Chi, Xurong; Chen, Jingrun; Yang, Zhouwang The random feature method for solving interface problems. (English) Zbl 07820263 Comput. Methods Appl. Mech. Eng. 420, Article ID 116719, 18 p. (2024). MSC: 65-XX 76-XX PDFBibTeX XMLCite \textit{X. Chi} et al., Comput. Methods Appl. Mech. Eng. 420, Article ID 116719, 18 p. (2024; Zbl 07820263) Full Text: DOI arXiv
Zhang, Shengning; Zhou, Yuqian; Liu, Qian; Li, Kebing Data-driven wave solutions of (2+1)-dimensional nonlinear dispersive long wave equation by deep learning. (English) Zbl 07801773 Commun. Nonlinear Sci. Numer. Simul. 129, Article ID 107688, 23 p. (2024). MSC: 68T07 35B32 35C07 35C08 35L05 65M70 76B15 PDFBibTeX XMLCite \textit{S. Zhang} et al., Commun. Nonlinear Sci. Numer. Simul. 129, Article ID 107688, 23 p. (2024; Zbl 07801773) Full Text: DOI
Cui, Tiangang; Wang, Zhongjian; Zhang, Zhiwen A variational neural network approach for glacier modelling with nonlinear rheology. (English) Zbl 07783915 Commun. Comput. Phys. 34, No. 4, 934-954 (2023). MSC: 65J15 35-XX 68T07 76A05 86A05 PDFBibTeX XMLCite \textit{T. Cui} et al., Commun. Comput. Phys. 34, No. 4, 934--954 (2023; Zbl 07783915) Full Text: DOI arXiv
Huang, Haoxiang; Yang, Vigor; Liu, Yingjie Neural networks with local converging inputs (NNLCI) for solving conservation laws. II: 2D problems. (English) Zbl 07783914 Commun. Comput. Phys. 34, No. 4, 907-933 (2023). MSC: 65L99 65M99 65N99 68T99 76L05 PDFBibTeX XMLCite \textit{H. Huang} et al., Commun. Comput. Phys. 34, No. 4, 907--933 (2023; Zbl 07783914) Full Text: DOI
Zhu, Xingwen; Hu, Xiaozhe; Sun, Pengtao Physics-informed neural networks for solving dynamic two-phase interface problems. (English) Zbl 1528.35105 SIAM J. Sci. Comput. 45, No. 6, A2912-A2944 (2023). MSC: 35Q30 65N99 65M06 65K10 65M15 68T07 68Q32 74F10 76D05 76T06 82C32 PDFBibTeX XMLCite \textit{X. Zhu} et al., SIAM J. Sci. Comput. 45, No. 6, A2912--A2944 (2023; Zbl 1528.35105) Full Text: DOI arXiv
Mohan, Manil T. Large deviations for the two-time-scale stochastic convective Brinkman-Forchheimer equations. (English) Zbl 07757715 J. Differ. Equations 376, 469-537 (2023). MSC: 60H15 60F10 76Dxx 35R60 35Q30 PDFBibTeX XMLCite \textit{M. T. Mohan}, J. Differ. Equations 376, 469--537 (2023; Zbl 07757715) Full Text: DOI arXiv
Nguwi, Jiang Yu; Privault, Nicolas Numerical solution of the modified and non-Newtonian Burgers equations by stochastic coded trees. (English) Zbl 07749868 Japan J. Ind. Appl. Math. 40, No. 3, 1745-1763 (2023). MSC: 65-XX 35G20 60H30 60J85 76M35 65C05 PDFBibTeX XMLCite \textit{J. Y. Nguwi} and \textit{N. Privault}, Japan J. Ind. Appl. Math. 40, No. 3, 1745--1763 (2023; Zbl 07749868) Full Text: DOI
Huang, Haoxiang; Yang, Vigor; Liu, Yingjie Neural networks with local converging inputs (NNLCI) for solving conservation laws. I: 1D problems. (English) Zbl 1519.65018 Commun. Comput. Phys. 34, No. 2, 290-317 (2023). MSC: 65L99 35L65 68T07 76L05 76M20 PDFBibTeX XMLCite \textit{H. Huang} et al., Commun. Comput. Phys. 34, No. 2, 290--317 (2023; Zbl 1519.65018) Full Text: DOI
Nguwi, Jiang Yu; Penent, Guillaume; Privault, Nicolas Numerical solution of the incompressible Navier-Stokes equation by a deep branching Algorithm. (English) Zbl 07738853 Commun. Comput. Phys. 34, No. 2, 261-289 (2023). MSC: 65-XX 35Q30 76M35 76D05 60H30 60J85 65C05 PDFBibTeX XMLCite \textit{J. Y. Nguwi} et al., Commun. Comput. Phys. 34, No. 2, 261--289 (2023; Zbl 07738853) Full Text: DOI arXiv
Menier, Emmanuel; Bucci, Michele Alessandro; Yagoubi, Mouadh; Mathelin, Lionel; Schoenauer, Marc CD-ROM: complemented deep – reduced order model. (English) Zbl 07737567 Comput. Methods Appl. Mech. Eng. 410, Article ID 115985, 31 p. (2023). MSC: 76-XX 65-XX PDFBibTeX XMLCite \textit{E. Menier} et al., Comput. Methods Appl. Mech. Eng. 410, Article ID 115985, 31 p. (2023; Zbl 07737567) Full Text: DOI arXiv
Craig, Katy; Elamvazhuthi, Karthik; Haberland, Matt; Turanova, Olga A blob method for inhomogeneous diffusion with applications to multi-agent control and sampling. (English) Zbl 1525.35200 Math. Comput. 92, No. 344, 2575-2654 (2023). Reviewer: Lucio Galeati (Lausanne) MSC: 35Q35 35Q62 35Q68 35Q82 35Q84 65M12 82C22 93A16 76S05 35B40 82C31 68T07 35R60 PDFBibTeX XMLCite \textit{K. Craig} et al., Math. Comput. 92, No. 344, 2575--2654 (2023; Zbl 1525.35200) Full Text: DOI arXiv
Hu, Ruimeng; Lin, Quyuan; Raydan, Alan; Tang, Sui Higher-order error estimates for physics-informed neural networks approximating the primitive equations. (English) Zbl 07726379 SN Partial Differ. Equ. Appl. 4, No. 4, Paper No. 34, 35 p. (2023). MSC: 35Q86 35Q35 86A05 86A10 76U60 35A35 68T07 68Q32 35B65 35B45 35D35 35A01 35A02 PDFBibTeX XMLCite \textit{R. Hu} et al., SN Partial Differ. Equ. Appl. 4, No. 4, Paper No. 34, 35 p. (2023; Zbl 07726379) Full Text: DOI arXiv
Goraya, Shoaib; Sobh, Nahil; Masud, Arif Error estimates and physics informed augmentation of neural networks for thermally coupled incompressible Navier Stokes equations. (English) Zbl 1523.76077 Comput. Mech. 72, No. 2, 267-289 (2023). MSC: 76M99 76D05 68T07 68T05 PDFBibTeX XMLCite \textit{S. Goraya} et al., Comput. Mech. 72, No. 2, 267--289 (2023; Zbl 1523.76077) Full Text: DOI arXiv
Meng, Xuhui Variational inference in neural functional prior using normalizing flows: application to differential equation and operator learning problems. (English) Zbl 1518.76046 AMM, Appl. Math. Mech., Engl. Ed. 44, No. 7, 1111-1124 (2023). MSC: 76M99 76S05 68T05 PDFBibTeX XMLCite \textit{X. Meng}, AMM, Appl. Math. Mech., Engl. Ed. 44, No. 7, 1111--1124 (2023; Zbl 1518.76046) Full Text: DOI arXiv
Sirignano, Justin; Macart, Jonathan F. Deep learning closure models for large-eddy simulation of flows around bluff bodies. (English) Zbl 07710508 J. Fluid Mech. 966, Paper No. A26, 23 p. (2023). MSC: 76F65 76M99 68T05 68T07 PDFBibTeX XMLCite \textit{J. Sirignano} and \textit{J. F. Macart}, J. Fluid Mech. 966, Paper No. A26, 23 p. (2023; Zbl 07710508) Full Text: DOI arXiv
Yang, Qihong; Yang, Yu; Cui, Tao; He, Qiaolin FDM-PINN: physics-informed neural network based on fictitious domain method. (English) Zbl 1524.76008 Int. J. Comput. Math. 100, No. 3, 511-524 (2023). MSC: 76-10 PDFBibTeX XMLCite \textit{Q. Yang} et al., Int. J. Comput. Math. 100, No. 3, 511--524 (2023; Zbl 1524.76008) Full Text: DOI
Zhang, Wen; Li, Jian The robust physics-informed neural networks for a typical fourth-order phase field model. (English) Zbl 07692035 Comput. Math. Appl. 140, 64-77 (2023). MSC: 65M60 76M10 65M12 68T05 35Q30 PDFBibTeX XMLCite \textit{W. Zhang} and \textit{J. Li}, Comput. Math. Appl. 140, 64--77 (2023; Zbl 07692035) Full Text: DOI
Liu, Wenkai; Liu, Yang; Li, Hong Time difference physics-informed neural network for fractional water wave models. (English) Zbl 1509.65074 Results Appl. Math. 17, Article ID 100347, 14 p. (2023). MSC: 65M06 68T07 26A33 35R11 76B15 35Q35 PDFBibTeX XMLCite \textit{W. Liu} et al., Results Appl. Math. 17, Article ID 100347, 14 p. (2023; Zbl 1509.65074) Full Text: DOI
Coti Zelati, Michele; Elgindi, Tarek M.; Widmayer, Klaus Stationary structures near the Kolmogorov and Poiseuille flows in the 2d Euler equations. (English) Zbl 1509.35195 Arch. Ration. Mech. Anal. 247, No. 1, Paper No. 12, 37 p. (2023). MSC: 35Q31 76B03 76D05 76E30 35B65 35B36 PDFBibTeX XMLCite \textit{M. Coti Zelati} et al., Arch. Ration. Mech. Anal. 247, No. 1, Paper No. 12, 37 p. (2023; Zbl 1509.35195) Full Text: DOI arXiv
Zhang, Wen; Li, Jian CPINNs: a coupled physics-informed neural networks for the closed-loop geothermal system. (English) Zbl 1524.76336 Comput. Math. Appl. 132, 161-179 (2023). MSC: 76M99 76M10 76D05 65M12 68T05 65N30 PDFBibTeX XMLCite \textit{W. Zhang} and \textit{J. Li}, Comput. Math. Appl. 132, 161--179 (2023; Zbl 1524.76336) Full Text: DOI
Yue, Jing; Li, Jian Efficient coupled deep neural networks for the time-dependent coupled Stokes-Darcy problems. (English) Zbl 1510.76173 Appl. Math. Comput. 437, Article ID 127514, 19 p. (2023). MSC: 76S05 76M10 76D07 35Q30 PDFBibTeX XMLCite \textit{J. Yue} and \textit{J. Li}, Appl. Math. Comput. 437, Article ID 127514, 19 p. (2023; Zbl 1510.76173) Full Text: DOI
Minakowski, P.; Richter, T. A priori and a posteriori error estimates for the deep Ritz method applied to the Laplace and Stokes problem. (English) Zbl 1502.65213 J. Comput. Appl. Math. 421, Article ID 114845, 16 p. (2023). MSC: 65N30 65N15 68T07 76D07 35J05 76M10 PDFBibTeX XMLCite \textit{P. Minakowski} and \textit{T. Richter}, J. Comput. Appl. Math. 421, Article ID 114845, 16 p. (2023; Zbl 1502.65213) Full Text: DOI arXiv
Naito, Riu; Yamada, Toshihiro Deep weak approximation of SDEs: a spatial approximation scheme for solving Kolmogorov equations. (English) Zbl 07714903 Int. J. Comput. Methods 19, No. 8, Article ID 2142014, 21 p. (2022). MSC: 65-XX 76-XX PDFBibTeX XMLCite \textit{R. Naito} and \textit{T. Yamada}, Int. J. Comput. Methods 19, No. 8, Article ID 2142014, 21 p. (2022; Zbl 07714903) Full Text: DOI
Wang, Yueyang; Chen, Guanggan; Yang, Min Deviation principles of a stochastic Leray-\(\alpha\) system with fractional dissipation. (English) Zbl 1512.35493 Stoch. Dyn. 22, No. 8, Article ID 2240027, 25 p. (2022). Reviewer: Alain Brillard (Riedisheim) MSC: 35Q35 76F55 60H15 60F05 60F10 26A33 35R11 35R60 PDFBibTeX XMLCite \textit{Y. Wang} et al., Stoch. Dyn. 22, No. 8, Article ID 2240027, 25 p. (2022; Zbl 1512.35493) Full Text: DOI
Zhang, Xin-Lei; Xiao, Heng; Luo, Xiaodong; He, Guowei Ensemble Kalman method for learning turbulence models from indirect observation data. (English) Zbl 1498.76050 J. Fluid Mech. 949, Paper No. A26, 35 p. (2022). MSC: 76F99 76M99 76-10 68T05 PDFBibTeX XMLCite \textit{X.-L. Zhang} et al., J. Fluid Mech. 949, Paper No. A26, 35 p. (2022; Zbl 1498.76050) Full Text: DOI arXiv
Lai, Ming-Chih; Chang, Che-Chia; Lin, Wei-Syuan; Hu, Wei-Fan; Lin, Te-Sheng A shallow Ritz method for elliptic problems with singular sources. (English) Zbl 07592144 J. Comput. Phys. 469, Article ID 111547, 14 p. (2022). MSC: 65Nxx 35Jxx 76Mxx PDFBibTeX XMLCite \textit{M.-C. Lai} et al., J. Comput. Phys. 469, Article ID 111547, 14 p. (2022; Zbl 07592144) Full Text: DOI arXiv
Li, Jian; Yue, Jing; Zhang, Wen; Duan, Wansuo The deep learning Galerkin method for the general Stokes equations. (English) Zbl 07590392 J. Sci. Comput. 93, No. 1, Paper No. 5, 20 p. (2022). MSC: 65Mxx 76-XX PDFBibTeX XMLCite \textit{J. Li} et al., J. Sci. Comput. 93, No. 1, Paper No. 5, 20 p. (2022; Zbl 07590392) Full Text: DOI arXiv
Zhu, Xingwen; He, Mingyan; Sun, Pengtao Comparative studies on mesh-free deep neural network approach versus finite element method for solving coupled nonlinear hyperbolic/wave equations. (English) Zbl 1513.65394 Int. J. Numer. Anal. Model. 19, No. 5, 603-629 (2022). MSC: 65M60 65M06 65N30 65K10 65M12 35L57 35L75 35L70 68Q32 68T07 76B25 35C08 35Q53 PDFBibTeX XMLCite \textit{X. Zhu} et al., Int. J. Numer. Anal. Model. 19, No. 5, 603--629 (2022; Zbl 1513.65394) Full Text: Link
Park, Kevin Min Seong; Stinchcombe, Adam R. Deep reinforcement learning of viscous incompressible flow. (English) Zbl 07568555 J. Comput. Phys. 467, Article ID 111455, 21 p. (2022). MSC: 76Dxx 35Qxx 65Mxx PDFBibTeX XMLCite \textit{K. M. S. Park} and \textit{A. R. Stinchcombe}, J. Comput. Phys. 467, Article ID 111455, 21 p. (2022; Zbl 07568555) Full Text: DOI
Biswas, A.; Tian, J.; Ulusoy, S. Error estimates for deep learning methods in fluid dynamics. (English) Zbl 1492.35216 Numer. Math. 151, No. 3, 753-777 (2022). MSC: 35Q35 35Q30 76D05 65M70 68T07 35B35 93C20 PDFBibTeX XMLCite \textit{A. Biswas} et al., Numer. Math. 151, No. 3, 753--777 (2022; Zbl 1492.35216) Full Text: DOI arXiv
Dong, Suchuan; Yang, Jielin On computing the hyperparameter of extreme learning machines: algorithm and application to computational PDEs, and comparison with classical and high-order finite elements. (English) Zbl 07536780 J. Comput. Phys. 463, Article ID 111290, 41 p. (2022). MSC: 68Txx 65Mxx 76Mxx PDFBibTeX XMLCite \textit{S. Dong} and \textit{J. Yang}, J. Comput. Phys. 463, Article ID 111290, 41 p. (2022; Zbl 07536780) Full Text: DOI arXiv
Chen, Yuyan; Dong, Bin; Xu, Jinchao Meta-mgnet: meta multigrid networks for solving parameterized partial differential equations. (English) Zbl 07518081 J. Comput. Phys. 455, Article ID 110996, 26 p. (2022). MSC: 65Nxx 68Txx 76Mxx PDFBibTeX XMLCite \textit{Y. Chen} et al., J. Comput. Phys. 455, Article ID 110996, 26 p. (2022; Zbl 07518081) Full Text: DOI arXiv
Hu, Jia-Wei; Zhang, Wei-Wei Mesh-Conv: convolution operator with mesh resolution independence for flow field modeling. (English) Zbl 07517729 J. Comput. Phys. 452, Article ID 110896, 20 p. (2022). MSC: 68Txx 76Mxx 65Mxx PDFBibTeX XMLCite \textit{J.-W. Hu} and \textit{W.-W. Zhang}, J. Comput. Phys. 452, Article ID 110896, 20 p. (2022; Zbl 07517729) Full Text: DOI
Liu, Yujie; Yang, Chao VPVnet: a velocity-pressure-vorticity neural network method for the Stokes’ equations under reduced regularity. (English) Zbl 1492.76040 Commun. Comput. Phys. 31, No. 3, 739-770 (2022). MSC: 76D07 65N12 65N15 35B45 PDFBibTeX XMLCite \textit{Y. Liu} and \textit{C. Yang}, Commun. Comput. Phys. 31, No. 3, 739--770 (2022; Zbl 1492.76040) Full Text: DOI arXiv
van der Meer, Remco; Oosterlee, Cornelis W.; Borovykh, Anastasia Optimally weighted loss functions for solving PDEs with neural networks. (English) Zbl 1518.65143 J. Comput. Appl. Math. 405, Article ID 113887, 18 p. (2022). Reviewer: José Augusto Ferreira (Coimbra) MSC: 65N99 68T07 65N35 65K10 65C20 65N75 35J15 76R50 PDFBibTeX XMLCite \textit{R. van der Meer} et al., J. Comput. Appl. Math. 405, Article ID 113887, 18 p. (2022; Zbl 1518.65143) Full Text: DOI arXiv
Lou, Qin; Meng, Xuhui; Karniadakis, George Em Physics-informed neural networks for solving forward and inverse flow problems via the Boltzmann-BGK formulation. (English) Zbl 07516434 J. Comput. Phys. 447, Article ID 110676, 20 p. (2021). MSC: 76Mxx 76Pxx 68Txx PDFBibTeX XMLCite \textit{Q. Lou} et al., J. Comput. Phys. 447, Article ID 110676, 20 p. (2021; Zbl 07516434) Full Text: DOI arXiv
Dong, Suchuan; Li, Zongwei A modified batch intrinsic plasticity method for pre-training the random coefficients of extreme learning machines. (English) Zbl 07515845 J. Comput. Phys. 445, Article ID 110585, 31 p. (2021). MSC: 68Txx 65Mxx 76Dxx PDFBibTeX XMLCite \textit{S. Dong} and \textit{Z. Li}, J. Comput. Phys. 445, Article ID 110585, 31 p. (2021; Zbl 07515845) Full Text: DOI arXiv
Xiao, Tianbai; Frank, Martin Using neural networks to accelerate the solution of the Boltzmann equation. (English) Zbl 07515420 J. Comput. Phys. 443, Article ID 110521, 22 p. (2021). MSC: 68Txx 76Pxx 90Cxx PDFBibTeX XMLCite \textit{T. Xiao} and \textit{M. Frank}, J. Comput. Phys. 443, Article ID 110521, 22 p. (2021; Zbl 07515420) Full Text: DOI arXiv
Cai, Shengze; Wang, Zhicheng; Lu, Lu; Zaki, Tamer A.; Karniadakis, George Em DeepM&Mnet: inferring the electroconvection multiphysics fields based on operator approximation by neural networks. (English) Zbl 07513856 J. Comput. Phys. 436, Article ID 110296, 17 p. (2021). MSC: 76Mxx 68Txx 76Fxx PDFBibTeX XMLCite \textit{S. Cai} et al., J. Comput. Phys. 436, Article ID 110296, 17 p. (2021; Zbl 07513856) Full Text: DOI arXiv
Dong, Suchuan; Ni, Naxian A method for representing periodic functions and enforcing exactly periodic boundary conditions with deep neural networks. (English) Zbl 07503727 J. Comput. Phys. 435, Article ID 110242, 30 p. (2021). MSC: 65Mxx 76Mxx 90Cxx PDFBibTeX XMLCite \textit{S. Dong} and \textit{N. Ni}, J. Comput. Phys. 435, Article ID 110242, 30 p. (2021; Zbl 07503727) 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
Kossaczká, Tatiana; Ehrhardt, Matthias; Günther, Michael Enhanced fifth order WENO shock-capturing schemes with deep learning. (English) Zbl 1481.65136 Results Appl. Math. 12, Article ID 100201, 20 p. (2021). MSC: 65M06 65N06 68T07 76L05 35Q31 35Q53 PDFBibTeX XMLCite \textit{T. Kossaczká} et al., Results Appl. Math. 12, Article ID 100201, 20 p. (2021; Zbl 1481.65136) Full Text: DOI arXiv
Zeng, Yang; Wu, Jin-Long; Xiao, Heng Enforcing imprecise constraints on generative adversarial networks for emulating physical systems. (English) Zbl 1490.76120 Commun. Comput. Phys. 30, No. 3, 635-665 (2021). MSC: 76F99 62P35 91A05 PDFBibTeX XMLCite \textit{Y. Zeng} et al., Commun. Comput. Phys. 30, No. 3, 635--665 (2021; Zbl 1490.76120) Full Text: DOI arXiv
Zhou, Xu-Hui; Han, Jiequn; Xiao, Heng Learning nonlocal constitutive models with neural networks. (English) Zbl 1506.76003 Comput. Methods Appl. Mech. Eng. 384, Article ID 113927, 27 p. (2021). MSC: 76-10 68T07 76M99 92B20 PDFBibTeX XMLCite \textit{X.-H. Zhou} et al., Comput. Methods Appl. Mech. Eng. 384, Article ID 113927, 27 p. (2021; Zbl 1506.76003) Full Text: DOI arXiv
Itzá Balam, Reymundo; Hernandez-Lopez, Francisco; Trejo-Sánchez, Joel; Uh Zapata, Miguel An immersed boundary neural network for solving elliptic equations with singular forces on arbitrary domains. (English) Zbl 1493.65246 Math. Biosci. Eng. 18, No. 1, 22-56 (2021). MSC: 65N35 65N06 68T07 35J30 35R02 76T06 PDFBibTeX XMLCite \textit{R. Itzá Balam} et al., Math. Biosci. Eng. 18, No. 1, 22--56 (2021; Zbl 1493.65246) Full Text: DOI
Chen, Xinyang; Yang, Gengchao; Yao, Qinghe; Nie, Zisen; Jiang, Zichao A compressed lattice Boltzmann method based on ConvLSTM and resnet. (English) Zbl 1524.76279 Comput. Math. Appl. 97, 162-174 (2021). MSC: 76M28 76D05 68T05 76P05 65M75 PDFBibTeX XMLCite \textit{X. Chen} et al., Comput. Math. Appl. 97, 162--174 (2021; Zbl 1524.76279) Full Text: DOI
Wang, Rui-Qi; Ling, Liming; Zeng, Delu; Feng, Bao-Feng A deep learning improved numerical method for the simulation of rogue waves of nonlinear Schrödinger equation. (English) Zbl 1480.35363 Commun. Nonlinear Sci. Numer. Simul. 101, Article ID 105896, 13 p. (2021). Reviewer: Jiqiang Zheng (Beijing) MSC: 35Q55 35Q41 76B25 65M70 65L06 65N35 68Q32 68T07 35C08 PDFBibTeX XMLCite \textit{R.-Q. Wang} et al., Commun. Nonlinear Sci. Numer. Simul. 101, Article ID 105896, 13 p. (2021; Zbl 1480.35363) Full Text: DOI
Cai, Shengze; Wang, Zhicheng; Fuest, Frederik; Jeon, Young Jin; Gray, Callum; Karniadakis, George Em Flow over an espresso cup: inferring 3-D velocity and pressure fields from tomographic background oriented Schlieren via physics-informed neural networks. (English) Zbl 1461.76417 J. Fluid Mech. 915, Paper No. A102, 17 p. (2021). MSC: 76R05 PDFBibTeX XMLCite \textit{S. Cai} et al., J. Fluid Mech. 915, Paper No. A102, 17 p. (2021; Zbl 1461.76417) Full Text: DOI arXiv
Zhong, Linlin; Gu, Qi; Wu, Bingyu Deep learning for thermal plasma simulation: solving 1-D arc model as an example. (English) Zbl 1511.82041 Comput. Phys. Commun. 257, Article ID 107496, 6 p. (2020). MSC: 82D10 68T05 76X05 PDFBibTeX XMLCite \textit{L. Zhong} et al., Comput. Phys. Commun. 257, Article ID 107496, 6 p. (2020; Zbl 1511.82041) Full Text: DOI arXiv
Sirignano, Justin; MacArt, Jonathan F.; Freund, Jonathan B. DPM: a deep learning PDE augmentation method with application to large-eddy simulation. (English) Zbl 07508424 J. Comput. Phys. 423, Article ID 109811, 21 p. (2020). MSC: 76-XX 86-XX PDFBibTeX XMLCite \textit{J. Sirignano} et al., J. Comput. Phys. 423, Article ID 109811, 21 p. (2020; Zbl 07508424) Full Text: DOI arXiv
Jagtap, Ameya D.; Karniadakis, George Em Extended physics-informed neural networks (XPINNs): a generalized space-time domain decomposition based deep learning framework for nonlinear partial differential equations. (English) Zbl 07419158 Commun. Comput. Phys. 28, No. 5, 2002-2041 (2020). MSC: 65N55 65M55 65N21 35E05 35E15 76L05 74B05 68T07 68Q32 35J05 35Q35 PDFBibTeX XMLCite \textit{A. D. Jagtap} and \textit{G. E. Karniadakis}, Commun. Comput. Phys. 28, No. 5, 2002--2041 (2020; Zbl 07419158) Full Text: DOI
Barré, J.; Bernardin, C.; Chétrite, R.; Chopra, Y.; Mariani, M. From fluctuating kinetics to fluctuating hydrodynamics: a \(\Gamma \)-convergence of large deviations functionals approach. (English) Zbl 1453.82053 J. Stat. Phys. 180, No. 1-6, 1095-1127 (2020). MSC: 82C22 82C40 82C31 60F10 76R50 35Q82 35Q83 35R60 PDFBibTeX XMLCite \textit{J. Barré} et al., J. Stat. Phys. 180, No. 1--6, 1095--1127 (2020; Zbl 1453.82053) Full Text: DOI arXiv
Beck, Margaret; Cooper, Eric; Lord, Gabriel; Spiliopoulos, Konstantinos Selection of quasi-stationary states in the stochastically forced Navier-Stokes equation on the torus. (English) Zbl 1446.37064 J. Nonlinear Sci. 30, No. 4, 1677-1702 (2020). Reviewer: Piotr Biler (Wrocław) MSC: 37L55 37N10 37H10 35Q30 76D05 76D06 76D17 PDFBibTeX XMLCite \textit{M. Beck} et al., J. Nonlinear Sci. 30, No. 4, 1677--1702 (2020; Zbl 1446.37064) Full Text: DOI arXiv
Sun, Luning; Gao, Han; Pan, Shaowu; Wang, Jian-Xun Surrogate modeling for fluid flows based on physics-constrained deep learning without simulation data. (English) Zbl 1442.76096 Comput. Methods Appl. Mech. Eng. 361, Article ID 112732, 25 p. (2020). MSC: 76M99 65Z05 76Z05 PDFBibTeX XMLCite \textit{L. Sun} et al., Comput. Methods Appl. Mech. Eng. 361, Article ID 112732, 25 p. (2020; Zbl 1442.76096) Full Text: DOI arXiv
Zhu, Yinhao; Zabaras, Nicholas; Koutsourelakis, Phaedon-Stelios; Perdikaris, Paris Physics-constrained deep learning for high-dimensional surrogate modeling and uncertainty quantification without labeled data. (English) Zbl 1452.68172 J. Comput. Phys. 394, 56-81 (2019). MSC: 68T07 35B30 65N75 76S05 PDFBibTeX XMLCite \textit{Y. Zhu} et al., J. Comput. Phys. 394, 56--81 (2019; Zbl 1452.68172) Full Text: DOI arXiv
Cruz, Matheus A.; Thompson, Roney L.; Sampaio, Luiz E. B.; Bacchi, Raphael D. A. The use of the Reynolds force vector in a physics informed machine learning approach for predictive turbulence modeling. (English) Zbl 1519.76081 Comput. Fluids 192, Article ID 104258, 14 p. (2019). MSC: 76F65 PDFBibTeX XMLCite \textit{M. A. Cruz} et al., Comput. Fluids 192, Article ID 104258, 14 p. (2019; Zbl 1519.76081) Full Text: DOI