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
Abbaszadeh, Mostafa; Azis, Mohammad Ivan; Dehghan, Mehdi; Mohammadi-Arani, Reza Reduced order model for simulation of air pollution model and application in 2D urban street canyons via the meshfree gradient smoothing method. (English) Zbl 07692044 Comput. Math. Appl. 140, 195-210 (2023). MSC: 76M25 76D05 76M12 65M06 76M20 PDFBibTeX XMLCite \textit{M. Abbaszadeh} et al., Comput. Math. Appl. 140, 195--210 (2023; Zbl 07692044) Full Text: DOI
MohammadiArani, Reza; Dehghan, Mehdi; Abbaszadeh, Mostafa Proper orthogonal decomposition-lattice Boltzmann method: simulating the air pollutant problem in street canyon areas. (English) Zbl 1492.76097 SIAM J. Sci. Comput. 44, No. 4, B885-B909 (2022). MSC: 76N15 65M22 76M28 PDFBibTeX XMLCite \textit{R. MohammadiArani} et al., SIAM J. Sci. Comput. 44, No. 4, B885--B909 (2022; Zbl 1492.76097) Full Text: DOI
Luo, Zhendong; Yang, Jing The reduced-order method of continuous space-time finite element scheme for the non-stationary incompressible flows. (English) Zbl 07518115 J. Comput. Phys. 456, Article ID 111044, 22 p. (2022). MSC: 65Mxx 76Mxx 76Dxx PDFBibTeX XMLCite \textit{Z. Luo} and \textit{J. Yang}, J. Comput. Phys. 456, Article ID 111044, 22 p. (2022; Zbl 07518115) Full Text: DOI
Dutta, Sourav; Farthing, Matthew W.; Perracchione, Emma; Savant, Gaurav; Putti, Mario A greedy non-intrusive reduced order model for shallow water equations. (English) Zbl 07512322 J. Comput. Phys. 439, Article ID 110378, 30 p. (2021). MSC: 41Axx 65Dxx 76Mxx PDFBibTeX XMLCite \textit{S. Dutta} et al., J. Comput. Phys. 439, Article ID 110378, 30 p. (2021; Zbl 07512322) Full Text: DOI arXiv
Abbaszadeh, Mostafa; Dehghan, Mehdi; Khodadadian, Amirreza; Noii, Nima; Heitzinger, Clemens; Wick, Thomas A reduced-order variational multiscale interpolating element free Galerkin technique based on proper orthogonal decomposition for solving Navier-Stokes equations coupled with a heat transfer equation: nonstationary incompressible Boussinesq equations. (English) Zbl 07510038 J. Comput. Phys. 426, Article ID 109875, 27 p. (2021). MSC: 80-XX 65-XX PDFBibTeX XMLCite \textit{M. Abbaszadeh} et al., J. Comput. Phys. 426, Article ID 109875, 27 p. (2021; Zbl 07510038) Full Text: DOI
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
Rungpitaxmana, Suchinthra; Chaturantabut, Saifon Model reduction for Fisher’s equation with an error bound. (English) Zbl 1482.65108 Thai J. Math. 19, No. 4, 1729-1762 (2021). MSC: 65L05 65L70 93B11 PDFBibTeX XMLCite \textit{S. Rungpitaxmana} and \textit{S. Chaturantabut}, Thai J. Math. 19, No. 4, 1729--1762 (2021; Zbl 1482.65108) Full Text: Link
Vu-Huu, T.; Le-Thanh, C.; Nguyen-Xuan, H.; Wahab, M. Abdel Equal-order polygonal analysis for fluid computation in curved domain. (English) Zbl 07446900 Int. J. Comput. Methods 18, No. 5, Article ID 2040003, 10 p. (2021). MSC: 76-XX 65-XX PDFBibTeX XMLCite \textit{T. Vu-Huu} et al., Int. J. Comput. Methods 18, No. 5, Article ID 2040003, 10 p. (2021; Zbl 07446900) Full Text: DOI
Li, Teng; Deng, Shiyuan; Zhang, Kun; Wei, Haibo; Wang, Runlong; Fan, Jun; Xin, Jianqiang; Yao, Jianyao A nonintrusive parametrized reduced-order model for periodic flows based on extended proper orthogonal decomposition. (English) Zbl 07446702 Int. J. Comput. Methods 18, No. 9, Article ID 2150035, 33 p. (2021). MSC: 76-XX 37-XX PDFBibTeX XMLCite \textit{T. Li} et al., Int. J. Comput. Methods 18, No. 9, Article ID 2150035, 33 p. (2021; Zbl 07446702) Full Text: DOI
Ahmed, Shady E.; Pawar, Suraj; San, Omer; Rasheed, Adil; Tabib, Mandar A nudged hybrid analysis and modeling approach for realtime wake-vortex transport and decay prediction. (English) Zbl 1521.76311 Comput. Fluids 221, Article ID 104895, 14 p. (2021). MSC: 76M10 76D25 76D17 PDFBibTeX XMLCite \textit{S. E. Ahmed} et al., Comput. Fluids 221, Article ID 104895, 14 p. (2021; Zbl 1521.76311) Full Text: DOI arXiv
Star, Sabrina; Stabile, Giovanni; Rozza, Gianluigi; Degroote, Joris A POD-Galerkin reduced order model of a turbulent convective buoyant flow of Sodium over a backward-facing step. (English) Zbl 1479.76049 Appl. Math. Modelling 89, Part 1, 486-503 (2021). MSC: 76F35 76M12 80A19 PDFBibTeX XMLCite \textit{S. Star} et al., Appl. Math. Modelling 89, Part 1, 486--503 (2021; Zbl 1479.76049) Full Text: DOI arXiv Link
Esmaeili, Mohammad; Ahmadi, Mohammad; Kazemi, Alireza A generalized DEIM technique for model order reduction of porous media simulations in reservoir optimizations. (English) Zbl 07508391 J. Comput. Phys. 422, Article ID 109769, 20 p. (2020). MSC: 76-XX 86-XX PDFBibTeX XMLCite \textit{M. Esmaeili} et al., J. Comput. Phys. 422, Article ID 109769, 20 p. (2020; Zbl 07508391) Full Text: DOI
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
Georgaka, Sokratia; Stabile, Giovanni; Star, Kelbij; Rozza, Gianluigi; Bluck, Michael J. A hybrid reduced order method for modelling turbulent heat transfer problems. (English) Zbl 1502.65087 Comput. Fluids 208, Article ID 104615, 13 p. (2020). MSC: 65M08 65D12 76D05 PDFBibTeX XMLCite \textit{S. Georgaka} et al., Comput. Fluids 208, Article ID 104615, 13 p. (2020; Zbl 1502.65087) Full Text: DOI arXiv
Abbaszadeh, Mostafa; Dehghan, Mehdi Simulation flows with multiple phases and components via the radial basis functions-finite difference (RBF-FD) procedure: Shan-Chen model. (English) Zbl 1464.65081 Eng. Anal. Bound. Elem. 119, 151-161 (2020). MSC: 65M06 65D12 65M70 PDFBibTeX XMLCite \textit{M. Abbaszadeh} and \textit{M. Dehghan}, Eng. Anal. Bound. Elem. 119, 151--161 (2020; Zbl 1464.65081) Full Text: DOI
Abbaszadeh, Mostafa; Dehghan, Mehdi A POD-based reduced-order Crank-Nicolson/fourth-order alternating direction implicit (ADI) finite difference scheme for solving the two-dimensional distributed-order Riesz space-fractional diffusion equation. (English) Zbl 1452.65145 Appl. Numer. Math. 158, 271-291 (2020). MSC: 65M06 65N06 65M99 65M15 65M12 65D30 35R11 26A33 35K57 PDFBibTeX XMLCite \textit{M. Abbaszadeh} and \textit{M. Dehghan}, Appl. Numer. Math. 158, 271--291 (2020; Zbl 1452.65145) Full Text: DOI
Abbaszadeh, Mostafa; Dehghan, Mehdi Reduced order modeling of time-dependent incompressible Navier-Stokes equation with variable density based on a local radial basis functions-finite difference (LRBF-FD) technique and the POD/DEIM method. (English) Zbl 1442.65287 Comput. Methods Appl. Mech. Eng. 364, Article ID 112914, 28 p. (2020). MSC: 65M70 65D12 76D05 PDFBibTeX XMLCite \textit{M. Abbaszadeh} and \textit{M. Dehghan}, Comput. Methods Appl. Mech. Eng. 364, Article ID 112914, 28 p. (2020; Zbl 1442.65287) Full Text: DOI
Abbaszadeh, Mostafa; Dehghan, Mehdi Investigation of the Oldroyd model as a generalized incompressible Navier-Stokes equation via the interpolating stabilized element free Galerkin technique. (English) Zbl 1444.76083 Appl. Numer. Math. 150, 274-294 (2020). Reviewer: Petr Sváček (Praha) MSC: 76M99 76M20 76A10 65M12 PDFBibTeX XMLCite \textit{M. Abbaszadeh} and \textit{M. Dehghan}, Appl. Numer. Math. 150, 274--294 (2020; Zbl 1444.76083) Full Text: DOI
Xiao, D. Error estimation of the parametric non-intrusive reduced order model using machine learning. (English) Zbl 1441.62081 Comput. Methods Appl. Mech. Eng. 355, 513-534 (2019). MSC: 62F15 62G05 62-08 PDFBibTeX XMLCite \textit{D. Xiao}, Comput. Methods Appl. Mech. Eng. 355, 513--534 (2019; Zbl 1441.62081) Full Text: DOI Link
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
Altaf, M. Umer; McCabe, M. F. A variational approach for parameter estimation based on balanced proper orthogonal decomposition. (English) Zbl 1441.65003 Comput. Methods Appl. Mech. Eng. 344, 694-710 (2019). MSC: 65C20 PDFBibTeX XMLCite \textit{M. U. Altaf} and \textit{M. F. McCabe}, Comput. Methods Appl. Mech. Eng. 344, 694--710 (2019; Zbl 1441.65003) 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
Dehghan, Mehdi; Abbaszadeh, Mostafa The use of proper orthogonal decomposition (POD) meshless RBF-FD technique to simulate the shallow water equations. (English) Zbl 1380.65301 J. Comput. Phys. 351, 478-510 (2017). MSC: 65M70 65D05 76M25 35Q35 PDFBibTeX XMLCite \textit{M. Dehghan} and \textit{M. Abbaszadeh}, J. Comput. Phys. 351, 478--510 (2017; Zbl 1380.65301) Full Text: DOI
Dehghan, Mehdi; Abbaszadeh, Mostafa Proper orthogonal decomposition variational multiscale element free Galerkin (POD-VMEFG) meshless method for solving incompressible Navier-Stokes equation. (English) Zbl 1439.76060 Comput. Methods Appl. Mech. Eng. 311, 856-888 (2016). MSC: 76M10 65M60 76D05 PDFBibTeX XMLCite \textit{M. Dehghan} and \textit{M. Abbaszadeh}, Comput. Methods Appl. Mech. Eng. 311, 856--888 (2016; Zbl 1439.76060) Full Text: DOI
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
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