Fu, R.; Xiao, D.; Navon, I. M.; Fang, F.; Yang, L.; Wang, C.; Cheng, S. A non-linear non-intrusive reduced order model of fluid flow by auto-encoder and self-attention deep learning methods. (English) Zbl 1524.76277 Int. J. Numer. Methods Eng. 124, No. 13, 3087-3111 (2023). MSC: 76M22 PDFBibTeX XMLCite \textit{R. Fu} et al., Int. J. Numer. Methods Eng. 124, No. 13, 3087--3111 (2023; Zbl 1524.76277) Full Text: DOI
Arcucci, Rossella; Xiao, Dunhui; Fang, Fangxin; Navon, Ionel Michael; Wu, Pin; Pain, Christopher C.; Guo, Yi-Ke A reduced order with data assimilation model: theory and practice. (English) Zbl 1521.76314 Comput. Fluids 257, Article ID 105862, 12 p. (2023). MSC: 76M10 65M60 62R07 76F50 PDFBibTeX XMLCite \textit{R. Arcucci} et al., Comput. Fluids 257, Article ID 105862, 12 p. (2023; Zbl 1521.76314) Full Text: DOI
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
Wang, Yuepeng; Ding, Xuemei; Hu, Kun; Fang, Fangxin; Navon, I. M.; Lin, Guang Feasibility of DEIM for retrieving the initial field via dimensionality reduction. (English) Zbl 07500740 J. Comput. Phys. 429, Article ID 110005, 15 p. (2021). MSC: 65Mxx 76Mxx 76Dxx PDFBibTeX XMLCite \textit{Y. Wang} et al., J. Comput. Phys. 429, Article ID 110005, 15 p. (2021; Zbl 07500740) Full Text: DOI
Cheng, M.; Fang, F.; Pain, C. C.; Navon, I. M. Data-driven modelling of nonlinear spatio-temporal fluid flows using a deep convolutional generative adversarial network. (English) Zbl 1442.76040 Comput. Methods Appl. Mech. Eng. 365, Article ID 113000, 17 p. (2020). MSC: 76D05 76-10 76M10 65M60 PDFBibTeX XMLCite \textit{M. Cheng} et al., Comput. Methods Appl. Mech. Eng. 365, Article ID 113000, 17 p. (2020; Zbl 1442.76040) Full Text: DOI arXiv
Xiao, D.; Fang, F.; Heaney, C. E.; Navon, I. M.; Pain, C. C. A domain decomposition method for the non-intrusive reduced order modelling of fluid flow. (English) Zbl 1441.76074 Comput. Methods Appl. Mech. Eng. 354, 307-330 (2019). MSC: 76M10 65M60 65M55 76D05 PDFBibTeX XMLCite \textit{D. Xiao} et al., Comput. Methods Appl. Mech. Eng. 354, 307--330 (2019; Zbl 1441.76074) Full Text: DOI Link
Xiao, D.; Heaney, C. E.; Fang, F.; Mottet, L.; Hu, R.; Bistrian, D. A.; Aristodemou, E.; Navon, I. M.; Pain, C. C. A domain decomposition non-intrusive reduced order model for turbulent flows. (English) Zbl 1411.76072 Comput. Fluids 182, 15-27 (2019). MSC: 76M10 65M60 76D05 PDFBibTeX XMLCite \textit{D. Xiao} et al., Comput. Fluids 182, 15--27 (2019; Zbl 1411.76072) Full Text: DOI Link
Bistrian, D. A.; Navon, I. M. Efficiency of randomised dynamic mode decomposition for reduced order modelling. (English) Zbl 07474458 Int. J. Comput. Fluid Dyn. 32, No. 2-3, 88-103 (2018). MSC: 65-XX 76-XX PDFBibTeX XMLCite \textit{D. A. Bistrian} and \textit{I. M. Navon}, Int. J. Comput. Fluid Dyn. 32, No. 2--3, 88--103 (2018; Zbl 07474458) Full Text: DOI
Wang, Yuepeng; Cheng, Yue; Navon, I. Michael; Guan, Yuanhong Parameter identification techniques applied to an environmental pollution model. (English) Zbl 1412.65043 J. Ind. Manag. Optim. 14, No. 2, 817-831 (2018). MSC: 65K10 PDFBibTeX XMLCite \textit{Y. Wang} et al., J. Ind. Manag. Optim. 14, No. 2, 817--831 (2018; Zbl 1412.65043) Full Text: DOI
Xiao, D.; Fang, F.; Pain, C. C.; Navon, I. M. A parameterized non-intrusive reduced order model and error analysis for general time-dependent nonlinear partial differential equations and its applications. (English) Zbl 1439.65124 Comput. Methods Appl. Mech. Eng. 317, 868-889 (2017). MSC: 65M60 PDFBibTeX XMLCite \textit{D. Xiao} et al., Comput. Methods Appl. Mech. Eng. 317, 868--889 (2017; Zbl 1439.65124) Full Text: DOI Link
Xiao, D.; Yang, P.; Fang, F.; Xiang, J.; Pain, C. C.; Navon, I. M.; Chen, M. A non-intrusive reduced-order model for compressible fluid and fractured solid coupling and its application to blasting. (English) Zbl 1378.74067 J. Comput. Phys. 330, 221-244 (2017). MSC: 74S05 76M10 74R99 PDFBibTeX XMLCite \textit{D. Xiao} et al., J. Comput. Phys. 330, 221--244 (2017; Zbl 1378.74067) Full Text: DOI Link
Xiao, D.; Yang, P.; Fang, F.; Xiang, J.; Pain, C. C.; Navon, I. M. Non-intrusive reduced order modelling of fluid-structure interactions. (English) Zbl 1425.74167 Comput. Methods Appl. Mech. Eng. 303, 35-54 (2016). MSC: 74F10 76M10 76D05 PDFBibTeX XMLCite \textit{D. Xiao} et al., Comput. Methods Appl. Mech. Eng. 303, 35--54 (2016; Zbl 1425.74167) Full Text: DOI
Xiao, D.; Fang, F.; Buchan, A. G.; Pain, C. C.; Navon, I. M.; Muggeridge, A. Non-intrusive reduced order modelling of the Navier-Stokes equations. (English) Zbl 1423.76287 Comput. Methods Appl. Mech. Eng. 293, 522-541 (2015). MSC: 76M10 65M60 76D05 35Q30 PDFBibTeX XMLCite \textit{D. Xiao} et al., Comput. Methods Appl. Mech. Eng. 293, 522--541 (2015; Zbl 1423.76287) Full Text: DOI
Buchan, A. G.; Calloo, A. A.; Goffin, M. G.; Dargaville, S.; Fang, F.; Pain, C. C.; Navon, I. M. A POD reduced order model for resolving angular direction in neutron/photon transport problems. (English) Zbl 1352.82030 J. Comput. Phys. 296, 138-157 (2015). MSC: 82D75 82C80 35Q20 45K05 65N30 PDFBibTeX XMLCite \textit{A. G. Buchan} et al., J. Comput. Phys. 296, 138--157 (2015; Zbl 1352.82030) Full Text: DOI
Ştefănescu, R.; Sandu, A.; Navon, I. M. POD/DEIM reduced-order strategies for efficient four dimensional variational data assimilation. (English) Zbl 1349.76535 J. Comput. Phys. 295, 569-595 (2015). MSC: 76M20 65M06 65M32 76B15 90C90 PDFBibTeX XMLCite \textit{R. Ştefănescu} et al., J. Comput. Phys. 295, 569--595 (2015; Zbl 1349.76535) Full Text: DOI arXiv
Ardjmandpour, N.; Pain, C. C.; Fang, F.; Buchan, A. G.; Singer, J.; Player, M. A.; Xu, Xu; Navon, I. M.; Carter, J. Reduced order borehole induction modelling. (English) Zbl 07512419 Int. J. Comput. Fluid Dyn. 28, No. 3-4, 140-157 (2014). MSC: 78-XX 65-XX PDFBibTeX XMLCite \textit{N. Ardjmandpour} et al., Int. J. Comput. Fluid Dyn. 28, No. 3--4, 140--157 (2014; Zbl 07512419) Full Text: DOI
Xiao, D.; Fang, F.; Buchan, A. G.; Pain, C. C.; Navon, I. M.; Du, J.; Hu, G. Nonlinear model reduction for the Navier-Stokes equations using residual DEIM method. (English) Zbl 1349.76288 J. Comput. Phys. 263, 1-18 (2014). MSC: 76M10 65M60 76D05 PDFBibTeX XMLCite \textit{D. Xiao} et al., J. Comput. Phys. 263, 1--18 (2014; Zbl 1349.76288) Full Text: DOI
Fang, F.; Pain, C. C.; Navon, I. M.; Cacuci, D. G.; Chen, X. The independent set perturbation method for efficient computation of sensitivities with applications to data assimilation and a finite element shallow water model. (English) Zbl 1391.76322 Comput. Fluids 76, 33-49 (2013). MSC: 76M10 76B15 PDFBibTeX XMLCite \textit{F. Fang} et al., Comput. Fluids 76, 33--49 (2013; Zbl 1391.76322) Full Text: DOI
Buchan, A. G.; Pain, C. C.; Fang, F.; Navon, I. M. A POD reduced-order model for eigenvalue problems with application to reactor physics. (English) Zbl 1352.82018 Int. J. Numer. Methods Eng. 95, No. 12, 1011-1032 (2013). MSC: 82C80 65N25 82D75 PDFBibTeX XMLCite \textit{A. G. Buchan} et al., Int. J. Numer. Methods Eng. 95, No. 12, 1011--1032 (2013; Zbl 1352.82018) Full Text: DOI
Xiao, D.; Fang, F.; Du, J.; Pain, C. C.; Navon, I. M.; Buchan, A. G.; ElSheikh, A. H.; Hu, G. Non-linear Petrov-Galerkin methods for reduced order modelling of the Navier-Stokes equations using a mixed finite element pair. (English) Zbl 1297.76107 Comput. Methods Appl. Mech. Eng. 255, 147-157 (2013). MSC: 76M10 65M60 76D05 PDFBibTeX XMLCite \textit{D. Xiao} et al., Comput. Methods Appl. Mech. Eng. 255, 147--157 (2013; Zbl 1297.76107) Full Text: DOI
Chen, X.; Akella, S.; Navon, I. M. A dual-weighted trust-region adaptive POD 4-D var applied to a finite-volume shallow water equations model on the sphere. (English) Zbl 1426.76347 Int. J. Numer. Methods Fluids 68, No. 3, 377-402 (2012). MSC: 76M12 76U05 86A05 PDFBibTeX XMLCite \textit{X. Chen} et al., Int. J. Numer. Methods Fluids 68, No. 3, 377--402 (2012; Zbl 1426.76347) Full Text: DOI
Fang, F.; Pain, C. C.; Navon, I. M.; Gorman, G. J.; Piggott, M. D.; Allison, P. A. The independent set perturbation adjoint method: a new method of differentiating mesh-based fluids models. (English) Zbl 1285.76015 Int. J. Numer. Methods Fluids 66, No. 8, 976-999 (2011). MSC: 76M10 65M99 PDFBibTeX XMLCite \textit{F. Fang} et al., Int. J. Numer. Methods Fluids 66, No. 8, 976--999 (2011; Zbl 1285.76015) Full Text: DOI
Chen, X.; Navon, I. M.; Fang, F. A dual-weighted trust-region adaptive POD 4D-VAR applied to a finite-element shallow-water equations model. (English) Zbl 1428.76145 Int. J. Numer. Methods Fluids 65, No. 5, 520-541 (2011). MSC: 76M21 76M10 35Q35 PDFBibTeX XMLCite \textit{X. Chen} et al., Int. J. Numer. Methods Fluids 65, No. 5, 520--541 (2011; Zbl 1428.76145) Full Text: DOI
Fang, F.; Pain, C. C.; Navon, I. M.; Gorman, G. J.; Piggott, M. D.; Allison, P. A.; Goddard, A. J. H. A POD goal-oriented error measure for mesh optimization. (English) Zbl 1425.65096 Int. J. Numer. Methods Fluids 63, No. 2, 185-206 (2010). MSC: 65M15 65M50 86A05 PDFBibTeX XMLCite \textit{F. Fang} et al., Int. J. Numer. Methods Fluids 63, No. 2, 185--206 (2010; Zbl 1425.65096) Full Text: DOI
Fang, F.; Pain, C. C.; Navon, I. M.; Piggott, M. D.; Gorman, G. J.; Farrell, P. E.; Allison, P. A.; Goddard, A. J. H. A POD reduced-order 4D-Var adaptive mesh ocean modelling approach. (English) Zbl 1163.86002 Int. J. Numer. Methods Fluids 60, No. 7, 709-732 (2009). MSC: 86A05 76M10 PDFBibTeX XMLCite \textit{F. Fang} et al., Int. J. Numer. Methods Fluids 60, No. 7, 709--732 (2009; Zbl 1163.86002) Full Text: DOI