Pub Date : 2023-06-01DOI: 10.4208/cicp.oa-2022-0226
H. Zhang, Yingying Fang, Hok Shing Wong, Lihua Li null, T. Zeng
{"title":"Saturation-Value Blind Color Image Deblurring with Geometric Spatial-Feature Prior","authors":"H. Zhang, Yingying Fang, Hok Shing Wong, Lihua Li null, T. Zeng","doi":"10.4208/cicp.oa-2022-0226","DOIUrl":"https://doi.org/10.4208/cicp.oa-2022-0226","url":null,"abstract":"","PeriodicalId":50661,"journal":{"name":"Communications in Computational Physics","volume":" ","pages":""},"PeriodicalIF":3.7,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43071387","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-06-01DOI: 10.4208/cicp.oa-2022-0085
Chunyuan Xu null, Qinghong Zeng
{"title":"Symmetry Preservation by a Compatible Staggered Lagrangian Scheme Using the Control-Volume Discretization Method in $r–z$ Coordinate","authors":"Chunyuan Xu null, Qinghong Zeng","doi":"10.4208/cicp.oa-2022-0085","DOIUrl":"https://doi.org/10.4208/cicp.oa-2022-0085","url":null,"abstract":"","PeriodicalId":50661,"journal":{"name":"Communications in Computational Physics","volume":" ","pages":""},"PeriodicalIF":3.7,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45255574","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-06-01DOI: 10.4208/cicp.oa-2022-0171
Meng Liu null, Jiaqing Yang
{"title":"Numerical Reconstruction of Locally Rough Surfaces with a Newton Iterative Algorithm","authors":"Meng Liu null, Jiaqing Yang","doi":"10.4208/cicp.oa-2022-0171","DOIUrl":"https://doi.org/10.4208/cicp.oa-2022-0171","url":null,"abstract":"","PeriodicalId":50661,"journal":{"name":"Communications in Computational Physics","volume":" ","pages":""},"PeriodicalIF":3.7,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42321405","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-06-01DOI: 10.4208/cicp.oa-2022-0138
Mingze Qin, Ruishu Wang, Qilong Zhai null, Ran Zhang
{"title":"Weak Galerkin Method for Second-Order Elliptic Equations with Newton Boundary Condition","authors":"Mingze Qin, Ruishu Wang, Qilong Zhai null, Ran Zhang","doi":"10.4208/cicp.oa-2022-0138","DOIUrl":"https://doi.org/10.4208/cicp.oa-2022-0138","url":null,"abstract":"","PeriodicalId":50661,"journal":{"name":"Communications in Computational Physics","volume":" ","pages":""},"PeriodicalIF":3.7,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49518473","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-06-01DOI: 10.4208/cicp.oa-2022-0204
Massimo Frittelli, Anotida Madzvamuse null, I. Sgura
{"title":"The Bulk-Surface Virtual Element Method for Reaction-Diffusion PDEs: Analysis and Applications","authors":"Massimo Frittelli, Anotida Madzvamuse null, I. Sgura","doi":"10.4208/cicp.oa-2022-0204","DOIUrl":"https://doi.org/10.4208/cicp.oa-2022-0204","url":null,"abstract":"","PeriodicalId":50661,"journal":{"name":"Communications in Computational Physics","volume":" ","pages":""},"PeriodicalIF":3.7,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46618390","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-06-01DOI: 10.4208/cicp.oa-2022-0285
Haoxiang Huang, Vigor Yang null, Yingjie Liu
{"title":"Neural Networks with Local Converging Inputs (NNLCI) for Solving Conservation Laws, Part I: 1D Problems","authors":"Haoxiang Huang, Vigor Yang null, Yingjie Liu","doi":"10.4208/cicp.oa-2022-0285","DOIUrl":"https://doi.org/10.4208/cicp.oa-2022-0285","url":null,"abstract":"","PeriodicalId":50661,"journal":{"name":"Communications in Computational Physics","volume":" ","pages":""},"PeriodicalIF":3.7,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44537425","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-06-01DOI: 10.4208/cicp.oa-2022-0216
Baiju Zhang null, Zhimin Zhang
{"title":"A New Family of Nonconforming Elements with $H$(curl)-Continuity for the 3D Quad-Curl Problem","authors":"Baiju Zhang null, Zhimin Zhang","doi":"10.4208/cicp.oa-2022-0216","DOIUrl":"https://doi.org/10.4208/cicp.oa-2022-0216","url":null,"abstract":"","PeriodicalId":50661,"journal":{"name":"Communications in Computational Physics","volume":" ","pages":""},"PeriodicalIF":3.7,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46542077","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-06-01DOI: 10.4208/cicp.oa-2023-0063
Yuling Jiao, Jerry Zhijian Yang, Cheng Yuan null, Junyu Zhou
. In this paper, we give the first rigorous error estimation of the Weak Ad-versarial Neural Networks (WAN) in solving the second order parabolic PDEs. By decomposing the error into approximation error and statistical error, we first show the weak solution can be approximated by the ReLU 2 with arbitrary accuracy, then prove that the statistical error can also be efficiently bounded by the Rademacher complexity of the network functions, which can be further bounded by some integral related with the covering numbers and pseudo-dimension of ReLU 2 space. Finally, by combining the two bounds, we prove that the error of the WAN method can be well controlled if the depth and width of the neural network as well as the sample numbers have been properly selected. Our result also reveals some kind of freedom in choosing sample numbers on ∂ Ω and in the time axis.
{"title":"A Rate of Convergence of Weak Adversarial Neural Networks for the Second Order Parabolic PDEs","authors":"Yuling Jiao, Jerry Zhijian Yang, Cheng Yuan null, Junyu Zhou","doi":"10.4208/cicp.oa-2023-0063","DOIUrl":"https://doi.org/10.4208/cicp.oa-2023-0063","url":null,"abstract":". In this paper, we give the first rigorous error estimation of the Weak Ad-versarial Neural Networks (WAN) in solving the second order parabolic PDEs. By decomposing the error into approximation error and statistical error, we first show the weak solution can be approximated by the ReLU 2 with arbitrary accuracy, then prove that the statistical error can also be efficiently bounded by the Rademacher complexity of the network functions, which can be further bounded by some integral related with the covering numbers and pseudo-dimension of ReLU 2 space. Finally, by combining the two bounds, we prove that the error of the WAN method can be well controlled if the depth and width of the neural network as well as the sample numbers have been properly selected. Our result also reveals some kind of freedom in choosing sample numbers on ∂ Ω and in the time axis.","PeriodicalId":50661,"journal":{"name":"Communications in Computational Physics","volume":"12 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135145209","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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