Zou, Zongren; Meng, Xuhui; Psaros, Apostolos F.; Karniadakis, George E. NeuralUQ: a comprehensive library for uncertainty quantification in neural differential equations and operators. (English) Zbl 07805456 SIAM Rev. 66, No. 1, 161-190 (2024). MSC: 68T07 PDFBibTeX XMLCite \textit{Z. Zou} et al., SIAM Rev. 66, No. 1, 161--190 (2024; Zbl 07805456) Full Text: DOI arXiv
Sethi, Harpreet; Pan, Doris; Dimitrov, Pavel; Shragge, Jeffrey; Roth, Gunter; Hester, Ken Hard enforcement of physics-informed neural network solutions of acoustic wave propagation. (English) Zbl 1528.76072 Comput. Geosci. 27, No. 5, 737-751 (2023). MSC: 76Q05 68T07 PDFBibTeX XMLCite \textit{H. Sethi} et al., Comput. Geosci. 27, No. 5, 737--751 (2023; Zbl 1528.76072) Full Text: DOI
Moseley, Ben; Markham, Andrew; Nissen-Meyer, Tarje Finite basis physics-informed neural networks (FBPINNs): a scalable domain decomposition approach for solving differential equations. (English) Zbl 07726220 Adv. Comput. Math. 49, No. 4, Paper No. 62, 39 p. (2023). MSC: 65M99 68T01 PDFBibTeX XMLCite \textit{B. Moseley} et al., Adv. Comput. Math. 49, No. 4, Paper No. 62, 39 p. (2023; Zbl 07726220) Full Text: DOI arXiv
Najera-Flores, David A.; Todd, Michael D. A structure-preserving neural differential operator with embedded Hamiltonian constraints for modeling structural dynamics. (English) Zbl 1525.70003 Comput. Mech. 72, No. 2, 241-252 (2023). MSC: 70-08 70K40 68T07 PDFBibTeX XMLCite \textit{D. A. Najera-Flores} and \textit{M. D. Todd}, Comput. Mech. 72, No. 2, 241--252 (2023; Zbl 1525.70003) Full Text: DOI
Xu, Chen; Cao, Ba Trung; Yuan, Yong; Meschke, Günther Transfer learning based physics-informed neural networks for solving inverse problems in engineering structures under different loading scenarios. (English) Zbl 07653053 Comput. Methods Appl. Mech. Eng. 405, Article ID 115852, 28 p. (2023). MSC: 68-XX 74-XX PDFBibTeX XMLCite \textit{C. Xu} et al., Comput. Methods Appl. Mech. Eng. 405, Article ID 115852, 28 p. (2023; Zbl 07653053) Full Text: DOI arXiv
Psaros, Apostolos F.; Meng, Xuhui; Zou, Zongren; Guo, Ling; Karniadakis, George Em Uncertainty quantification in scientific machine learning: methods, metrics, and comparisons. (English) Zbl 07652802 J. Comput. Phys. 477, Article ID 111902, 83 p. (2023). MSC: 68Txx 65Cxx 62Fxx PDFBibTeX XMLCite \textit{A. F. Psaros} et al., J. Comput. Phys. 477, Article ID 111902, 83 p. (2023; Zbl 07652802) Full Text: DOI arXiv
Wang, Sifan; Perdikaris, Paris Long-time integration of parametric evolution equations with physics-informed DeepONets. (English) Zbl 07649276 J. Comput. Phys. 475, Article ID 111855, 18 p. (2023). MSC: 68Txx 65Lxx 65-XX PDFBibTeX XMLCite \textit{S. Wang} and \textit{P. Perdikaris}, J. Comput. Phys. 475, Article ID 111855, 18 p. (2023; Zbl 07649276) Full Text: DOI arXiv
Sheng, Hailong; Yang, Chao PFNN-2: a domain decomposed penalty-free neural network method for solving partial differential equations. (English) Zbl 1498.65155 Commun. Comput. Phys. 32, No. 4, 980-1006 (2022). MSC: 65M55 35K55 65M60 68T07 PDFBibTeX XMLCite \textit{H. Sheng} and \textit{C. Yang}, Commun. Comput. Phys. 32, No. 4, 980--1006 (2022; Zbl 1498.65155) Full Text: DOI arXiv
Cuomo, Salvatore; Schiano Di Cola, Vincenzo; Giampaolo, Fabio; Rozza, Gianluigi; Raissi, Maziar; Piccialli, Francesco Scientific machine learning through physics-informed neural networks: where we are and what’s next. (English) Zbl 07568980 J. Sci. Comput. 92, No. 3, Paper No. 88, 62 p. (2022). MSC: 68Txx 65Mxx 35Qxx PDFBibTeX XMLCite \textit{S. Cuomo} et al., J. Sci. Comput. 92, No. 3, Paper No. 88, 62 p. (2022; Zbl 07568980) Full Text: DOI arXiv
Chiu, Pao-Hsiung; Wong, Jian Cheng; Ooi, Chinchun; Dao, My Ha; Ong, Yew-Soon CAN-PINN: a fast physics-informed neural network based on coupled-automatic-numerical differentiation method. (English) Zbl 1507.65204 Comput. Methods Appl. Mech. Eng. 395, Article ID 114909, 24 p. (2022). MSC: 65M99 68T07 PDFBibTeX XMLCite \textit{P.-H. Chiu} et al., Comput. Methods Appl. Mech. Eng. 395, Article ID 114909, 24 p. (2022; Zbl 1507.65204) Full Text: DOI arXiv
Sukumar, N.; Srivastava, Ankit Exact imposition of boundary conditions with distance functions in physics-informed deep neural networks. (English) Zbl 1507.65284 Comput. Methods Appl. Mech. Eng. 389, Article ID 114333, 50 p. (2022). MSC: 65N99 68T07 PDFBibTeX XMLCite \textit{N. Sukumar} and \textit{A. Srivastava}, Comput. Methods Appl. Mech. Eng. 389, Article ID 114333, 50 p. (2022; Zbl 1507.65284) Full Text: DOI arXiv
Kovacs, Alexander; Exl, Lukas; Kornell, Alexander; Fischbacher, Johann; Hovorka, Markus; Gusenbauer, Markus; Breth, Leoni; Oezelt, Harald; Yano, Masao; Sakuma, Noritsugu; Kinoshita, Akihito; Shoji, Tetsuya; Kato, Akira; Schrefl, Thomas Conditional physics informed neural networks. (English) Zbl 1485.65086 Commun. Nonlinear Sci. Numer. Simul. 104, Article ID 106041, 15 p. (2022). MSC: 65L15 68T07 PDFBibTeX XMLCite \textit{A. Kovacs} et al., Commun. Nonlinear Sci. Numer. Simul. 104, Article ID 106041, 15 p. (2022; Zbl 1485.65086) Full Text: DOI arXiv