Yang, Yibo; Bhouri, Mohamed Aziz; Perdikaris, Paris Bayesian differential programming for robust systems identification under uncertainty. (English) Zbl 1472.68166 Proc. R. Soc. Lond., A, Math. Phys. Eng. Sci. 476, No. 2243, Article ID 20200290, 23 p. (2020). MSC: 68T05 93-10 93B30 PDFBibTeX XMLCite \textit{Y. Yang} et al., Proc. R. Soc. Lond., A, Math. Phys. Eng. Sci. 476, No. 2243, Article ID 20200290, 23 p. (2020; Zbl 1472.68166) Full Text: DOI arXiv Link
Kaheman, Kadierdan; Kutz, J. Nathan; Brunton, Steven L. SINDy-PI: a robust algorithm for parallel implicit sparse identification of nonlinear dynamics. (English) Zbl 1473.93007 Proc. R. Soc. Lond., A, Math. Phys. Eng. Sci. 476, No. 2242, Article ID 20200279, 25 p. (2020). MSC: 93B30 93-10 PDFBibTeX XMLCite \textit{K. Kaheman} et al., Proc. R. Soc. Lond., A, Math. Phys. Eng. Sci. 476, No. 2242, Article ID 20200279, 25 p. (2020; Zbl 1473.93007) Full Text: DOI arXiv
Erichson, N. Benjamin; Mathelin, Lionel; Yao, Zhewei; Brunton, Steven L.; Mahoney, Michael W.; Kutz, J. Nathan Shallow neural networks for fluid flow reconstruction with limited sensors. (English) Zbl 1472.68172 Proc. R. Soc. Lond., A, Math. Phys. Eng. Sci. 476, No. 2238, Article ID 20200097, 25 p. (2020). MSC: 68T07 76M99 PDFBibTeX XMLCite \textit{N. B. Erichson} et al., Proc. R. Soc. Lond., A, Math. Phys. Eng. Sci. 476, No. 2238, Article ID 20200097, 25 p. (2020; Zbl 1472.68172) Full Text: DOI arXiv Link
Huang, Xun Deep neural networks for waves assisted by the Wiener-Hopf method. (English) Zbl 1472.68174 Proc. R. Soc. Lond., A, Math. Phys. Eng. Sci. 476, No. 2235, Article ID 20190846, 22 p. (2020). MSC: 68T07 35Q35 76B15 PDFBibTeX XMLCite \textit{X. Huang}, Proc. R. Soc. Lond., A, Math. Phys. Eng. Sci. 476, No. 2235, Article ID 20190846, 22 p. (2020; Zbl 1472.68174) Full Text: DOI
Sapsis, Themistoklis P. Output-weighted optimal sampling for Bayesian regression and rare event statistics using few samples. (English) Zbl 1439.62177 Proc. R. Soc. Lond., A, Math. Phys. Eng. Sci. 476, No. 2234, Article ID 20190834, 23 p. (2020). MSC: 62K05 62F15 62D05 PDFBibTeX XMLCite \textit{T. P. Sapsis}, Proc. R. Soc. Lond., A, Math. Phys. Eng. Sci. 476, No. 2234, Article ID 20190834, 23 p. (2020; Zbl 1439.62177) Full Text: DOI arXiv Link
Lagergren, John H.; Nardini, John T.; Lavigne, G. Michael; Rutter, Erica M.; Flores, Kevin B. Learning partial differential equations for biological transport models from noisy spatio-temporal data. (English) Zbl 1439.35493 Proc. R. Soc. Lond., A, Math. Phys. Eng. Sci. 476, No. 2234, Article ID 20190800, 21 p. (2020). MSC: 35Q92 62F10 92B20 PDFBibTeX XMLCite \textit{J. H. Lagergren} et al., Proc. R. Soc. Lond., A, Math. Phys. Eng. Sci. 476, No. 2234, Article ID 20190800, 21 p. (2020; Zbl 1439.35493) Full Text: DOI arXiv Link
Babaee, H. An observation-driven time-dependent basis for a reduced description of transient stochastic systems. (English) Zbl 1472.60004 Proc. R. Soc. Lond., A, Math. Phys. Eng. Sci. 475, No. 2231, Article ID 20190506, 22 p. (2019). MSC: 60-08 37H10 60H15 PDFBibTeX XMLCite \textit{H. Babaee}, Proc. R. Soc. Lond., A, Math. Phys. Eng. Sci. 475, No. 2231, Article ID 20190506, 22 p. (2019; Zbl 1472.60004) Full Text: DOI arXiv Link
Krueger, Paul S.; Hahsler, Michael; Olinick, Eli V.; Williams, Sheila H.; Zharfa, Mohammadreza Quantitative classification of vortical flows based on topological features using graph matching. (English) Zbl 1472.76036 Proc. R. Soc. Lond., A, Math. Phys. Eng. Sci. 475, No. 2228, Article ID 20180897, 16 p. (2019). MSC: 76D17 05C22 76D25 PDFBibTeX XMLCite \textit{P. S. Krueger} et al., Proc. R. Soc. Lond., A, Math. Phys. Eng. Sci. 475, No. 2228, Article ID 20180897, 16 p. (2019; Zbl 1472.76036) Full Text: DOI Link
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
Kaiser, E.; Kutz, J. N.; Brunton, S. L. Sparse identification of nonlinear dynamics for model predictive control in the low-data limit. (English) Zbl 1425.93175 Proc. R. Soc. Lond., A, Math. Phys. Eng. Sci. 474, No. 2219, Article ID 20180335, 25 p. (2018). MSC: 93C55 93B40 68T05 PDFBibTeX XMLCite \textit{E. Kaiser} et al., Proc. R. Soc. Lond., A, Math. Phys. Eng. Sci. 474, No. 2219, Article ID 20180335, 25 p. (2018; Zbl 1425.93175) Full Text: DOI arXiv
Zhang, Sheng; Lin, Guang Robust data-driven discovery of governing physical laws with error bars. (English) Zbl 1407.62267 Proc. R. Soc. Lond., A, Math. Phys. Eng. Sci. 474, No. 2217, Article ID 20180305, 22 p. (2018). MSC: 62J05 62F15 62P35 PDFBibTeX XMLCite \textit{S. Zhang} and \textit{G. Lin}, Proc. R. Soc. Lond., A, Math. Phys. Eng. Sci. 474, No. 2217, Article ID 20180305, 22 p. (2018; Zbl 1407.62267) Full Text: DOI
Vlachas, Pantelis R.; Byeon, Wonmin; Wan, Zhong Y.; Sapsis, Themistoklis P.; Koumoutsakos, Petros Data-driven forecasting of high-dimensional chaotic systems with long short-term memory networks. (English) Zbl 1402.92030 Proc. R. Soc. Lond., A, Math. Phys. Eng. Sci. 474, No. 2213, Article ID 20170844, 20 p. (2018). MSC: 92B20 62H30 86A32 PDFBibTeX XMLCite \textit{P. R. Vlachas} et al., Proc. R. Soc. Lond., A, Math. Phys. Eng. Sci. 474, No. 2213, Article ID 20170844, 20 p. (2018; Zbl 1402.92030) Full Text: DOI arXiv
Mangan, N. M.; Kutz, J. N.; Brunton, S. L.; Proctor, J. L. Model selection for dynamical systems via sparse regression and information criteria. (English) Zbl 1404.65308 Proc. R. Soc. Lond., A, Math. Phys. Eng. Sci. 473, No. 2204, Article ID 20170009, 16 p. (2017). MSC: 65Pxx 37M10 62B10 PDFBibTeX XMLCite \textit{N. M. Mangan} et al., Proc. R. Soc. Lond., A, Math. Phys. Eng. Sci. 473, No. 2204, Article ID 20170009, 16 p. (2017; Zbl 1404.65308) Full Text: DOI arXiv
Schaeffer, Hayden Learning partial differential equations via data discovery and sparse optimization. (English) Zbl 1404.35397 Proc. R. Soc. Lond., A, Math. Phys. Eng. Sci. 473, No. 2197, Article ID 20160446, 20 p. (2017). MSC: 35Q53 37M99 76L05 76R10 76Fxx 65M99 62P35 PDFBibTeX XMLCite \textit{H. Schaeffer}, Proc. R. Soc. Lond., A, Math. Phys. Eng. Sci. 473, No. 2197, Article ID 20160446, 20 p. (2017; Zbl 1404.35397) Full Text: DOI Link