Lin, Shuning; Chen, Yong Gradient-enhanced physics-informed neural networks based on transfer learning for inverse problems of the variable coefficient differential equations. (English) Zbl 07814534 Physica D 459, Article ID 134023, 21 p. (2024). MSC: 35Q55 35Q41 35R30 35C08 68T07 78A60 76U65 65K10 65M99 35R60 PDFBibTeX XMLCite \textit{S. Lin} and \textit{Y. Chen}, Physica D 459, Article ID 134023, 21 p. (2024; Zbl 07814534) Full Text: DOI arXiv
Zheng, Haoyang; Huang, Yao; Huang, Ziyang; Hao, Wenrui; Lin, Guang HomPINNs: homotopy physics-informed neural networks for solving the inverse problems of nonlinear differential equations with multiple solutions. (English) Zbl 07811337 J. Comput. Phys. 500, Article ID 112751, 16 p. (2024). MSC: 65Nxx 68Txx 35Qxx PDFBibTeX XMLCite \textit{H. Zheng} et al., J. Comput. Phys. 500, Article ID 112751, 16 p. (2024; Zbl 07811337) Full Text: DOI arXiv
Nguyen, Hai V.; Bui-Thanh, Tan TNet: a model-constrained Tikhonov network approach for inverse problems. (English) Zbl 07805922 SIAM J. Sci. Comput. 46, No. 1, C77-C100 (2024). MSC: 68T07 65M32 PDFBibTeX XMLCite \textit{H. V. Nguyen} and \textit{T. Bui-Thanh}, SIAM J. Sci. Comput. 46, No. 1, C77--C100 (2024; Zbl 07805922) Full Text: DOI arXiv
Zhang, Xiaoxuan; Garikipati, Krishna Label-free learning of elliptic partial differential equation solvers with generalizability across boundary value problems. (English) Zbl 07788072 Comput. Methods Appl. Mech. Eng. 417, Part B, Article ID 116214, 18 p. (2023). MSC: 68-XX 35-XX PDFBibTeX XMLCite \textit{X. Zhang} and \textit{K. Garikipati}, Comput. Methods Appl. Mech. Eng. 417, Part B, Article ID 116214, 18 p. (2023; Zbl 07788072) Full Text: DOI arXiv
Ma, Lei; Li, Rongxin; Zeng, Fanhai; Guo, Ling; Karniadakis, George Em Bi-orthogonal fPINN: a physics-informed neural network method for solving time-dependent stochastic fractional PDEs. (English) Zbl 07783920 Commun. Comput. Phys. 34, No. 4, 1133-1176 (2023). MSC: 65M32 68T07 68Q32 65C05 65M06 65D32 49M41 65M12 65M15 35R30 35R60 26A33 35R11 PDFBibTeX XMLCite \textit{L. Ma} et al., Commun. Comput. Phys. 34, No. 4, 1133--1176 (2023; Zbl 07783920) Full Text: DOI arXiv
Wang, Honghui; Lu, Lu; Song, Shiji; Huang, Gao Learning specialized activation functions for physics-informed neural networks. (English) Zbl 07783913 Commun. Comput. Phys. 34, No. 4, 869-906 (2023). MSC: 65M99 68T07 PDFBibTeX XMLCite \textit{H. Wang} et al., Commun. Comput. Phys. 34, No. 4, 869--906 (2023; Zbl 07783913) Full Text: DOI arXiv
Jiao, Yuling; Yang, Jerry Zhijian; Yuan, Cheng; Zhou, Junyu A rate of convergence of weak adversarial neural networks for the second order parabolic PDEs. (English) Zbl 07783561 Commun. Comput. Phys. 34, No. 3, 813-836 (2023). MSC: 62G05 65N12 65N15 68T07 PDFBibTeX XMLCite \textit{Y. Jiao} et al., Commun. Comput. Phys. 34, No. 3, 813--836 (2023; Zbl 07783561) Full Text: DOI
Cao, Fujun; Gao, Fei; Guo, Xiaobin; Yuan, Dongfang Physics-informed neural networks with parameter asymptotic strategy for learning singularly perturbed convection-dominated problem. (English) Zbl 1525.65098 Comput. Math. Appl. 150, 229-242 (2023). MSC: 65M70 68T07 76D10 80A19 PDFBibTeX XMLCite \textit{F. Cao} et al., Comput. Math. Appl. 150, 229--242 (2023; Zbl 1525.65098) Full Text: DOI
Vadeboncoeur, Arnaud; Akyildiz, Ömer Deniz; Kazlauskaite, Ieva; Girolami, Mark; Cirak, Fehmi Fully probabilistic deep models for forward and inverse problems in parametric PDEs. (English) Zbl 07771285 J. Comput. Phys. 491, Article ID 112369, 25 p. (2023). MSC: 68Txx 65Nxx 65Mxx PDFBibTeX XMLCite \textit{A. Vadeboncoeur} et al., J. Comput. Phys. 491, Article ID 112369, 25 p. (2023; Zbl 07771285) Full Text: DOI arXiv
Nganyu Tanyu, Derick; Ning, Jianfeng; Freudenberg, Tom; Heilenkötter, Nick; Rademacher, Andreas; Iben, Uwe; Maass, Peter Deep learning methods for partial differential equations and related parameter identification problems. (English) Zbl 1527.35501 Inverse Probl. 39, No. 10, Article ID 103001, 75 p. (2023). MSC: 35R30 65M32 PDFBibTeX XMLCite \textit{D. Nganyu Tanyu} et al., Inverse Probl. 39, No. 10, Article ID 103001, 75 p. (2023; Zbl 1527.35501) Full Text: DOI arXiv OA License
Zeng, Li; Wan, Xiaoliang; Zhou, Tao Adaptive deep density approximation for fractional Fokker-Planck equations. (English) Zbl 07766138 J. Sci. Comput. 97, No. 3, Paper No. 68, 31 p. (2023). MSC: 65M75 65C30 68T07 PDFBibTeX XMLCite \textit{L. Zeng} et al., J. Sci. Comput. 97, No. 3, Paper No. 68, 31 p. (2023; Zbl 07766138) Full Text: DOI arXiv
Shang, Yong; Wang, Fei; Sun, Jingbo Randomized neural network with Petrov-Galerkin methods for solving linear and nonlinear partial differential equations. (English) Zbl 1525.65128 Commun. Nonlinear Sci. Numer. Simul. 127, Article ID 107518, 20 p. (2023). MSC: 65N30 68T07 PDFBibTeX XMLCite \textit{Y. Shang} et al., Commun. Nonlinear Sci. Numer. Simul. 127, Article ID 107518, 20 p. (2023; Zbl 1525.65128) Full Text: DOI
Pu, Juncai; Chen, Yong Complex dynamics on the one-dimensional quantum droplets via time piecewise PINNs. (English) Zbl 07736381 Physica D 454, Article ID 133851, 14 p. (2023). MSC: 68-XX 92-XX PDFBibTeX XMLCite \textit{J. Pu} and \textit{Y. Chen}, Physica D 454, Article ID 133851, 14 p. (2023; Zbl 07736381) Full Text: DOI arXiv
Moseley, Ben; Markham, Andrew; Nissen-Meyer, Tarje Finite basis physics-informed neural networks (FBPINNs): a scalable domain decomposition approach for solving differential equations. (English) Zbl 07726220 Adv. Comput. Math. 49, No. 4, Paper No. 62, 39 p. (2023). MSC: 65M99 68T01 PDFBibTeX XMLCite \textit{B. Moseley} et al., Adv. Comput. Math. 49, No. 4, Paper No. 62, 39 p. (2023; Zbl 07726220) Full Text: DOI arXiv
Guo, Jiawei; Yao, Yanzhong; Wang, Han; Gu, Tongxiang Pre-training strategy for solving evolution equations based on physics-informed neural networks. (English) Zbl 07705900 J. Comput. Phys. 489, Article ID 112258, 19 p. (2023). MSC: 65Mxx 68Txx 90Cxx PDFBibTeX XMLCite \textit{J. Guo} et al., J. Comput. Phys. 489, Article ID 112258, 19 p. (2023; Zbl 07705900) Full Text: DOI arXiv
Eliasof, Moshe; Ephrath, Jonathan; Ruthotto, Lars; Treister, Eran MGIC: Multigrid-in-channels neural network architectures. (English) Zbl 07704375 SIAM J. Sci. Comput. 45, No. 3, S307-S328 (2023). MSC: 68T07 65N55 68T45 PDFBibTeX XMLCite \textit{M. Eliasof} et al., SIAM J. Sci. Comput. 45, No. 3, S307--S328 (2023; Zbl 07704375) Full Text: DOI arXiv
Heldmann, Fabian; Berkhahn, Sarah; Ehrhardt, Matthias; Klamroth, Kathrin PINN training using biobjective optimization: the trade-off between data loss and residual loss. (English) Zbl 07696976 J. Comput. Phys. 488, Article ID 112211, 21 p. (2023). MSC: 65Mxx 68Txx 90Cxx PDFBibTeX XMLCite \textit{F. Heldmann} et al., J. Comput. Phys. 488, Article ID 112211, 21 p. (2023; Zbl 07696976) Full Text: DOI arXiv
Mostajeran, F.; Hosseini, S. M. Radial basis function neural network (RBFNN) approximation of Cauchy inverse problems of the Laplace equation. (English) Zbl 07691972 Comput. Math. Appl. 141, 129-144 (2023). MSC: 65-XX 35R30 68T05 65N21 90C25 65M06 PDFBibTeX XMLCite \textit{F. Mostajeran} and \textit{S. M. Hosseini}, Comput. Math. Appl. 141, 129--144 (2023; Zbl 07691972) Full Text: DOI
Song, Jin; Yan, Zhenya Deep learning soliton dynamics and complex potentials recognition for 1D and 2D \(\mathcal{PT}\)-symmetric saturable nonlinear Schrödinger equations. (English) Zbl 07683358 Physica D 448, Article ID 133729, 21 p. (2023). MSC: 68T07 68T05 35C08 68T10 35Q55 PDFBibTeX XMLCite \textit{J. Song} and \textit{Z. Yan}, Physica D 448, Article ID 133729, 21 p. (2023; Zbl 07683358) Full Text: DOI
Siegel, Jonathan W.; Hong, Qingguo; Jin, Xianlin; Hao, Wenrui; Xu, Jinchao Greedy training algorithms for neural networks and applications to PDEs. (English) Zbl 07679188 J. Comput. Phys. 484, Article ID 112084, 27 p. (2023). MSC: 68Txx 41Axx 65Nxx PDFBibTeX XMLCite \textit{J. W. Siegel} et al., J. Comput. Phys. 484, Article ID 112084, 27 p. (2023; Zbl 07679188) Full Text: DOI arXiv
Wu, Sidi; Zhu, Aiqing; Tang, Yifa; Lu, Benzhuo Convergence of physics-informed neural networks applied to linear second-order elliptic interface problems. (English) Zbl 1509.65145 Commun. Comput. Phys. 33, No. 2, 596-627 (2023). MSC: 65N75 68T07 82B24 PDFBibTeX XMLCite \textit{S. Wu} et al., Commun. Comput. Phys. 33, No. 2, 596--627 (2023; Zbl 1509.65145) Full Text: DOI arXiv
Beck, Christian; Hutzenthaler, Martin; Jentzen, Arnulf; Kuckuck, Benno An overview on deep learning-based approximation methods for partial differential equations. (English) Zbl 07675828 Discrete Contin. Dyn. Syst., Ser. B 28, No. 6, 3697-3746 (2023). MSC: 65-02 68T07 35-02 65M99 PDFBibTeX XMLCite \textit{C. Beck} et al., Discrete Contin. Dyn. Syst., Ser. B 28, No. 6, 3697--3746 (2023; Zbl 07675828) Full Text: DOI arXiv
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
Pu, Jun-Cai; Chen, Yong Data-driven forward-inverse problems for Yajima-Oikawa system using deep learning with parameter regularization. (English) Zbl 1523.76019 Commun. Nonlinear Sci. Numer. Simul. 118, Article ID 107051, 19 p. (2023). MSC: 76B15 76M99 76M21 68T07 PDFBibTeX XMLCite \textit{J.-C. Pu} and \textit{Y. Chen}, Commun. Nonlinear Sci. Numer. Simul. 118, Article ID 107051, 19 p. (2023; Zbl 1523.76019) Full Text: DOI arXiv
Darbon, Jérôme; Dower, Peter M.; Meng, Tingwei Neural network architectures using min-plus algebra for solving certain high-dimensional optimal control problems and Hamilton-Jacobi PDEs. (English) Zbl 1507.49019 Math. Control Signals Syst. 35, No. 1, 1-44 (2023). MSC: 49K20 35F21 93B70 PDFBibTeX XMLCite \textit{J. Darbon} et al., Math. Control Signals Syst. 35, No. 1, 1--44 (2023; Zbl 1507.49019) Full Text: DOI arXiv
Penwarden, Michael; Zhe, Shandian; Narayan, Akil; Kirby, Robert M. A metalearning approach for physics-informed neural networks (PINNs): application to parameterized PDEs. (English) Zbl 07652806 J. Comput. Phys. 477, Article ID 111912, 17 p. (2023). MSC: 65Mxx 68Txx 41Axx PDFBibTeX XMLCite \textit{M. Penwarden} et al., J. Comput. Phys. 477, Article ID 111912, 17 p. (2023; Zbl 07652806) Full Text: DOI arXiv
Psaros, Apostolos F.; Meng, Xuhui; Zou, Zongren; Guo, Ling; Karniadakis, George Em Uncertainty quantification in scientific machine learning: methods, metrics, and comparisons. (English) Zbl 07652802 J. Comput. Phys. 477, Article ID 111902, 83 p. (2023). MSC: 68Txx 65Cxx 62Fxx PDFBibTeX XMLCite \textit{A. F. Psaros} et al., J. Comput. Phys. 477, Article ID 111902, 83 p. (2023; Zbl 07652802) Full Text: DOI arXiv
Fernández de la Mata, Félix; Gijón, Alfonso; Molina-Solana, Miguel; Gómez-Romero, Juan Physics-informed neural networks for data-driven simulation: advantages, limitations, and opportunities. (English) Zbl 07649318 Physica A 610, Article ID 128415, 10 p. (2023). MSC: 82-XX PDFBibTeX XMLCite \textit{F. Fernández de la Mata} et al., Physica A 610, Article ID 128415, 10 p. (2023; Zbl 07649318) Full Text: DOI
Li, Yongchao; Wang, Yanyan; Yan, Liang Surrogate modeling for Bayesian inverse problems based on physics-informed neural networks. (English) Zbl 07649264 J. Comput. Phys. 475, Article ID 111841, 17 p. (2023). MSC: 65Cxx 68Txx 62Fxx PDFBibTeX XMLCite \textit{Y. Li} et al., J. Comput. Phys. 475, Article ID 111841, 17 p. (2023; Zbl 07649264) Full Text: DOI
Wu, Chenxi; Zhu, Min; Tan, Qinyang; Kartha, Yadhu; Lu, Lu A comprehensive study of non-adaptive and residual-based adaptive sampling for physics-informed neural networks. (English) Zbl 07644158 Comput. Methods Appl. Mech. Eng. 403, Part A, Article ID 115671, 23 p. (2023). MSC: 62-XX 65-XX PDFBibTeX XMLCite \textit{C. Wu} et al., Comput. Methods Appl. Mech. Eng. 403, Part A, Article ID 115671, 23 p. (2023; Zbl 07644158) Full Text: DOI arXiv
Mowlavi, Saviz; Nabi, Saleh Optimal control of PDEs using physics-informed neural networks. (English) Zbl 07625400 J. Comput. Phys. 473, Article ID 111731, 22 p. (2023). MSC: 65Mxx 35Rxx 76Fxx PDFBibTeX XMLCite \textit{S. Mowlavi} and \textit{S. Nabi}, J. Comput. Phys. 473, Article ID 111731, 22 p. (2023; Zbl 07625400) Full Text: DOI arXiv
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
Liu, Qian; Zhou, Yuqian; Li, Kebing; Zhang, Shengning Application of the dynamical system method and the deep learning method to solve the new (3+1)-dimensional fractional modified Benjamin-Bona-Mahony equation. (English) Zbl 1523.35108 Nonlinear Dyn. 110, No. 4, 3737-3750 (2022). MSC: 35C07 35R11 37C29 68T07 PDFBibTeX XMLCite \textit{Q. Liu} et al., Nonlinear Dyn. 110, No. 4, 3737--3750 (2022; Zbl 1523.35108) Full Text: DOI
Cuomo, Salvatore; Giampaolo, Fabio; Izzo, Stefano; Nitsch, Carlo; Piccialli, Francesco; Trombetti, Cristina A physics-informed learning approach to Bernoulli-type free boundary problems. (English) Zbl 1504.65231 Comput. Math. Appl. 128, 34-43 (2022). MSC: 65M99 35Q35 PDFBibTeX XMLCite \textit{S. Cuomo} et al., Comput. Math. Appl. 128, 34--43 (2022; Zbl 1504.65231) Full Text: DOI
De Ryck, Tim; Mishra, Siddhartha Error analysis for physics-informed neural networks (PINNs) approximating Kolmogorov PDEs. (English) Zbl 1502.65170 Adv. Comput. Math. 48, No. 6, Paper No. 79, 40 p. (2022). MSC: 65M99 68T07 65M15 35K55 35K05 91G20 35Q53 PDFBibTeX XMLCite \textit{T. De Ryck} and \textit{S. Mishra}, Adv. Comput. Math. 48, No. 6, Paper No. 79, 40 p. (2022; Zbl 1502.65170) Full Text: DOI arXiv
Jin, Pengzhan; Meng, Shuai; Lu, Lu MIONet: learning multiple-input operators via tensor product. (English) Zbl 07617460 SIAM J. Sci. Comput. 44, No. 6, A3490-A3514 (2022). MSC: 47-08 47H99 65D15 68Q32 68T07 PDFBibTeX XMLCite \textit{P. Jin} et al., SIAM J. Sci. Comput. 44, No. 6, A3490--A3514 (2022; Zbl 07617460) Full Text: DOI arXiv
Wilson, Joshua P.; Dai, Weizhong; Bora, Aniruddha; Boyt, Jacob C. A new artificial neural network method for solving Schrödinger equations on unbounded domains. (English) Zbl 1498.65189 Commun. Comput. Phys. 32, No. 4, 1039-1060 (2022). MSC: 65N06 65N12 68T07 PDFBibTeX XMLCite \textit{J. P. Wilson} et al., Commun. Comput. Phys. 32, No. 4, 1039--1060 (2022; Zbl 1498.65189) Full Text: DOI
Zhou, Zijian; Wang, Li; Yan, Zhenya Data-driven discoveries of Bäcklund transformations and soliton evolution equations via deep neural network learning schemes. (English) Zbl 07600402 Phys. Lett., A 450, Article ID 128373, 15 p. (2022). MSC: 35C08 35Q53 68T07 PDFBibTeX XMLCite \textit{Z. Zhou} et al., Phys. Lett., A 450, Article ID 128373, 15 p. (2022; Zbl 07600402) Full Text: DOI arXiv
Guo, Ling; Wu, Hao; Yu, Xiaochen; Zhou, Tao Monte Carlo fPINNs: deep learning method for forward and inverse problems involving high dimensional fractional partial differential equations. (English) Zbl 1507.65012 Comput. Methods Appl. Mech. Eng. 400, Article ID 115523, 17 p. (2022). MSC: 65C05 68T07 PDFBibTeX XMLCite \textit{L. Guo} et al., Comput. Methods Appl. Mech. Eng. 400, Article ID 115523, 17 p. (2022; Zbl 1507.65012) Full Text: DOI arXiv
Wu, Wei; Feng, Xinlong; Xu, Hui Improved deep neural networks with domain decomposition in solving partial differential equations. (English) Zbl 07589948 J. Sci. Comput. 93, No. 1, Paper No. 20, 34 p. (2022). MSC: 68Txx 65Nxx 65Mxx PDFBibTeX XMLCite \textit{W. Wu} et al., J. Sci. Comput. 93, No. 1, Paper No. 20, 34 p. (2022; Zbl 07589948) Full Text: DOI
Huang, Yao; Hao, Wenrui; Lin, Guang HomPINNs: homotopy physics-informed neural networks for learning multiple solutions of nonlinear elliptic differential equations. (English) Zbl 1524.65937 Comput. Math. Appl. 121, 62-73 (2022). MSC: 65N99 68T07 35K57 PDFBibTeX XMLCite \textit{Y. Huang} et al., Comput. Math. Appl. 121, 62--73 (2022; Zbl 1524.65937) Full Text: DOI
Zhong, Ming; Gong, Shibo; Tian, Shou-Fu; Yan, Zhenya Data-driven rogue waves and parameters discovery in nearly integrable \(\mathcal{PT}\)-symmetric Gross-Pitaevskii equations via PINNs deep learning. (English) Zbl 1496.35373 Physica D 439, Article ID 133430, 12 p. (2022). MSC: 35Q55 35Q35 76B15 68T07 35R30 PDFBibTeX XMLCite \textit{M. Zhong} et al., Physica D 439, Article ID 133430, 12 p. (2022; Zbl 1496.35373) Full Text: DOI
Cuomo, Salvatore; Schiano Di Cola, Vincenzo; Giampaolo, Fabio; Rozza, Gianluigi; Raissi, Maziar; Piccialli, Francesco Scientific machine learning through physics-informed neural networks: where we are and what’s next. (English) Zbl 07568980 J. Sci. Comput. 92, No. 3, Paper No. 88, 62 p. (2022). MSC: 68Txx 65Mxx 35Qxx PDFBibTeX XMLCite \textit{S. Cuomo} et al., J. Sci. Comput. 92, No. 3, Paper No. 88, 62 p. (2022; Zbl 07568980) Full Text: DOI arXiv
Glau, Kathrin; Wunderlich, Linus The deep parametric PDE method and applications to option pricing. (English) Zbl 1510.91197 Appl. Math. Comput. 432, Article ID 127355, 21 p. (2022). MSC: 91G80 91G20 68T07 91G60 PDFBibTeX XMLCite \textit{K. Glau} and \textit{L. Wunderlich}, Appl. Math. Comput. 432, Article ID 127355, 21 p. (2022; Zbl 1510.91197) Full Text: DOI arXiv
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
Gao, Yihang; Ng, Michael K. Wasserstein generative adversarial uncertainty quantification in physics-informed neural networks. (English) Zbl 07536770 J. Comput. Phys. 463, Article ID 111270, 28 p. (2022). MSC: 68Txx 65Cxx 65Mxx PDFBibTeX XMLCite \textit{Y. Gao} and \textit{M. K. Ng}, J. Comput. Phys. 463, Article ID 111270, 28 p. (2022; Zbl 07536770) Full Text: DOI arXiv
Jiao, Yuling; Lai, Yanming; Li, Dingwei; Lu, Xiliang; Wang, Fengru; Wang, Yang; Yang, Jerry Zhijian A rate of convergence of physics informed neural networks for the linear second order elliptic PDEs. (English) Zbl 1491.65118 Commun. Comput. Phys. 31, No. 4, 1272-1295 (2022). MSC: 65N12 65N15 65D07 62G05 68T07 92B20 PDFBibTeX XMLCite \textit{Y. Jiao} et al., Commun. Comput. Phys. 31, No. 4, 1272--1295 (2022; Zbl 1491.65118) Full Text: DOI arXiv
Duan, Chenguang; Jiao, Yuling; Lai, Yanming; Li, Dingwei; Lu, Xiliang; Yang, Jerry Zhijian Convergence rate analysis for deep Ritz method. (English) Zbl 1491.65117 Commun. Comput. Phys. 31, No. 4, 1020-1048 (2022). MSC: 65N12 62G05 65N15 68T07 35A15 35J15 35J25 35R02 92B20 PDFBibTeX XMLCite \textit{C. Duan} et al., Commun. Comput. Phys. 31, No. 4, 1020--1048 (2022; Zbl 1491.65117) Full Text: DOI arXiv
Yu, Jeremy; Lu, Lu; Meng, Xuhui; Karniadakis, George Em Gradient-enhanced physics-informed neural networks for forward and inverse PDE problems. (English) Zbl 1507.65217 Comput. Methods Appl. Mech. Eng. 393, Article ID 114823, 22 p. (2022). MSC: 65M99 65M32 68T07 PDFBibTeX XMLCite \textit{J. Yu} et al., Comput. Methods Appl. Mech. Eng. 393, Article ID 114823, 22 p. (2022; Zbl 1507.65217) Full Text: DOI arXiv
Lu, Lu; Meng, Xuhui; Cai, Shengze; Mao, Zhiping; Goswami, Somdatta; Zhang, Zhongqiang; Karniadakis, George Em A comprehensive and fair comparison of two neural operators (with practical extensions) based on FAIR data. (English) Zbl 1507.65050 Comput. Methods Appl. Mech. Eng. 393, Article ID 114778, 35 p. (2022). MSC: 65D15 68T07 PDFBibTeX XMLCite \textit{L. Lu} et al., Comput. Methods Appl. Mech. Eng. 393, Article ID 114778, 35 p. (2022; Zbl 1507.65050) Full Text: DOI arXiv
Rivera, Jon A.; Taylor, Jamie M.; Omella, Ángel J.; Pardo, David On quadrature rules for solving partial differential equations using neural networks. (English) Zbl 1507.65272 Comput. Methods Appl. Mech. Eng. 393, Article ID 114710, 21 p. (2022). MSC: 65N50 35A25 68T07 PDFBibTeX XMLCite \textit{J. A. Rivera} et al., Comput. Methods Appl. Mech. Eng. 393, Article ID 114710, 21 p. (2022; Zbl 1507.65272) Full Text: DOI arXiv
Wang, Sifan; Yu, Xinling; Perdikaris, Paris When and why PINNs fail to train: a neural tangent kernel perspective. (English) Zbl 07524768 J. Comput. Phys. 449, Article ID 110768, 28 p. (2022). MSC: 68Txx 65Mxx 35Qxx PDFBibTeX XMLCite \textit{S. Wang} et al., J. Comput. Phys. 449, Article ID 110768, 28 p. (2022; Zbl 07524768) Full Text: DOI arXiv
Tang, Kejun; Wan, Xiaoliang; Liao, Qifeng Adaptive deep density approximation for Fokker-Planck equations. (English) Zbl 1515.65265 J. Comput. Phys. 457, Article ID 111080, 19 p. (2022). MSC: 65M99 35Q84 62-08 62G07 68T07 PDFBibTeX XMLCite \textit{K. Tang} et al., J. Comput. Phys. 457, Article ID 111080, 19 p. (2022; Zbl 1515.65265) Full Text: DOI arXiv
Lin, Shuning; Chen, Yong A two-stage physics-informed neural network method based on conserved quantities and applications in localized wave solutions. (English) Zbl 1515.65264 J. Comput. Phys. 457, Article ID 111053, 26 p. (2022). MSC: 65M99 68T07 PDFBibTeX XMLCite \textit{S. Lin} and \textit{Y. Chen}, J. Comput. Phys. 457, Article ID 111053, 26 p. (2022; Zbl 1515.65264) Full Text: DOI arXiv
Penwarden, Michael; Zhe, Shandian; Narayan, Akil; Kirby, Robert M. Multifidelity modeling for physics-informed neural networks (PINNs). (English) Zbl 07517154 J. Comput. Phys. 451, Article ID 110844, 13 p. (2022). MSC: 65Mxx 35Rxx 68Txx PDFBibTeX XMLCite \textit{M. Penwarden} et al., J. Comput. Phys. 451, Article ID 110844, 13 p. (2022; Zbl 07517154) Full Text: DOI arXiv
Wang, Hengjie; Planas, Robert; Chandramowlishwaran, Aparna; Bostanabad, Ramin Mosaic flows: a transferable deep learning framework for solving PDEs on unseen domains. (English) Zbl 1507.65215 Comput. Methods Appl. Mech. Eng. 389, Article ID 114424, 26 p. (2022). MSC: 65M99 68T07 PDFBibTeX XMLCite \textit{H. Wang} et al., Comput. Methods Appl. Mech. Eng. 389, Article ID 114424, 26 p. (2022; Zbl 1507.65215) Full Text: DOI arXiv
Li, Yixin; Hu, Xianliang Artificial neural network approximations of Cauchy inverse problem for linear PDEs. (English) Zbl 1510.65230 Appl. Math. Comput. 414, Article ID 126678, 14 p. (2022). MSC: 65M32 35Q49 49N45 68T07 35R30 PDFBibTeX XMLCite \textit{Y. Li} and \textit{X. Hu}, Appl. Math. Comput. 414, Article ID 126678, 14 p. (2022; Zbl 1510.65230) Full Text: DOI
Mo, Yifan; Ling, Liming; Zeng, Delu Data-driven vector soliton solutions of coupled nonlinear Schrödinger equation using a deep learning algorithm. (English) Zbl 1483.35217 Phys. Lett., A 421, Article ID 127739, 10 p. (2022). Reviewer: Claudia Simionescu-Badea (Wien) MSC: 35Q55 35C08 68T07 82C32 PDFBibTeX XMLCite \textit{Y. Mo} et al., Phys. Lett., A 421, Article ID 127739, 10 p. (2022; Zbl 1483.35217) Full Text: DOI
Bai, Genming; Koley, Ujjwal; Mishra, Siddhartha; Molinaro, Roberto Physics informed neural networks (PINNs) for approximating nonlinear dispersive PDEs. (English) Zbl 1499.65205 J. Comput. Math. 39, No. 6, 816-847 (2021). MSC: 65J15 35Q53 68T07 PDFBibTeX XMLCite \textit{G. Bai} et al., J. Comput. Math. 39, No. 6, 816--847 (2021; Zbl 1499.65205) Full Text: DOI arXiv
Wang, Sifan; Perdikaris, Paris Deep learning of free boundary and Stefan problems. (English) Zbl 07511408 J. Comput. Phys. 428, Article ID 109914, 24 p. (2021). MSC: 65-XX 35-XX PDFBibTeX XMLCite \textit{S. Wang} and \textit{P. Perdikaris}, J. Comput. Phys. 428, Article ID 109914, 24 p. (2021; Zbl 07511408) Full Text: DOI arXiv
Darbon, Jérôme; Meng, Tingwei On some neural network architectures that can represent viscosity solutions of certain high dimensional Hamilton-Jacobi partial differential equations. (English) Zbl 07508503 J. Comput. Phys. 425, Article ID 109907, 16 p. (2021). MSC: 68-XX 65-XX PDFBibTeX XMLCite \textit{J. Darbon} and \textit{T. Meng}, J. Comput. Phys. 425, Article ID 109907, 16 p. (2021; Zbl 07508503) Full Text: DOI arXiv
Ålund, Oskar; Iaccarino, Gianluca; Nordström, Jan Learning to differentiate. (English) Zbl 07508475 J. Comput. Phys. 424, Article ID 109873, 13 p. (2021). MSC: 68-XX 65-XX PDFBibTeX XMLCite \textit{O. Ålund} et al., J. Comput. Phys. 424, Article ID 109873, 13 p. (2021; Zbl 07508475) Full Text: DOI
Wang, Li; Yan, Zhenya Data-driven peakon and periodic peakon solutions and parameter discovery of some nonlinear dispersive equations via deep learning. (English) Zbl 1484.35134 Physica D 428, Article ID 133037, 15 p. (2021). MSC: 35C08 35G31 PDFBibTeX XMLCite \textit{L. Wang} and \textit{Z. Yan}, Physica D 428, Article ID 133037, 15 p. (2021; Zbl 1484.35134) Full Text: DOI arXiv
Ibrahim, Wubshet; Bijiga, Lelisa Kebena Neural network method for solving time-fractional telegraph equation. (English) Zbl 1512.35621 Math. Probl. Eng. 2021, Article ID 7167801, 10 p. (2021). MSC: 35R11 68T07 PDFBibTeX XMLCite \textit{W. Ibrahim} and \textit{L. K. Bijiga}, Math. Probl. Eng. 2021, Article ID 7167801, 10 p. (2021; Zbl 1512.35621) Full Text: DOI
Chen, Xiaoli; Duan, Jinqiao; Karniadakis, George Em Learning and meta-learning of stochastic advection-diffusion-reaction systems from sparse measurements. (English) Zbl 07441294 Eur. J. Appl. Math. 32, No. 3, 397-420 (2021). MSC: 68T05 35R30 PDFBibTeX XMLCite \textit{X. Chen} et al., Eur. J. Appl. Math. 32, No. 3, 397--420 (2021; Zbl 07441294) Full Text: DOI arXiv
Lu, Lu; Pestourie, Raphaël; Yao, Wenjie; Wang, Zhicheng; Verdugo, Francesc; Johnson, Steven G. Physics-informed neural networks with hard constraints for inverse design. (English) Zbl 1478.35242 SIAM J. Sci. Comput. 43, No. 6, B1105-B1132 (2021). MSC: 35R30 65K10 68T20 92B20 PDFBibTeX XMLCite \textit{L. Lu} et al., SIAM J. Sci. Comput. 43, No. 6, B1105--B1132 (2021; Zbl 1478.35242) Full Text: DOI arXiv
Nguyen-Thanh, Vien Minh; Anitescu, Cosmin; Alajlan, Naif; Rabczuk, Timon; Zhuang, Xiaoying Parametric deep energy approach for elasticity accounting for strain gradient effects. (English) Zbl 1507.74571 Comput. Methods Appl. Mech. Eng. 386, Article ID 114096, 27 p. (2021). MSC: 74S99 65Z05 74B05 PDFBibTeX XMLCite \textit{V. M. Nguyen-Thanh} et al., Comput. Methods Appl. Mech. Eng. 386, Article ID 114096, 27 p. (2021; Zbl 1507.74571) Full Text: DOI
Zhou, Zijian; Yan, Zhenya Solving forward and inverse problems of the logarithmic nonlinear Schrödinger equation with \(\mathcal{PT}\)-symmetric harmonic potential via deep learning. (English) Zbl 1472.81089 Phys. Lett., A 387, Article ID 127010, 12 p. (2021). MSC: 81Q05 35Q55 81R05 35Q41 81P68 68T05 35C06 PDFBibTeX XMLCite \textit{Z. Zhou} and \textit{Z. Yan}, Phys. Lett., A 387, Article ID 127010, 12 p. (2021; Zbl 1472.81089) Full Text: DOI arXiv
Chen, Xiaoli; Yang, Liu; Duan, Jinqiao; Karniadakis, George Em Solving inverse stochastic problems from discrete particle observations using the Fokker-Planck equation and physics-informed neural networks. (English) Zbl 1480.35377 SIAM J. Sci. Comput. 43, No. 3, B811-B830 (2021). Reviewer: Wasiur Rahman Khuda Bukhsh (Nottingham) MSC: 35Q84 62M45 60H35 60J65 35B30 92B20 PDFBibTeX XMLCite \textit{X. Chen} et al., SIAM J. Sci. Comput. 43, No. 3, B811--B830 (2021; Zbl 1480.35377) Full Text: DOI arXiv
Yin, Minglang; Zheng, Xiaoning; Humphrey, Jay D.; Karniadakis, George Em Non-invasive inference of thrombus material properties with physics-informed neural networks. (English) Zbl 1506.74215 Comput. Methods Appl. Mech. Eng. 375, Article ID 113603, 23 p. (2021). MSC: 74L15 PDFBibTeX XMLCite \textit{M. Yin} et al., Comput. Methods Appl. Mech. Eng. 375, Article ID 113603, 23 p. (2021; Zbl 1506.74215) Full Text: DOI arXiv
Kharazmi, Ehsan; Zhang, Zhongqiang; Karniadakis, George E. M. hp-VPINNs: variational physics-informed neural networks with domain decomposition. (English) Zbl 1506.68105 Comput. Methods Appl. Mech. Eng. 374, Article ID 113547, 25 p. (2021). MSC: 68T07 92B20 65M55 PDFBibTeX XMLCite \textit{E. Kharazmi} et al., Comput. Methods Appl. Mech. Eng. 374, Article ID 113547, 25 p. (2021; Zbl 1506.68105) Full Text: DOI arXiv
Lu, Lu; Meng, Xuhui; Mao, Zhiping; Karniadakis, George Em DeepXDE: a deep learning library for solving differential equations. (English) Zbl 1459.65002 SIAM Rev. 63, No. 1, 208-228 (2021). MSC: 65-01 65-04 68T07 65L99 65M99 65N99 PDFBibTeX XMLCite \textit{L. Lu} et al., SIAM Rev. 63, No. 1, 208--228 (2021; Zbl 1459.65002) Full Text: DOI arXiv
Pang, G.; D’Elia, M.; Parks, M.; Karniadakis, G. E. nPINNs: nonlocal physics-informed neural networks for a parametrized nonlocal universal Laplacian operator. Algorithms and applications. (English) Zbl 07508384 J. Comput. Phys. 422, Article ID 109760, 26 p. (2020). MSC: 35-XX 86-XX PDFBibTeX XMLCite \textit{G. Pang} et al., J. Comput. Phys. 422, Article ID 109760, 26 p. (2020; Zbl 07508384) Full Text: DOI arXiv
Shin, Yeonjong; Darbon, Jérôme; Karniadakis, George Em On the convergence of physics informed neural networks for linear second-order elliptic and parabolic type PDEs. (English) Zbl 1473.65349 Commun. Comput. Phys. 28, No. 5, 2042-2074 (2020). MSC: 65N99 65M99 65M12 65N12 35J25 35K20 68T07 PDFBibTeX XMLCite \textit{Y. Shin} et al., Commun. Comput. Phys. 28, No. 5, 2042--2074 (2020; Zbl 1473.65349) 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
Meng, Xuhui; Li, Zhen; Zhang, Dongkun; Karniadakis, George Em PPINN: parareal physics-informed neural network for time-dependent PDEs. (English) Zbl 1506.65181 Comput. Methods Appl. Mech. Eng. 370, Article ID 113250, 16 p. (2020). MSC: 65M99 65Y05 68T07 PDFBibTeX XMLCite \textit{X. Meng} et al., Comput. Methods Appl. Mech. Eng. 370, Article ID 113250, 16 p. (2020; Zbl 1506.65181) Full Text: DOI arXiv
Opschoor, Joost A. A.; Petersen, Philipp C.; Schwab, Christoph Deep ReLU networks and high-order finite element methods. (English) Zbl 1452.65354 Anal. Appl., Singap. 18, No. 5, 715-770 (2020). MSC: 65N30 65D07 65N12 41A25 41A46 35B65 35R02 68T07 92B20 PDFBibTeX XMLCite \textit{J. A. A. Opschoor} et al., Anal. Appl., Singap. 18, No. 5, 715--770 (2020; Zbl 1452.65354) Full Text: DOI
Darbon, Jérôme; Langlois, Gabriel P.; Meng, Tingwei Overcoming the curse of dimensionality for some Hamilton-Jacobi partial differential equations via neural network architectures. (English) Zbl 1445.35119 Res. Math. Sci. 7, No. 3, Paper No. 20, 50 p. (2020). MSC: 35F21 35F25 92C20 35R30 PDFBibTeX XMLCite \textit{J. Darbon} et al., Res. Math. Sci. 7, No. 3, Paper No. 20, 50 p. (2020; Zbl 1445.35119) Full Text: DOI arXiv
Mao, Zhiping; Jagtap, Ameya D.; Karniadakis, George Em Physics-informed neural networks for high-speed flows. (English) Zbl 1442.76092 Comput. Methods Appl. Mech. Eng. 360, Article ID 112789, 26 p. (2020). MSC: 76M60 65M70 35L65 PDFBibTeX XMLCite \textit{Z. Mao} et al., Comput. Methods Appl. Mech. Eng. 360, Article ID 112789, 26 p. (2020; Zbl 1442.76092) Full Text: DOI
Mehta, Pavan Pranjivan; Pang, Guofei; Song, Fangying; Karniadakis, George Em Discovering a universal variable-order fractional model for turbulent Couette flow using a physics-informed neural network. (English) Zbl 1434.76053 Fract. Calc. Appl. Anal. 22, No. 6, 1675-1688 (2019). MSC: 76F40 35R11 76F65 68T20 PDFBibTeX XMLCite \textit{P. P. Mehta} et al., Fract. Calc. Appl. Anal. 22, No. 6, 1675--1688 (2019; Zbl 1434.76053) Full Text: DOI