Venturi, Daniele; Li, Xiantao The Mori-Zwanzig formulation of deep learning. (English) Zbl 07696874 Res. Math. Sci. 10, No. 2, Paper No. 23, 47 p. (2023). MSC: 68-XX 92-XX PDFBibTeX XMLCite \textit{D. Venturi} and \textit{X. Li}, Res. Math. Sci. 10, No. 2, Paper No. 23, 47 p. (2023; Zbl 07696874) Full Text: DOI arXiv
Barros de Moraes, Eduardo A.; D’Elia, Marta; Zayernouri, Mohsen Machine learning of nonlocal micro-structural defect evolutions in crystalline materials. (English) Zbl 07644208 Comput. Methods Appl. Mech. Eng. 403, Part B, Article ID 115743, 20 p. (2023). MSC: 74-XX 82-XX PDFBibTeX XMLCite \textit{E. A. Barros de Moraes} et al., Comput. Methods Appl. Mech. Eng. 403, Part B, Article ID 115743, 20 p. (2023; Zbl 07644208) Full Text: DOI arXiv
Schilling, Tanja Coarse-grained modelling out of equilibrium. (English) Zbl 07566487 Phys. Rep. 972, 1-45 (2022). MSC: 82C40 82C35 60J65 82D15 82C31 82M36 35Q84 35R60 PDFBibTeX XMLCite \textit{T. Schilling}, Phys. Rep. 972, 1--45 (2022; Zbl 07566487) Full Text: DOI arXiv
González, David; Chinesta, Francisco; Cueto, Elías Learning non-Markovian physics from data. (English) Zbl 07511420 J. Comput. Phys. 428, Article ID 109982, 14 p. (2021). MSC: 68-XX 00-XX PDFBibTeX XMLCite \textit{D. González} et al., J. Comput. Phys. 428, Article ID 109982, 14 p. (2021; Zbl 07511420) Full Text: DOI Link
Zhu, Yuanran; Venturi, Daniele Hypoellipticity and the Mori-Zwanzig formulation of stochastic differential equations. (English) Zbl 1489.60107 J. Math. Phys. 62, No. 10, Article ID 103505, 20 p. (2021). MSC: 60H10 47D07 47F10 PDFBibTeX XMLCite \textit{Y. Zhu} and \textit{D. Venturi}, J. Math. Phys. 62, No. 10, Article ID 103505, 20 p. (2021; Zbl 1489.60107) Full Text: DOI arXiv
Venturi, Daniele; Dektor, Alec Spectral methods for nonlinear functionals and functional differential equations. (English) Zbl 1477.46079 Res. Math. Sci. 8, No. 2, Paper No. 27, 39 p. (2021). MSC: 46T20 46N40 35R15 47J05 46G05 65J15 PDFBibTeX XMLCite \textit{D. Venturi} and \textit{A. Dektor}, Res. Math. Sci. 8, No. 2, Paper No. 27, 39 p. (2021; Zbl 1477.46079) Full Text: DOI arXiv
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
Zhu, Yuanran; Venturi, Daniele Generalized Langevin equations for systems with local interactions. (English) Zbl 1437.82019 J. Stat. Phys. 178, No. 5, 1217-1247 (2020). MSC: 82C31 82C22 82M60 35Q82 PDFBibTeX XMLCite \textit{Y. Zhu} and \textit{D. Venturi}, J. Stat. Phys. 178, No. 5, 1217--1247 (2020; Zbl 1437.82019) Full Text: DOI arXiv