Churchill, Victor; Chen, Yuan; Xu, Zhongshu; Xiu, Dongbin DNN modeling of partial differential equations with incomplete data. (English) Zbl 07748076 J. Comput. Phys. 493, Article ID 112502, 20 p. (2023). MSC: 68Txx 65Lxx 37Mxx PDFBibTeX XMLCite \textit{V. Churchill} et al., J. Comput. Phys. 493, Article ID 112502, 20 p. (2023; Zbl 07748076) Full Text: DOI
Churchill, Victor; Manns, Steve; Chen, Zhen; Xiu, Dongbin Robust modeling of unknown dynamical systems via ensemble averaged learning. (English) Zbl 07640582 J. Comput. Phys. 474, Article ID 111842, 12 p. (2023). MSC: 68Txx 65Lxx 35Qxx PDFBibTeX XMLCite \textit{V. Churchill} et al., J. Comput. Phys. 474, Article ID 111842, 12 p. (2023; Zbl 07640582) Full Text: DOI arXiv
Chen, Zhen; Churchill, Victor; Wu, Kailiang; Xiu, Dongbin Deep neural network modeling of unknown partial differential equations in nodal space. (English) Zbl 07524779 J. Comput. Phys. 449, Article ID 110782, 20 p. (2022). MSC: 68Txx 35Qxx 37Mxx PDFBibTeX XMLCite \textit{Z. Chen} et al., J. Comput. Phys. 449, Article ID 110782, 20 p. (2022; Zbl 07524779) Full Text: DOI arXiv
Chen, Zhen; Xiu, Dongbin On generalized residual network for deep learning of unknown dynamical systems. (English) Zbl 07505957 J. Comput. Phys. 438, Article ID 110362, 16 p. (2021). MSC: 68Txx 35Qxx 37Mxx PDFBibTeX XMLCite \textit{Z. Chen} and \textit{D. Xiu}, J. Comput. Phys. 438, Article ID 110362, 16 p. (2021; Zbl 07505957) Full Text: DOI arXiv
Qin, Tong; Chen, Zhen; Jakeman, John D.; Xiu, Dongbin Data-driven learning of nonautonomous systems. (English) Zbl 1512.65174 SIAM J. Sci. Comput. 43, No. 3, A1607-A1624 (2021). MSC: 65L99 37B55 37M10 68T07 PDFBibTeX XMLCite \textit{T. Qin} et al., SIAM J. Sci. Comput. 43, No. 3, A1607--A1624 (2021; Zbl 1512.65174) Full Text: DOI arXiv
Wu, Kailiang; Xiu, Dongbin Data-driven deep learning of partial differential equations in modal space. (English) Zbl 07505629 J. Comput. Phys. 408, Article ID 109307, 22 p. (2020). MSC: 35-XX 65-XX PDFBibTeX XMLCite \textit{K. Wu} and \textit{D. Xiu}, J. Comput. Phys. 408, Article ID 109307, 22 p. (2020; Zbl 07505629) Full Text: DOI arXiv
Wu, Kailiang; Qin, Tong; Xiu, Dongbin Structure-preserving method for reconstructing unknown Hamiltonian systems from trajectory data. (English) Zbl 1462.65219 SIAM J. Sci. Comput. 42, No. 6, A3704-A3729 (2020). MSC: 65P10 65P99 PDFBibTeX XMLCite \textit{K. Wu} et al., SIAM J. Sci. Comput. 42, No. 6, A3704--A3729 (2020; Zbl 1462.65219) Full Text: DOI arXiv
Chen, Zhen; Wu, Kailiang; Xiu, Dongbin Methods to recover unknown processes in partial differential equations using data. (English) Zbl 1455.65159 J. Sci. Comput. 85, No. 2, Paper No. 23, 22 p. (2020). Reviewer: Christian Clason (Graz) MSC: 65M32 65M60 65M70 65M06 65N30 65N35 65J22 35R30 PDFBibTeX XMLCite \textit{Z. Chen} et al., J. Sci. Comput. 85, No. 2, Paper No. 23, 22 p. (2020; Zbl 1455.65159) Full Text: DOI arXiv
Qin, Tong; Wu, Kailiang; Xiu, Dongbin Data driven governing equations approximation using deep neural networks. (English) Zbl 1455.65125 J. Comput. Phys. 395, 620-635 (2019). MSC: 65L99 37C10 37M10 68T07 PDFBibTeX XMLCite \textit{T. Qin} et al., J. Comput. Phys. 395, 620--635 (2019; Zbl 1455.65125) Full Text: DOI arXiv
Wu, Kailiang; Xiu, Dongbin Numerical aspects for approximating governing equations using data. (English) Zbl 1451.65008 J. Comput. Phys. 384, 200-221 (2019). MSC: 65C20 37M10 34A55 34A09 62G08 PDFBibTeX XMLCite \textit{K. Wu} and \textit{D. Xiu}, J. Comput. Phys. 384, 200--221 (2019; Zbl 1451.65008) Full Text: DOI arXiv