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
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
Akushevich, I.; Yashkin, A.; Kravchenko, J.; Fang, F.; Arbeev, K.; Sloan, F.; Yashin, A. I. A forecasting model of disease prevalence based on the McKendrick-von Foerster equation. (English) Zbl 1425.92123 Math. Biosci. 311, 31-38 (2019). MSC: 92C60 92D30 35Q92 PDFBibTeX XMLCite \textit{I. Akushevich} et al., Math. Biosci. 311, 31--38 (2019; Zbl 1425.92123) Full Text: DOI Link
Yang, P.; Xiang, J.; Fang, F.; Pavlidis, D.; Pain, C. C. Modelling of fluid-structure interaction for moderate Reynolds number flows using an immersed-body method. (English) Zbl 1411.76073 Comput. Fluids 179, 613-631 (2019). MSC: 76M10 76F60 65M60 74F10 76D05 PDFBibTeX XMLCite \textit{P. Yang} et al., Comput. Fluids 179, 613--631 (2019; Zbl 1411.76073) Full Text: DOI
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
Xiao, D.; Du, J.; Fang, F.; Pain, C. C.; Li, J. Parameterised non-intrusive reduced order methods for ensemble Kalman filter data assimilation. (English) Zbl 1410.76397 Comput. Fluids 177, 69-77 (2018). MSC: 76M35 PDFBibTeX XMLCite \textit{D. Xiao} et al., Comput. Fluids 177, 69--77 (2018; Zbl 1410.76397) 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
Akushevich, I.; Yashkin, A. P.; Kravchenko, J.; Fang, F.; Arbeev, K.; Sloan, F.; Yashin, A. I. Theory of partitioning of disease prevalence and mortality in observational data. (English) Zbl 1369.92109 Theor. Popul. Biol. 114, 117-127 (2017). MSC: 92D30 92C50 PDFBibTeX XMLCite \textit{I. Akushevich} et al., Theor. Popul. Biol. 114, 117--127 (2017; Zbl 1369.92109) 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
Yang, P.; Xiang, J.; Fang, F.; Pavlidis, D.; Latham, J.-P.; Pain, C. C. Modelling of fluid-structure interaction with multiphase viscous flows using an immersed-body method. (English) Zbl 1349.76291 J. Comput. Phys. 321, 571-592 (2016). MSC: 76M10 74S05 65M60 74F10 76D05 76T30 PDFBibTeX XMLCite \textit{P. Yang} et al., J. Comput. Phys. 321, 571--592 (2016; Zbl 1349.76291) Full Text: DOI
Adam, A.; Pavlidis, D.; Percival, J. R.; Salinas, P.; Xie, Z.; Fang, F.; Pain, C. C.; Muggeridge, A. H.; Jackson, M. D. Higher-order conservative interpolation between control-volume meshes: application to advection and multiphase flow problems with dynamic mesh adaptivity. (English) Zbl 1349.76164 J. Comput. Phys. 321, 512-531 (2016). MSC: 76M10 65M60 76T30 PDFBibTeX XMLCite \textit{A. Adam} et al., J. Comput. Phys. 321, 512--531 (2016; Zbl 1349.76164) Full Text: DOI
Xiao, D.; Fang, F.; Pain, C.; Hu, G. Non-intrusive reduced-order modelling of the Navier-Stokes equations based on RBF interpolation. (English) Zbl 1455.76099 Int. J. Numer. Methods Fluids 79, No. 11, 580-595 (2015). MSC: 76M10 76D05 65M60 PDFBibTeX XMLCite \textit{D. Xiao} et al., Int. J. Numer. Methods Fluids 79, No. 11, 580--595 (2015; Zbl 1455.76099) 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
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
Du, Juan; Navon, I. M.; Zhu, Jiang; Fang, Fangxin; Alekseev, A. K. Reduced order modeling based on POD of a parabolized Navier-Stokes equations model II: trust region POD 4D VAR data assimilation. (English) Zbl 1319.76030 Comput. Math. Appl. 65, No. 3, 380-394 (2013). MSC: 76M20 65M32 65M06 76D05 PDFBibTeX XMLCite \textit{J. Du} et al., Comput. Math. Appl. 65, No. 3, 380--394 (2013; Zbl 1319.76030) Full Text: DOI
Du, J.; Fang, F.; Pain, C. C.; Navon, I. M.; Zhu, J.; Ham, D. A. POD reduced-order unstructured mesh modeling applied to 2D and 3D fluid flow. (English) Zbl 1319.76026 Comput. Math. Appl. 65, No. 3, 362-379 (2013). MSC: 76M10 65M60 76D05 PDFBibTeX XMLCite \textit{J. Du} et al., Comput. Math. Appl. 65, No. 3, 362--379 (2013; Zbl 1319.76026) 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
Fang, F.; Pain, C. C.; Navon, I. M.; Elsheikh, A. H.; Du, J.; Xiao, D. Non-linear Petrov-Galerkin methods for reduced order hyperbolic equations and discontinuous finite element methods. (English) Zbl 1284.65132 J. Comput. Phys. 234, 540-559 (2013). MSC: 65M60 35L02 PDFBibTeX XMLCite \textit{F. Fang} et al., J. Comput. Phys. 234, 540--559 (2013; Zbl 1284.65132) Full Text: DOI
Hossen, M. J.; Navon, I. M.; Fang, F. A penalized four-dimensional variational data assimilation method for reducing forecast error related to adaptive observations. (English) Zbl 1412.86004 Int. J. Numer. Methods Fluids 70, No. 10, 1207-1220 (2012). MSC: 86A10 65N08 76M12 PDFBibTeX XMLCite \textit{M. J. Hossen} et al., Int. J. Numer. Methods Fluids 70, No. 10, 1207--1220 (2012; Zbl 1412.86004) 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
Fang, F.; Pain, C. C.; Navon, I. M.; Piggott, M. D.; Gorman, G. J.; Allison, P. A.; Goddard, A. J. H. Reduced-order modelling of an adaptive mesh ocean model. (English) Zbl 1155.86004 Int. J. Numer. Methods Fluids 59, No. 8, 827-851 (2009). MSC: 86A05 PDFBibTeX XMLCite \textit{F. Fang} et al., Int. J. Numer. Methods Fluids 59, No. 8, 827--851 (2009; Zbl 1155.86004) Full Text: DOI
Power, P. W.; Pain, C. C.; Piggott, M. D.; Fang, F.; Gorman, G. J.; Umpleby, A. P.; Goddard, A. J. H.; Navon, I. M. Adjoint a posteriori error measures for anisotropic mesh optimisation. (English) Zbl 1206.65250 Comput. Math. Appl. 52, No. 8-9, 1213-1242 (2006). MSC: 65N50 65N15 PDFBibTeX XMLCite \textit{P. W. Power} et al., Comput. Math. Appl. 52, No. 8--9, 1213--1242 (2006; Zbl 1206.65250) Full Text: DOI
Butz, C. J.; Fang, F. Incorporating evidence in Bayesian networks with the select operator. (English) Zbl 1121.68365 Kégl, Balázs (ed.) et al., Advances in artificial intelligence. 18th conference of the Canadian Society for Computational Studies of Intelligence, Canadian AI 2005, Victoria, Canada, May 9–11, 2005. Proceedings. Berlin: Springer (ISBN 3-540-25864-7/pbk). Lecture Notes in Computer Science 3501. Lecture Notes in Artificial Intelligence, 297-301 (2005). MSC: 68T05 68P15 68T35 PDFBibTeX XMLCite \textit{C. J. Butz} and \textit{F. Fang}, Lect. Notes Comput. Sci. 3501, 297--301 (2005; Zbl 1121.68365) Full Text: DOI
Fang, F.; Pain, C. C.; Piggott, M. D.; Gorman, G. J.; Goddard, A. J. H. An adaptive mesh adjoint data assimilation method applied to free surface flows. (English) Zbl 1134.86004 Int. J. Numer. Methods Fluids 47, No. 8-9, 995-1001 (2005). MSC: 86-08 86A05 PDFBibTeX XMLCite \textit{F. Fang} et al., Int. J. Numer. Methods Fluids 47, No. 8--9, 995--1001 (2005; Zbl 1134.86004) Full Text: DOI
Fang, Fangxin; Qi, Li; Chen, Zhaohe; Peng, Yu Application of body-fitted curvilinear coordinate transformation in 3-D seepage flow computation. (English) Zbl 0851.76048 J. Hydrodyn., Ser. B 6, No. 4, 9-15 (1994). MSC: 76M20 76S05 PDFBibTeX XMLCite \textit{F. Fang} et al., J. Hydrodyn., Ser. B 6, No. 4, 9--15 (1994; Zbl 0851.76048)