Li, Mengnan; Jiang, Lijian Data-driven reduced-order modeling for nonautonomous dynamical systems in multiscale media. (English) Zbl 07640556 J. Comput. Phys. 474, Article ID 111799, 22 p. (2023). MSC: 37Mxx 65Pxx 37Cxx PDFBibTeX XMLCite \textit{M. Li} and \textit{L. Jiang}, J. Comput. Phys. 474, Article ID 111799, 22 p. (2023; Zbl 07640556) Full Text: DOI arXiv
Li, Mengnan; Jiang, Lijian Deep learning nonlinear multiscale dynamic problems using Koopman operator. (English) Zbl 07516470 J. Comput. Phys. 446, Article ID 110660, 19 p. (2021). MSC: 65Nxx 76Mxx 37Mxx PDFBibTeX XMLCite \textit{M. Li} and \textit{L. Jiang}, J. Comput. Phys. 446, Article ID 110660, 19 p. (2021; Zbl 07516470) Full Text: DOI
Messenger, Daniel A.; Bortz, David M. Weak SINDy for partial differential equations. (English) Zbl 07515424 J. Comput. Phys. 443, Article ID 110525, 27 p. (2021). MSC: 65Mxx 37Mxx 65Lxx PDFBibTeX XMLCite \textit{D. A. Messenger} and \textit{D. M. Bortz}, J. Comput. Phys. 443, Article ID 110525, 27 p. (2021; Zbl 07515424) Full Text: DOI arXiv
Bunder, J. E.; Kevrekidis, I. G.; Roberts, A. J. Equation-free patch scheme for efficient computational homogenisation via self-adjoint coupling. (English) Zbl 1484.37098 Numer. Math. 149, No. 2, 229-272 (2021). MSC: 37M99 65P99 PDFBibTeX XMLCite \textit{J. E. Bunder} et al., Numer. Math. 149, No. 2, 229--272 (2021; Zbl 1484.37098) Full Text: DOI arXiv
Mangan, N. M.; Askham, T.; Brunton, S. L.; Kutz, J. N.; Proctor, J. L. Model selection for hybrid dynamical systems via sparse regression. (English) Zbl 1427.93253 Proc. R. Soc. Lond., A, Math. Phys. Eng. Sci. 475, No. 2223, Article ID 20180534, 22 p. (2019). MSC: 93E12 37M10 93-10 PDFBibTeX XMLCite \textit{N. M. Mangan} et al., Proc. R. Soc. Lond., A, Math. Phys. Eng. Sci. 475, No. 2223, Article ID 20180534, 22 p. (2019; Zbl 1427.93253) Full Text: DOI arXiv
Fan, Yuwei; Feliu-Fabà, Jordi; Lin, Lin; Ying, Lexing; Zepeda-Núñez, Leonardo A multiscale neural network based on hierarchical nested bases. (English) Zbl 07096701 Res. Math. Sci. 6, No. 2, Paper No. 21, 28 p. (2019). MSC: 65-XX 37-XX PDFBibTeX XMLCite \textit{Y. Fan} et al., Res. Math. Sci. 6, No. 2, Paper No. 21, 28 p. (2019; Zbl 07096701) Full Text: DOI arXiv
Druskin, Vladimir; Remis, Rob F.; Zaslavsky, Mikhail; Zimmerling, Jörn T. Compressing large-scale wave propagation models via phase-preconditioned rational Krylov subspaces. (English) Zbl 1412.65139 Multiscale Model. Simul. 16, No. 4, 1486-1518 (2018). Reviewer: Michael Jung (Dresden) MSC: 65M60 65M80 93B11 37M05 78A05 65F08 65F10 78M34 35J05 PDFBibTeX XMLCite \textit{V. Druskin} et al., Multiscale Model. Simul. 16, No. 4, 1486--1518 (2018; Zbl 1412.65139) Full Text: DOI arXiv
Bunder, J. E.; Roberts, A. J.; Kevrekidis, I. G. Good coupling for the multiscale patch scheme on systems with microscale heterogeneity. (English) Zbl 1415.65185 J. Comput. Phys. 337, 154-174 (2017). MSC: 65M06 82C20 82C80 76R50 37N20 37M05 PDFBibTeX XMLCite \textit{J. E. Bunder} et al., J. Comput. Phys. 337, 154--174 (2017; Zbl 1415.65185) Full Text: DOI
Alexanderian, Alen Expository paper: A primer on homogenization of elliptic PDEs with stationary and ergodic random coefficient functions. (English) Zbl 1354.37085 Rocky Mt. J. Math. 45, No. 3, 703-735 (2015). MSC: 37N15 37A05 37A25 78A48 78M40 74Q99 35B27 35J25 PDFBibTeX XMLCite \textit{A. Alexanderian}, Rocky Mt. J. Math. 45, No. 3, 703--735 (2015; Zbl 1354.37085) Full Text: DOI arXiv Euclid
Beyn, Wolf-Jürgen; Gess, Benjamin; Lescot, Paul; Röckner, Michael The global random attractor for a class of stochastic porous media equations. (English) Zbl 1284.60124 Commun. Partial Differ. Equations 36, No. 1-3, 446-469 (2011). MSC: 60H15 35L55 37H10 37L30 37L55 76M35 PDFBibTeX XMLCite \textit{W.-J. Beyn} et al., Commun. Partial Differ. Equations 36, No. 1--3, 446--469 (2011; Zbl 1284.60124) Full Text: DOI arXiv
Novruzov, Emil Quantitative homogenization of attractors of non-Newtonian filtration equations. (English) Zbl 1333.37115 Math. Probl. Eng. 2010, Article ID 173408, 25 p. (2010). MSC: 37L30 35B27 35Q35 37N10 76A05 76S05 PDFBibTeX XMLCite \textit{E. Novruzov}, Math. Probl. Eng. 2010, Article ID 173408, 25 p. (2010; Zbl 1333.37115) Full Text: DOI