for the high-frequency image features that are activated by the edge priors;2)the overall computation burdens are largely reduced compared with the traditional spatial-wise attention.With the help of EAM,the predicted edge priors can effectively guide the model to reconstruct high-quality MR images with accurate edges.Extensive experiments show that our proposed EAMRI outperforms other methods with fewer parameters and can recover more accurate edges.展开更多
基金supported by NSFC(No.11971296)National Key Research and Development Program of China(No.2021YFA1003004).
文摘We propose new hybrid Lagrange neural networks called LaNets to predict the numerical solutions of partial differential equations.That is,we embed Lagrange interpolation and small sample learning into deep neural network frameworks.Concretely,we first perform Lagrange interpolation in front of the deep feedforward neural network.The Lagrange basis function has a neat structure and a strong expression ability,which is suitable to be a preprocessing tool for pre-fitting and feature extraction.Second,we introduce small sample learning into training,which is beneficial to guide themodel to be corrected quickly.Taking advantages of the theoretical support of traditional numerical method and the efficient allocation of modern machine learning,LaNets achieve higher predictive accuracy compared to the state-of-the-artwork.The stability and accuracy of the proposed algorithmare demonstrated through a series of classical numerical examples,including one-dimensional Burgers equation,onedimensional carburizing diffusion equations,two-dimensional Helmholtz equation and two-dimensional Burgers equation.Experimental results validate the robustness,effectiveness and flexibility of the proposed algorithm.
基金supported by the National Natural Science Foundation of China(11971296)National Key R&D Program of China(2021YFA1003004).
文摘Scene segmentation is widely used in autonomous driving for environmental perception.Semantic scene segmentation has gained considerable attention owing to its rich semantic information.It assigns labels to the pixels in an image,thereby enabling automatic image labeling.Current approaches are based mainly on convolutional neural networks(CNN),however,they rely on numerous labels.Therefore,the use of a small amount of labeled data to achieve semantic segmentation has become increasingly important.In this study,we developed a domain adaptation framework based on optimal transport(OT)and an attention mechanism to address this issue.Specifically,we first generated the output space via a CNN owing to its superior of feature representation.Second,we utilized OT to achieve a more robust alignment of the source and target domains in the output space,where the OT plan defined a well attention mechanism to improve the adaptation of the model.In particular,the OT reduced the number of network parameters and made the network more interpretable.Third,to better describe the multiscale properties of the features,we constructed a multiscale segmentation network to perform domain adaptation.Finally,to verify the performance of the proposed method,we conducted an experiment to compare the proposed method with three benchmark and four SOTA methods using three scene datasets.The mean intersection-over-union(mIOU)was significantly improved,and visualization results under multiple domain adaptation scenarios also show that the proposed method performed better than semantic segmentation methods.
基金This work is supported in part by the National Key R&D Program of China under Grant 2021YFE0203700 and 2021YFA1003004in part by the Natural Science Foundation of Shanghai under Grand 23ZR1422200+1 种基金in part by the Shanghai Sailing Program under Grant 23YF1412800in part by the NSFC/RGC N CUHK 415/19,Grant ITF MHP/038/20,Grant CRF 8730063,Grant RGC 14300219,14302920,14301121,and CUHK Direct Grant for Research.
文摘Fast and accurate MRI reconstruction is a key concern in modern clinical practice.Recently,numerous Deep-Learning methods have been proposed for MRI reconstruction,however,they usually fail to reconstruct sharp details from the subsampled k-space data.To solve this problem,we propose a lightweight and accurate Edge Attention MRI Reconstruction Network(EAMRI)to reconstruct images with edge guidance.Specifically,we design an efficient Edge Prediction Network to directly predict accurate edges from the blurred image.Meanwhile,we propose a novel Edge Attention Module(EAM)to guide the image reconstruction utilizing the extracted edge priors,as inspired by the popular self-attention mechanism.EAM first projects the input image and edges into Q_(image),K_(edge),and V_(image),respectively.Then EAM pairs the Q_(image)with K_(edge)along the channel dimension,such that 1)it can search globally for the high-frequency image features that are activated by the edge priors;2)the overall computation burdens are largely reduced compared with the traditional spatial-wise attention.With the help of EAM,the predicted edge priors can effectively guide the model to reconstruct high-quality MR images with accurate edges.Extensive experiments show that our proposed EAMRI outperforms other methods with fewer parameters and can recover more accurate edges.
