Cheng, Sibo; Liu, Che; Guo, Yike; Arcucci, Rossella Efficient deep data assimilation with sparse observations and time-varying sensors. (English) Zbl 07807988 J. Comput. Phys. 496, Article ID 112581, 20 p. (2024). MSC: 68Txx 65Kxx 90Cxx PDFBibTeX XMLCite \textit{S. Cheng} et al., J. Comput. Phys. 496, Article ID 112581, 20 p. (2024; Zbl 07807988) Full Text: DOI arXiv
Wu, Zhizhang; Zhang, Cheng; Zhang, Zhiwen Reduced-order model-based variational inference with normalizing flows for Bayesian elliptic inverse problems. (English) Zbl 07797178 J. Comput. Appl. Math. 441, Article ID 115659, 17 p. (2024). MSC: 35R30 35J25 35R60 62F15 68T07 78M34 PDFBibTeX XMLCite \textit{Z. Wu} et al., J. Comput. Appl. Math. 441, Article ID 115659, 17 p. (2024; Zbl 07797178) Full Text: DOI
Cicci, Ludovica; Fresca, Stefania; Guo, Mengwu; Manzoni, Andrea; Zunino, Paolo Uncertainty quantification for nonlinear solid mechanics using reduced order models with Gaussian process regression. (English) Zbl 07750303 Comput. Math. Appl. 149, 1-23 (2023). MSC: 65M60 65N30 68T05 68T07 65M99 PDFBibTeX XMLCite \textit{L. Cicci} et al., Comput. Math. Appl. 149, 1--23 (2023; Zbl 07750303) Full Text: DOI arXiv
Yang, Qihong; Deng, Yangtao; Yang, Yu; He, Qiaolin; Zhang, Shiquan Neural networks based on power method and inverse power method for solving linear eigenvalue problems. (English) Zbl 07741346 Comput. Math. Appl. 147, 14-24 (2023). MSC: 65N25 68Txx 68T05 68T07 65L12 PDFBibTeX XMLCite \textit{Q. Yang} et al., Comput. Math. Appl. 147, 14--24 (2023; Zbl 07741346) Full Text: DOI arXiv
Akbari, Saeed; Dabaghian, Pedram H.; San, Omer Blending machine learning and sequential data assimilation over latent spaces for surrogate modeling of Boussinesq systems. (English) Zbl 07683345 Physica D 448, Article ID 133711, 17 p. (2023). MSC: 68Txx PDFBibTeX XMLCite \textit{S. Akbari} et al., Physica D 448, Article ID 133711, 17 p. (2023; Zbl 07683345) Full Text: DOI
Silva, Vinicius L. S.; Heaney, Claire E.; Li, Yaqi; Pain, Christopher C. Data assimilation predictive GAN (DA-PredGAN) applied to a spatio-temporal compartmental model in epidemiology. (English) Zbl 1510.68090 J. Sci. Comput. 94, No. 1, Paper No. 25, 31 p. (2023); correction ibid. 95, No. 2, Paper No. 47, 2 p. (2023). MSC: 68T05 68T07 92D30 PDFBibTeX XMLCite \textit{V. L. S. Silva} et al., J. Sci. Comput. 94, No. 1, Paper No. 25, 31 p. (2023; Zbl 1510.68090) Full Text: DOI arXiv
Fu, Jinlong; Xiao, Dunhui; Fu, Rui; Li, Chenfeng; Zhu, Chuanhua; Arcucci, Rossella; Navon, Ionel M. Physics-data combined machine learning for parametric reduced-order modelling of nonlinear dynamical systems in small-data regimes. (English) Zbl 07644844 Comput. Methods Appl. Mech. Eng. 404, Article ID 115771, 49 p. (2023). MSC: 68-XX 65-XX PDFBibTeX XMLCite \textit{J. Fu} et al., Comput. Methods Appl. Mech. Eng. 404, Article ID 115771, 49 p. (2023; Zbl 07644844) Full Text: DOI
Dabaghian, Pedram H.; Ahmed, Shady E.; San, Omer Nonintrusive reduced order modelling of convective Boussinesq flows. (English) Zbl 1508.76089 Int. J. Comput. Fluid Dyn. 36, No. 7, 578-598 (2022). MSC: 76M99 76D99 76R10 80A19 68T05 PDFBibTeX XMLCite \textit{P. H. Dabaghian} et al., Int. J. Comput. Fluid Dyn. 36, No. 7, 578--598 (2022; Zbl 1508.76089) Full Text: DOI arXiv
Cheng, Fangxiong; Xu, Hui; Feng, Xinlong Model order reduction method based on (r)POD-ANNs for parameterized time-dependent partial differential equations. (English) Zbl 1521.65112 Comput. Fluids 241, Article ID 105481, 13 p. (2022). MSC: 65M99 68T07 PDFBibTeX XMLCite \textit{F. Cheng} et al., Comput. Fluids 241, Article ID 105481, 13 p. (2022; Zbl 1521.65112) Full Text: DOI
Huang, Juntao; Cheng, Yingda; Christlieb, Andrew J.; Roberts, Luke F. Machine learning moment closure models for the radiative transfer equation. I: Directly learning a gradient based closure. (English) Zbl 1522.65143 J. Comput. Phys. 453, Article ID 110941, 21 p. (2022). MSC: 65M06 65L06 65N06 85A25 80A21 68Q32 68T07 68T09 82C70 35R09 35Q20 PDFBibTeX XMLCite \textit{J. Huang} et al., J. Comput. Phys. 453, Article ID 110941, 21 p. (2022; Zbl 1522.65143) Full Text: DOI arXiv
Kim, Youngkyu; Choi, Youngsoo; Widemann, David; Zohdi, Tarek A fast and accurate physics-informed neural network reduced order model with shallow masked autoencoder. (English) Zbl 07517153 J. Comput. Phys. 451, Article ID 110841, 29 p. (2022). MSC: 65Mxx 65Lxx 68Txx PDFBibTeX XMLCite \textit{Y. Kim} et al., J. Comput. Phys. 451, Article ID 110841, 29 p. (2022; Zbl 07517153) Full Text: DOI arXiv
Maulik, Romit; Botsas, Themistoklis; Ramachandra, Nesar; Mason, Lachlan R.; Pan, Indranil Latent-space time evolution of non-intrusive reduced-order models using Gaussian process emulation. (English) Zbl 07493969 Physica D 416, Article ID 132797, 17 p. (2021). MSC: 65P99 37M99 68T07 76B15 PDFBibTeX XMLCite \textit{R. Maulik} et al., Physica D 416, Article ID 132797, 17 p. (2021; Zbl 07493969) Full Text: DOI arXiv
Kalogeris, Ioannis; Papadopoulos, Vissarion Diffusion maps-aided neural networks for the solution of parametrized PDEs. (English) Zbl 1506.65180 Comput. Methods Appl. Mech. Eng. 376, Article ID 113568, 24 p. (2021). MSC: 65M99 68T05 PDFBibTeX XMLCite \textit{I. Kalogeris} and \textit{V. Papadopoulos}, Comput. Methods Appl. Mech. Eng. 376, Article ID 113568, 24 p. (2021; Zbl 1506.65180) Full Text: DOI
Hernandez, Quercus; Badías, Alberto; González, David; Chinesta, Francisco; Cueto, Elías Deep learning of thermodynamics-aware reduced-order models from data. (English) Zbl 1506.80005 Comput. Methods Appl. Mech. Eng. 379, Article ID 113763, 18 p. (2021). MSC: 80M99 65Q99 80A99 68T05 PDFBibTeX XMLCite \textit{Q. Hernandez} et al., Comput. Methods Appl. Mech. Eng. 379, Article ID 113763, 18 p. (2021; Zbl 1506.80005) Full Text: DOI arXiv Link
Lu, Chuan; Zhu, Xueyu Bifidelity data-assisted neural networks in nonintrusive reduced-order modeling. (English) Zbl 1466.65225 J. Sci. Comput. 87, No. 1, Paper No. 8, 30 p. (2021). MSC: 65N99 68T07 PDFBibTeX XMLCite \textit{C. Lu} and \textit{X. Zhu}, J. Sci. Comput. 87, No. 1, Paper No. 8, 30 p. (2021; Zbl 1466.65225) Full Text: DOI arXiv
Gao, Han; Wang, Jian-Xun; Zahr, Matthew J. Non-intrusive model reduction of large-scale, nonlinear dynamical systems using deep learning. (English) Zbl 1489.93013 Physica D 412, Article ID 132614, 12 p. (2020). MSC: 93B11 93A15 93C10 68T07 PDFBibTeX XMLCite \textit{H. Gao} et al., Physica D 412, Article ID 132614, 12 p. (2020; Zbl 1489.93013) Full Text: DOI arXiv
Ahmed, Shady E.; San, Omer; Rasheed, Adil; Iliescu, Traian A long short-term memory embedding for hybrid uplifted reduced order models. (English) Zbl 1505.76071 Physica D 409, Article ID 132471, 16 p. (2020). MSC: 76M99 76D05 76D99 68T05 PDFBibTeX XMLCite \textit{S. E. Ahmed} et al., Physica D 409, Article ID 132471, 16 p. (2020; Zbl 1505.76071) Full Text: DOI arXiv
Maulik, Romit; San, Omer; Jacob, Jamey D. Spatiotemporally dynamic implicit large eddy simulation using machine learning classifiers. (English) Zbl 1489.76030 Physica D 406, Article ID 132409, 12 p. (2020). MSC: 76F65 76M99 68T05 PDFBibTeX XMLCite \textit{R. Maulik} et al., Physica D 406, Article ID 132409, 12 p. (2020; Zbl 1489.76030) Full Text: DOI
Puligilla, Shivakanth Chary; Jayaraman, Balaji Assessment of end-to-end and sequential data-driven learning for non-intrusive modeling of fluid flows. (English) Zbl 1450.76032 Adv. Comput. Math. 46, No. 4, Paper No. 55, 44 p. (2020). MSC: 76M99 76M20 76D05 68T05 92B20 PDFBibTeX XMLCite \textit{S. C. Puligilla} and \textit{B. Jayaraman}, Adv. Comput. Math. 46, No. 4, Paper No. 55, 44 p. (2020; Zbl 1450.76032) Full Text: DOI arXiv
Yu, Jian; Yan, Chao; Jiang, Zhenhua; Yuan, Wu; Chen, Shusheng Adaptive non-intrusive reduced order modeling for compressible flows. (English) Zbl 1453.76118 J. Comput. Phys. 397, Article ID 108855, 27 p. (2019). MSC: 76M12 65M08 68T05 35B30 76N15 PDFBibTeX XMLCite \textit{J. Yu} et al., J. Comput. Phys. 397, Article ID 108855, 27 p. (2019; Zbl 1453.76118) Full Text: DOI
San, Omer; Maulik, Romit; Ahmed, Mansoor An artificial neural network framework for reduced order modeling of transient flows. (English) Zbl 1479.76082 Commun. Nonlinear Sci. Numer. Simul. 77, 271-287 (2019). MSC: 76M99 76D33 68T05 92B20 PDFBibTeX XMLCite \textit{O. San} et al., Commun. Nonlinear Sci. Numer. Simul. 77, 271--287 (2019; Zbl 1479.76082) Full Text: DOI arXiv
Nino Ruiz, Elias D.; Sandu, Adrian A derivative-free trust region framework for variational data assimilation. (English) Zbl 1326.65070 J. Comput. Appl. Math. 293, 164-179 (2016). MSC: 65K05 68Q10 86A10 90C15 90C51 90C59 65C05 PDFBibTeX XMLCite \textit{E. D. Nino Ruiz} and \textit{A. Sandu}, J. Comput. Appl. Math. 293, 164--179 (2016; Zbl 1326.65070) Full Text: DOI arXiv