Zheng, Haoyang; Huang, Yao; Huang, Ziyang; Hao, Wenrui; Lin, Guang HomPINNs: homotopy physics-informed neural networks for solving the inverse problems of nonlinear differential equations with multiple solutions. (English) Zbl 07811337 J. Comput. Phys. 500, Article ID 112751, 16 p. (2024). MSC: 65Nxx 68Txx 35Qxx PDFBibTeX XMLCite \textit{H. Zheng} et al., J. Comput. Phys. 500, Article ID 112751, 16 p. (2024; Zbl 07811337) Full Text: DOI arXiv
Huang, Yao; Hao, Wenrui; Lin, Guang HomPINNs: homotopy physics-informed neural networks for learning multiple solutions of nonlinear elliptic differential equations. (English) Zbl 1524.65937 Comput. Math. Appl. 121, 62-73 (2022). MSC: 65N99 68T07 35K57 PDFBibTeX XMLCite \textit{Y. Huang} et al., Comput. Math. Appl. 121, 62--73 (2022; Zbl 1524.65937) Full Text: DOI
Wang, Yuepeng; Ren, Lanlan; Zhang, Zongyuan; Lin, Guang; Xu, Chao Sparsity-promoting elastic net method with rotations for high-dimensional nonlinear inverse problem. (English) Zbl 1440.65065 Comput. Methods Appl. Mech. Eng. 345, 263-282 (2019). MSC: 65K05 90C90 PDFBibTeX XMLCite \textit{Y. Wang} et al., Comput. Methods Appl. Mech. Eng. 345, 263--282 (2019; Zbl 1440.65065) Full Text: DOI
Wan, Xiaoliang; Zheng, Bin; Lin, Guang An \(hp\)-adaptive minimum action method based on a posteriori error estimate. (English) Zbl 1499.65025 Commun. Comput. Phys. 23, No. 2, 408-439 (2018). MSC: 65C30 60H35 65C20 65N20 65N30 PDFBibTeX XMLCite \textit{X. Wan} et al., Commun. Comput. Phys. 23, No. 2, 408--439 (2018; Zbl 1499.65025) Full Text: DOI
Wang, Yuepeng; Cheng, Yue; Zhang, Zongyuan; Lin, Guang Calibration of reduced-order model for a coupled Burgers equations based on PC-EnKF. (English) Zbl 1405.65130 Math. Model. Nat. Phenom. 13, No. 2, Paper No. 21, 18 p. (2018). MSC: 65M60 35Q53 35R60 60H35 35R30 PDFBibTeX XMLCite \textit{Y. Wang} et al., Math. Model. Nat. Phenom. 13, No. 2, Paper No. 21, 18 p. (2018; Zbl 1405.65130) Full Text: DOI
Guo, Wei; Lin, Guang; Christlieb, Andrew J.; Qiu, Jingmei An adaptive WENO collocation method for differential equations with random coefficients. (English) Zbl 1360.65034 Mathematics 4, No. 2, Paper No. 29, 14 p. (2016). MSC: 65C30 60H15 35R60 65C05 60H35 65M70 35Q53 65M50 65M12 PDFBibTeX XMLCite \textit{W. Guo} et al., Mathematics 4, No. 2, Paper No. 29, 14 p. (2016; Zbl 1360.65034) Full Text: DOI
Yang, Xiu; Lei, Huan; Baker, Nathan A.; Lin, Guang Enhancing sparsity of Hermite polynomial expansions by iterative rotations. (English) Zbl 1351.60041 J. Comput. Phys. 307, 94-109 (2016). MSC: 60G15 PDFBibTeX XMLCite \textit{X. Yang} et al., J. Comput. Phys. 307, 94--109 (2016; Zbl 1351.60041) Full Text: DOI arXiv