Petromichelakis, Ioannis; Kougioumtzoglou, Ioannis A. Addressing the curse of dimensionality in stochastic dynamics: a Wiener path integral variational formulation with free boundaries. (English) Zbl 1472.60089 Proc. R. Soc. Lond., A, Math. Phys. Eng. Sci. 476, No. 2243, Article ID 20200385, 18 p. (2020). MSC: 60H05 37H10 PDFBibTeX XMLCite \textit{I. Petromichelakis} and \textit{I. A. Kougioumtzoglou}, Proc. R. Soc. Lond., A, Math. Phys. Eng. Sci. 476, No. 2243, Article ID 20200385, 18 p. (2020; Zbl 1472.60089) Full Text: DOI Link
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
Jagtap, Ameya D.; Kawaguchi, Kenji; Karniadakis, George Em Locally adaptive activation functions with slope recovery for deep and physics-informed neural networks. (English) Zbl 1472.68175 Proc. R. Soc. Lond., A, Math. Phys. Eng. Sci. 476, No. 2239, Article ID 20200334, 20 p. (2020). MSC: 68T07 00A79 PDFBibTeX XMLCite \textit{A. D. Jagtap} et al., Proc. R. Soc. Lond., A, Math. Phys. Eng. Sci. 476, No. 2239, Article ID 20200334, 20 p. (2020; Zbl 1472.68175) Full Text: DOI arXiv Link
Boso, F.; Tartakovsky, D. M. Learning on dynamic statistical manifolds. (English) Zbl 1472.62011 Proc. R. Soc. Lond., A, Math. Phys. Eng. Sci. 476, No. 2239, Article ID 20200213, 19 p. (2020). MSC: 62B11 35L60 62M20 62M40 62R40 PDFBibTeX XMLCite \textit{F. Boso} and \textit{D. M. Tartakovsky}, Proc. R. Soc. Lond., A, Math. Phys. Eng. Sci. 476, No. 2239, Article ID 20200213, 19 p. (2020; Zbl 1472.62011) Full Text: DOI arXiv Link
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
Patnaik, Sansit; Hollkamp, John P.; Semperlotti, Fabio Applications of variable-order fractional operators: a review. (English) Zbl 1439.26028 Proc. R. Soc. Lond., A, Math. Phys. Eng. Sci. 476, No. 2234, Article ID 20190498, 32 p. (2020). MSC: 26A33 34A08 35R11 82C70 93C80 PDFBibTeX XMLCite \textit{S. Patnaik} et al., Proc. R. Soc. Lond., A, Math. Phys. Eng. Sci. 476, No. 2234, Article ID 20190498, 32 p. (2020; Zbl 1439.26028) Full Text: DOI
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
Mamis, K. I.; Athanassoulis, G. A.; Kapelonis, Z. G. A systematic path to non-Markovian dynamics: new response probability density function evolution equations under Gaussian coloured noise excitation. (English) Zbl 1472.60107 Proc. R. Soc. Lond., A, Math. Phys. Eng. Sci. 475, No. 2226, Article ID 20180837, 18 p. (2019). MSC: 60H25 60H30 PDFBibTeX XMLCite \textit{K. I. Mamis} et al., Proc. R. Soc. Lond., A, Math. Phys. Eng. Sci. 475, No. 2226, Article ID 20180837, 18 p. (2019; Zbl 1472.60107) Full Text: DOI arXiv
Mukherjee, Siddhartha; Dhar, Jayabrata; DasGupta, Sunando; Chakraborty, Suman Patterned surface charges coupled with thermal gradients may create giant augmentations of solute dispersion in electro-osmosis of viscoelastic fluids. (English) Zbl 1425.76306 Proc. R. Soc. Lond., A, Math. Phys. Eng. Sci. 475, No. 2221, Article ID 20180522, 18 p. (2019). MSC: 76W05 76A10 PDFBibTeX XMLCite \textit{S. Mukherjee} et al., Proc. R. Soc. Lond., A, Math. Phys. Eng. Sci. 475, No. 2221, Article ID 20180522, 18 p. (2019; Zbl 1425.76306) Full Text: DOI arXiv
Tsilifis, P.; Ghanem, R. G. Bayesian adaptation of chaos representations using variational inference and sampling on geodesics. (English) Zbl 1407.62087 Proc. R. Soc. Lond., A, Math. Phys. Eng. Sci. 474, No. 2217, Article ID 20180285, 27 p. (2018). MSC: 62F15 37D40 37D45 60G15 60G12 60H35 65C60 PDFBibTeX XMLCite \textit{P. Tsilifis} and \textit{R. G. Ghanem}, Proc. R. Soc. Lond., A, Math. Phys. Eng. Sci. 474, No. 2217, Article ID 20180285, 27 p. (2018; Zbl 1407.62087) Full Text: DOI
Perdikaris, P.; Raissi, M.; Damianou, A.; Lawrence, N. D.; Karniadakis, G. E. Nonlinear information fusion algorithms for data-efficient multi-fidelity modelling. (English) Zbl 1407.62252 Proc. R. Soc. Lond., A, Math. Phys. Eng. Sci. 473, No. 2198, Article ID 20160751, 16 p. (2017). MSC: 62J02 62M10 62H30 62P35 PDFBibTeX XMLCite \textit{P. Perdikaris} et al., Proc. R. Soc. Lond., A, Math. Phys. Eng. Sci. 473, No. 2198, Article ID 20160751, 16 p. (2017; Zbl 1407.62252) Full Text: DOI
Gouasmi, Ayoub; Parish, Eric J.; Duraisamy, Karthik A priori estimation of memory effects in reduced-order models of nonlinear systems using the Mori-Zwanzig formalism. (English) Zbl 1402.76065 Proc. R. Soc. Lond., A, Math. Phys. Eng. Sci. 473, No. 2205, Article ID 20170385, 24 p. (2017). MSC: 76G25 37N10 35Q35 PDFBibTeX XMLCite \textit{A. Gouasmi} et al., Proc. R. Soc. Lond., A, Math. Phys. Eng. Sci. 473, No. 2205, Article ID 20170385, 24 p. (2017; Zbl 1402.76065) Full Text: DOI arXiv
Qiao, Z. X.; Zhou, Y.; Wu, Z. Turbulent boundary layer under the control of different schemes. (English) Zbl 1402.76055 Proc. R. Soc. Lond., A, Math. Phys. Eng. Sci. 473, No. 2202, Article ID 20170038, 24 p. (2017). MSC: 76F40 74F10 76D55 PDFBibTeX XMLCite \textit{Z. X. Qiao} et al., Proc. R. Soc. Lond., A, Math. Phys. Eng. Sci. 473, No. 2202, Article ID 20170038, 24 p. (2017; Zbl 1402.76055) Full Text: DOI