Wang, Yiran; Dong, Suchuan An extreme learning machine-based method for computational PDEs in higher dimensions. (English) Zbl 07823460 Comput. Methods Appl. Mech. Eng. 418, Part B, Article ID 116578, 31 p. (2024). MSC: 65-XX 82-XX PDFBibTeX XMLCite \textit{Y. Wang} and \textit{S. Dong}, Comput. Methods Appl. Mech. Eng. 418, Part B, Article ID 116578, 31 p. (2024; Zbl 07823460) Full Text: DOI arXiv
Braun, Alina; Kohler, Michael; Cho, Jeongik; Krzyżak, Adam Analysis of the rate of convergence of two regression estimates defined by neural features which are easy to implement. (English) Zbl 07823222 Electron. J. Stat. 18, No. 1, 553-598 (2024). MSC: 62G08 62M45 PDFBibTeX XMLCite \textit{A. Braun} et al., Electron. J. Stat. 18, No. 1, 553--598 (2024; Zbl 07823222) Full Text: DOI Link
Frischauf, Leon; Scherzer, Otmar; Shi, Cong Quadratic neural networks for solving inverse problems. (English) Zbl 07820070 Numer. Funct. Anal. Optim. 45, No. 2, 112-135 (2024). MSC: 68T07 65J22 65K10 65F20 PDFBibTeX XMLCite \textit{L. Frischauf} et al., Numer. Funct. Anal. Optim. 45, No. 2, 112--135 (2024; Zbl 07820070) Full Text: DOI arXiv OA License
Ismailov, Vugar E. Approximation error of single hidden layer neural networks with fixed weights. (English) Zbl 07817062 Inf. Process. Lett. 185, Article ID 106467, 6 p. (2024). MSC: 68Qxx PDFBibTeX XMLCite \textit{V. E. Ismailov}, Inf. Process. Lett. 185, Article ID 106467, 6 p. (2024; Zbl 07817062) Full Text: DOI arXiv
Binev, Peter; Bonito, Andrea; DeVore, Ronald; Petrova, Guergana Optimal learning. (English) Zbl 07814909 Calcolo 61, No. 1, Paper No. 15, 37 p. (2024). MSC: 68T05 65J20 62J05 PDFBibTeX XMLCite \textit{P. Binev} et al., Calcolo 61, No. 1, Paper No. 15, 37 p. (2024; Zbl 07814909) Full Text: DOI arXiv
Chen, Shi; Ding, Zhiyan; Li, Qin; Wright, Stephen J. A reduced order Schwarz method for nonlinear multiscale elliptic equations based on two-layer neural networks. (English) Zbl 07806684 J. Comput. Math. 42, No. 2, 570-596 (2024). MSC: 65N55 35J66 41A46 68T07 PDFBibTeX XMLCite \textit{S. Chen} et al., J. Comput. Math. 42, No. 2, 570--596 (2024; Zbl 07806684) Full Text: DOI arXiv
Chen, Xiaohong; Liu, Ying; Ma, Shujie; Zhang, Zheng Causal inference of general treatment effects using neural networks with a diverging number of confounders. (English) Zbl 07803932 J. Econom. 238, No. 1, Article ID 105555, 27 p. (2024). MSC: 62-XX 91-XX PDFBibTeX XMLCite \textit{X. Chen} et al., J. Econom. 238, No. 1, Article ID 105555, 27 p. (2024; Zbl 07803932) Full Text: DOI arXiv
Li, Yuanyuan; Lu, Shuai; Mathé, Peter; Pereverzev, Sergei V. Two-layer networks with the \(\text{ReLU}^k\) activation function: Barron spaces and derivative approximation. (English) Zbl 07802489 Numer. Math. 156, No. 1, 319-344 (2024). MSC: 41A25 42B35 42C40 65D15 65D25 PDFBibTeX XMLCite \textit{Y. Li} et al., Numer. Math. 156, No. 1, 319--344 (2024; Zbl 07802489) Full Text: DOI
Baek, Jonghyuk; Chen, Jiun-Shyan A neural network-based enrichment of reproducing kernel approximation for modeling brittle fracture. (English) Zbl 07796651 Comput. Methods Appl. Mech. Eng. 419, Article ID 116590, 24 p. (2024). MSC: 65-XX 68-XX PDFBibTeX XMLCite \textit{J. Baek} and \textit{J.-S. Chen}, Comput. Methods Appl. Mech. Eng. 419, Article ID 116590, 24 p. (2024; Zbl 07796651) Full Text: DOI arXiv
Li, Lingfeng; Tai, Xue-Cheng; Yang, Jiang; Zhu, Quanhui A priori error estimate of deep mixed residual method for elliptic PDEs. (English) Zbl 07794699 J. Sci. Comput. 98, No. 2, Paper No. 44, 30 p. (2024). MSC: 65N15 68Q25 PDFBibTeX XMLCite \textit{L. Li} et al., J. Sci. Comput. 98, No. 2, Paper No. 44, 30 p. (2024; Zbl 07794699) Full Text: DOI arXiv
Braun, Alina; Kohler, Michael; Langer, Sophie; Walk, Harro Convergence rates for shallow neural networks learned by gradient descent. (English) Zbl 07788892 Bernoulli 30, No. 1, 475-502 (2024). Reviewer: Raffaele Marino (Roma) MSC: 68T07 65K10 PDFBibTeX XMLCite \textit{A. Braun} et al., Bernoulli 30, No. 1, 475--502 (2024; Zbl 07788892) Full Text: DOI arXiv
Benth, Fred Espen; Detering, Nils; Galimberti, Luca Pricing options on flow forwards by neural networks in a Hilbert space. (English) Zbl 07782839 Finance Stoch. 28, No. 1, 81-121 (2024). MSC: 91G20 60H15 68T07 46E20 PDFBibTeX XMLCite \textit{F. E. Benth} et al., Finance Stoch. 28, No. 1, 81--121 (2024; Zbl 07782839) Full Text: DOI arXiv
Bach, Francis; Chizat, Lénaïc Gradient descent on infinitely wide neural networks: global convergence and generalization. (English) Zbl 07822598 Beliaev, Dmitry (ed.) et al., International congress of mathematicians 2022, ICM 2022, Helsinki, Finland, virtual, July 6–14, 2022. Volume 7. Sections 15–20. Berlin: European Mathematical Society (EMS). 5398-5419 (2023). MSC: 68T07 90C30 62G08 65K10 PDFBibTeX XMLCite \textit{F. Bach} and \textit{L. Chizat}, in: International congress of mathematicians 2022, ICM 2022, Helsinki, Finland, virtual, July 6--14, 2022. Volume 7. Sections 15--20. Berlin: European Mathematical Society (EMS). 5398--5419 (2023; Zbl 07822598) Full Text: DOI arXiv OA License
E, Weinan A mathematical perspective of machine learning. (English) Zbl 07821730 Beliaev, Dmitry (ed.) et al., International congress of mathematicians 2022, ICM 2022, Helsinki, Finland, virtual, July 6–14, 2022. Volume 2. Plenary lectures. Berlin: European Mathematical Society (EMS). 914-954 (2023). MSC: 68-06 68T05 68Q32 PDFBibTeX XMLCite \textit{W. E}, in: International congress of mathematicians 2022, ICM 2022, Helsinki, Finland, virtual, July 6--14, 2022. Volume 2. Plenary lectures. Berlin: European Mathematical Society (EMS). 914--954 (2023; Zbl 07821730) Full Text: DOI OA License
Liu, Hao; Tai, Xue-Cheng; Chan, Raymond Connections between operator-splitting methods and deep neural networks with applications in image segmentation. (English) Zbl 07814792 Ann. Appl. Math. 39, No. 4, 406-428 (2023). MSC: 68U10 94A08 PDFBibTeX XMLCite \textit{H. Liu} et al., Ann. Appl. Math. 39, No. 4, 406--428 (2023; Zbl 07814792) Full Text: DOI arXiv
Jiao, Yuling; Lu, Xiliang; Yang, Jerry Zhijian; Yuan, Cheng; Zhang, Pingwen Improved analysis of PINNs: alleviate the CoD for compositional solutions. (English) Zbl 07814785 Ann. Appl. Math. 39, No. 3, 239-263 (2023). MSC: 68T07 65N99 PDFBibTeX XMLCite \textit{Y. Jiao} et al., Ann. Appl. Math. 39, No. 3, 239--263 (2023; Zbl 07814785) Full Text: DOI
Kadak, Uğur Fractional type multivariate neural network operators. (English) Zbl 07781838 Math. Methods Appl. Sci. 46, No. 3, 3045-3065 (2023). MSC: 41A25 41A30 41A05 68T07 PDFBibTeX XMLCite \textit{U. Kadak}, Math. Methods Appl. Sci. 46, No. 3, 3045--3065 (2023; Zbl 07781838) Full Text: DOI
Bao, Chenglong; Li, Qianxiao; Shen, Zuowei; Tai, Cheng; Wu, Lei; Xiang, Xueshuang Approximation analysis of convolutional neural networks. (English) Zbl 07779658 East Asian J. Appl. Math. 13, No. 3, 524-549 (2023). MSC: 41A63 68T01 PDFBibTeX XMLCite \textit{C. Bao} et al., East Asian J. Appl. Math. 13, No. 3, 524--549 (2023; Zbl 07779658) Full Text: DOI
Mao, Tong; Zhou, Ding-Xuan Rates of approximation by ReLU shallow neural networks. (English) Zbl 1524.68322 J. Complexity 79, Article ID 101784, 21 p. (2023). MSC: 68T07 41A25 PDFBibTeX XMLCite \textit{T. Mao} and \textit{D.-X. Zhou}, J. Complexity 79, Article ID 101784, 21 p. (2023; Zbl 1524.68322) Full Text: DOI arXiv
Mandel, Francesca; Ghosh, Riddhi Pratim; Barnett, Ian Neural networks for clustered and longitudinal data using mixed effects models. (English) Zbl 1522.62194 Biometrics 79, No. 2, 711-721 (2023). MSC: 62P10 PDFBibTeX XMLCite \textit{F. Mandel} et al., Biometrics 79, No. 2, 711--721 (2023; Zbl 1522.62194) Full Text: DOI
Sorourifar, Farshud; Choksi, Naitik; Paulson, Joel A. Computationally efficient integrated design and predictive control of flexible energy systems using multi-fidelity simulation-based Bayesian optimization. (English) Zbl 07754188 Optim. Control Appl. Methods 44, No. 2, 549-576 (2023). MSC: 93B45 93C10 93C41 PDFBibTeX XMLCite \textit{F. Sorourifar} et al., Optim. Control Appl. Methods 44, No. 2, 549--576 (2023; Zbl 07754188) Full Text: DOI
Gu, Yiqi; Ng, Michael K. Deep neural networks for solving large linear systems arising from high-dimensional problems. (English) Zbl 1525.65026 SIAM J. Sci. Comput. 45, No. 5, A2356-A2381 (2023). MSC: 65F10 65F50 65N22 68T07 60K25 PDFBibTeX XMLCite \textit{Y. Gu} and \textit{M. K. Ng}, SIAM J. Sci. Comput. 45, No. 5, A2356--A2381 (2023; Zbl 1525.65026) Full Text: DOI arXiv
Zhang, Jie; Wang, Chunxiao; Wu, Yuqiang Adaptive neural network control for nonholonomic systems with partial/full or without state constraints. (English) Zbl 1521.93098 J. Franklin Inst. 360, No. 14, 10633-10655 (2023). MSC: 93C40 70F25 93D30 PDFBibTeX XMLCite \textit{J. Zhang} et al., J. Franklin Inst. 360, No. 14, 10633--10655 (2023; Zbl 1521.93098) Full Text: DOI
Meng, Xinhong; Yan, Jinyao; Ye, Hailiang; Cao, Feilong Construction and approximation for a class of feedforward neural networks with sigmoidal function. (English) Zbl 07741317 Int. J. Wavelets Multiresolut. Inf. Process. 21, No. 6, Article ID 2350028, 12 p. (2023). MSC: 41A25 PDFBibTeX XMLCite \textit{X. Meng} et al., Int. J. Wavelets Multiresolut. Inf. Process. 21, No. 6, Article ID 2350028, 12 p. (2023; Zbl 07741317) Full Text: DOI
Han, Jiequn; Hu, Ruimeng; Long, Jihao A class of dimension-free metrics for the convergence of empirical measures. (English) Zbl 1522.60015 Stochastic Processes Appl. 164, 242-287 (2023). MSC: 60B10 60E15 60K35 91A16 60H10 PDFBibTeX XMLCite \textit{J. Han} et al., Stochastic Processes Appl. 164, 242--287 (2023; Zbl 1522.60015) Full Text: DOI arXiv
Wang, Guoshun; Yu, Dansheng; Guan, Lingmin Neural network interpolation operators of multivariate functions. (English) Zbl 07733947 J. Comput. Appl. Math. 431, Article ID 115266, 22 p. (2023). MSC: 41A25 41A05 41A27 41A28 62D05 PDFBibTeX XMLCite \textit{G. Wang} et al., J. Comput. Appl. Math. 431, Article ID 115266, 22 p. (2023; Zbl 07733947) Full Text: DOI
Jiao, Yuling; Lai, Yanming; Lu, Xiliang; Wang, Fengru; Yang, Jerry Zhijian; Yang, Yuanyuan Deep neural networks with ReLU-sine-exponential activations break curse of dimensionality in approximation on Hölder class. (English) Zbl 07733773 SIAM J. Math. Anal. 55, No. 4, 3635-3649 (2023). MSC: 41A63 41A30 65D15 PDFBibTeX XMLCite \textit{Y. Jiao} et al., SIAM J. Math. Anal. 55, No. 4, 3635--3649 (2023; Zbl 07733773) Full Text: DOI arXiv
Song, Linhao; Fan, Jun; Chen, Di-Rong; Zhou, Ding-Xuan Approximation of nonlinear functionals using deep ReLU networks. (English) Zbl 07727372 J. Fourier Anal. Appl. 29, No. 4, Paper No. 50, 23 p. (2023); correction ibid. 29, No. 5, Paper No. 57, 1 p. (2023). MSC: 68Q32 68T05 41A25 PDFBibTeX XMLCite \textit{L. Song} et al., J. Fourier Anal. Appl. 29, No. 4, Paper No. 50, 23 p. (2023; Zbl 07727372) Full Text: DOI arXiv
Yu, Zhan; Zhou, Ding-Xuan Deep learning theory of distribution regression with CNNs. (English) Zbl 07723892 Adv. Comput. Math. 49, No. 4, Paper No. 51, 40 p. (2023). MSC: 41A25 92B20 PDFBibTeX XMLCite \textit{Z. Yu} and \textit{D.-X. Zhou}, Adv. Comput. Math. 49, No. 4, Paper No. 51, 40 p. (2023; Zbl 07723892) Full Text: DOI
Caragea, Andrei; Petersen, Philipp; Voigtlaender, Felix Neural network approximation and estimation of classifiers with classification boundary in a Barron class. (English) Zbl 07720498 Ann. Appl. Probab. 33, No. 4, 3039-3079 (2023). MSC: 68T07 41A25 41A46 42B35 46E15 PDFBibTeX XMLCite \textit{A. Caragea} et al., Ann. Appl. Probab. 33, No. 4, 3039--3079 (2023; Zbl 07720498) Full Text: DOI arXiv Link
Calvo-Pardo, Hector; Mancini, Tullio; Olmo, Jose Optimal deep neural networks by maximization of the approximation power. (English) Zbl 07706755 Comput. Oper. Res. 156, Article ID 106264, 15 p. (2023). MSC: 90Bxx PDFBibTeX XMLCite \textit{H. Calvo-Pardo} et al., Comput. Oper. Res. 156, Article ID 106264, 15 p. (2023; Zbl 07706755) Full Text: DOI
Chen, Jiafeng; Chen, Xiaohong; Tamer, Elie Efficient estimation of average derivatives in NPIV models: simulation comparisons of neural network estimators. (English) Zbl 07704517 J. Econom. 235, No. 2, 1848-1875 (2023). MSC: 62-XX 91-XX PDFBibTeX XMLCite \textit{J. Chen} et al., J. Econom. 235, No. 2, 1848--1875 (2023; Zbl 07704517) Full Text: DOI arXiv
Chen, Fan; Huang, Jianguo; Wang, Chunmei; Yang, Haizhao Friedrichs learning: weak solutions of partial differential equations via deep learning. (English) Zbl 07704383 SIAM J. Sci. Comput. 45, No. 3, A1271-A1299 (2023). MSC: 65M75 65N75 62M45 PDFBibTeX XMLCite \textit{F. Chen} et al., SIAM J. Sci. Comput. 45, No. 3, A1271--A1299 (2023; Zbl 07704383) Full Text: DOI arXiv
Jentzen, Arnulf; Welti, Timo Overall error analysis for the training of deep neural networks via stochastic gradient descent with random initialisation. (English) Zbl 07704193 Appl. Math. Comput. 455, Article ID 127907, 34 p. (2023). MSC: 68Txx 41Axx 65Mxx PDFBibTeX XMLCite \textit{A. Jentzen} and \textit{T. Welti}, Appl. Math. Comput. 455, Article ID 127907, 34 p. (2023; Zbl 07704193) Full Text: DOI arXiv
Gong, Qi; Kang, Wei; Fahroo, Fariba Approximation of compositional functions with ReLU neural networks. (English) Zbl 1519.93089 Syst. Control Lett. 175, Article ID 105508, 8 p. (2023). MSC: 93B70 93B25 93C15 68T07 PDFBibTeX XMLCite \textit{Q. Gong} et al., Syst. Control Lett. 175, Article ID 105508, 8 p. (2023; Zbl 1519.93089) Full Text: DOI
Hertrich, Christoph; Basu, Amitabh; Di Summa, Marco; Skutella, Martin Towards lower bounds on the depth of ReLU neural networks. (English) Zbl 07700269 SIAM J. Discrete Math. 37, No. 2, 997-1029 (2023). MSC: 68T07 52B55 90C11 90C90 PDFBibTeX XMLCite \textit{C. Hertrich} et al., SIAM J. Discrete Math. 37, No. 2, 997--1029 (2023; Zbl 07700269) Full Text: DOI arXiv
Qiu, Changxin; Bendickson, Aaron; Kalyanapu, Joshua; Yan, Jue Accuracy and architecture studies of residual neural network method for ordinary differential equations. (English) Zbl 07698856 J. Sci. Comput. 95, No. 2, Paper No. 50, 31 p. (2023). MSC: 65-XX PDFBibTeX XMLCite \textit{C. Qiu} et al., J. Sci. Comput. 95, No. 2, Paper No. 50, 31 p. (2023; Zbl 07698856) Full Text: DOI arXiv
Kratsios, Anastasis Universal regular conditional distributions via probabilistic transformers. (English) Zbl 07698581 Constr. Approx. 57, No. 3, 1145-1212 (2023). MSC: 68T07 28A50 41A30 49Q22 60E05 PDFBibTeX XMLCite \textit{A. Kratsios}, Constr. Approx. 57, No. 3, 1145--1212 (2023; Zbl 07698581) Full Text: DOI arXiv
Siegel, Jonathan W.; Xu, Jinchao Characterization of the variation spaces corresponding to shallow neural networks. (English) Zbl 07698579 Constr. Approx. 57, No. 3, 1109-1132 (2023). MSC: 68T05 46B99 PDFBibTeX XMLCite \textit{J. W. Siegel} and \textit{J. Xu}, Constr. Approx. 57, No. 3, 1109--1132 (2023; Zbl 07698579) Full Text: DOI arXiv
Grohs, Philipp; Ibragimov, Shokhrukh; Jentzen, Arnulf; Koppensteiner, Sarah Lower bounds for artificial neural network approximations: a proof that shallow neural networks fail to overcome the curse of dimensionality. (English) Zbl 07693253 J. Complexity 77, Article ID 101746, 47 p. (2023). MSC: 68Txx 41Axx 65Mxx PDFBibTeX XMLCite \textit{P. Grohs} et al., J. Complexity 77, Article ID 101746, 47 p. (2023; Zbl 07693253) Full Text: DOI arXiv
Liu, Xinling; Hou, Jingyao Error bounds for approximations using multichannel deep convolutional neural networks with downsampling. (English) Zbl 1517.68343 J. Appl. Math. 2023, Article ID 8208424, 12 p. (2023). MSC: 68T07 41A25 PDFBibTeX XMLCite \textit{X. Liu} and \textit{J. Hou}, J. Appl. Math. 2023, Article ID 8208424, 12 p. (2023; Zbl 1517.68343) Full Text: DOI
Gonon, Lukas; Grigoryeva, Lyudmila; Ortega, Juan-Pablo Approximation bounds for random neural networks and reservoir systems. (English) Zbl 07692253 Ann. Appl. Probab. 33, No. 1, 28-69 (2023). MSC: 68T07 41A30 60-08 60H25 93E35 PDFBibTeX XMLCite \textit{L. Gonon} et al., Ann. Appl. Probab. 33, No. 1, 28--69 (2023; Zbl 07692253) Full Text: DOI arXiv
Jiao, Yuling; Wang, Yang; Yang, Yunfei Approximation bounds for norm constrained neural networks with applications to regression and GANs. (English) Zbl 1528.41035 Appl. Comput. Harmon. Anal. 65, 249-278 (2023). MSC: 41A25 62G08 68T07 PDFBibTeX XMLCite \textit{Y. Jiao} et al., Appl. Comput. Harmon. Anal. 65, 249--278 (2023; Zbl 1528.41035) Full Text: DOI arXiv
Grohs, Philipp; Voigtlaender, Felix Sobolev-type embeddings for neural network approximation spaces. (English) Zbl 07680071 Constr. Approx. 57, No. 2, 579-599 (2023). MSC: 41A63 41A30 46E30 46E35 65D05 68T07 PDFBibTeX XMLCite \textit{P. Grohs} and \textit{F. Voigtlaender}, Constr. Approx. 57, No. 2, 579--599 (2023; Zbl 07680071) Full Text: DOI arXiv
Grohs, Philipp; Hornung, Fabian; Jentzen, Arnulf; von Wurstemberger, Philippe A proof that artificial neural networks overcome the curse of dimensionality in the numerical approximation of Black-Scholes partial differential equations. (English) Zbl 07679303 Memoirs of the American Mathematical Society 1410. Providence, RI: American Mathematical Society (AMS) (ISBN 978-1-4704-5632-0/pbk; 978-1-4704-7448-5/ebook). v, 93 p. (2023). MSC: 65-02 65D99 35Kxx 60Hxx PDFBibTeX XMLCite \textit{P. Grohs} et al., A proof that artificial neural networks overcome the curse of dimensionality in the numerical approximation of Black-Scholes partial differential equations. Providence, RI: American Mathematical Society (AMS) (2023; Zbl 07679303) Full Text: DOI arXiv
Wang, Min; Lu, Jianfeng Neural network-based variational methods for solving quadratic porous medium equations in high dimensions. (English) Zbl 07679277 Commun. Math. Stat. 11, No. 1, 21-57 (2023). MSC: 68T07 65M12 35A15 PDFBibTeX XMLCite \textit{M. Wang} and \textit{J. Lu}, Commun. Math. Stat. 11, No. 1, 21--57 (2023; Zbl 07679277) Full Text: DOI arXiv
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
Chen, Ziang; Lu, Jianfeng; Lu, Yulong; Zhou, Shengxuan A regularity theory for static Schrödinger equations on \(\mathbb{R}^d\) in spectral barron spaces. (English) Zbl 07674170 SIAM J. Math. Anal. 55, No. 1, 557-570 (2023). MSC: 68T07 65N99 35Q40 PDFBibTeX XMLCite \textit{Z. Chen} et al., SIAM J. Math. Anal. 55, No. 1, 557--570 (2023; Zbl 07674170) Full Text: DOI arXiv
Webster, Kevin N. Low-rank kernel approximation of Lyapunov functions using neural networks. (English) Zbl 1515.37098 J. Comput. Dyn. 10, No. 1, 152-174 (2023). MSC: 37M21 37M22 65P40 68T05 PDFBibTeX XMLCite \textit{K. N. Webster}, J. Comput. Dyn. 10, No. 1, 152--174 (2023; Zbl 1515.37098) Full Text: DOI
Gu, Yiqi; Harlim, John; Liang, Senwei; Yang, Haizhao Stationary density estimation of Itô diffusions using deep learning. (English) Zbl 07670858 SIAM J. Numer. Anal. 61, No. 1, 45-82 (2023). MSC: 68T05 68T07 37N30 65N12 PDFBibTeX XMLCite \textit{Y. Gu} et al., SIAM J. Numer. Anal. 61, No. 1, 45--82 (2023; Zbl 07670858) Full Text: DOI arXiv
Yu, Dansheng; Qian, Yunyou; Li, Fengjun On approximation by neural networks with optimized activation functions and fixed weights. (English) Zbl 1524.41039 Anal. Theory Appl. 39, No. 1, 93-104 (2023). MSC: 41A30 68T07 PDFBibTeX XMLCite \textit{D. Yu} et al., Anal. Theory Appl. 39, No. 1, 93--104 (2023; Zbl 1524.41039) Full Text: DOI
He, Juncai; Tsai, Richard; Ward, Rachel Side effects of learning from low-dimensional data embedded in a Euclidean space. (English) Zbl 1508.68290 Res. Math. Sci. 10, No. 1, Paper No. 13, 41 p. (2023). MSC: 68T05 PDFBibTeX XMLCite \textit{J. He} et al., Res. Math. Sci. 10, No. 1, Paper No. 13, 41 p. (2023; Zbl 1508.68290) Full Text: DOI arXiv
Taylor, Jamie M.; Pardo, David; Muga, Ignacio A deep Fourier residual method for solving PDEs using neural networks. (English) Zbl 07653051 Comput. Methods Appl. Mech. Eng. 405, Article ID 115850, 27 p. (2023). MSC: 65-XX 92-XX PDFBibTeX XMLCite \textit{J. M. Taylor} et al., Comput. Methods Appl. Mech. Eng. 405, Article ID 115850, 27 p. (2023; Zbl 07653051) Full Text: DOI arXiv
Mao, Tong; Shi, Zhongjie; Zhou, Ding-Xuan Approximating functions with multi-features by deep convolutional neural networks. (English) Zbl 07652562 Anal. Appl., Singap. 21, No. 1, 93-125 (2023). MSC: 68T07 68Q32 41A25 PDFBibTeX XMLCite \textit{T. Mao} et al., Anal. Appl., Singap. 21, No. 1, 93--125 (2023; Zbl 07652562) Full Text: DOI
Gonon, Lukas; Schwab, Christoph Deep ReLU neural networks overcome the curse of dimensionality for partial integrodifferential equations. (English) Zbl 07652560 Anal. Appl., Singap. 21, No. 1, 1-47 (2023). MSC: 68T07 45K05 60H35 PDFBibTeX XMLCite \textit{L. Gonon} and \textit{C. Schwab}, Anal. Appl., Singap. 21, No. 1, 1--47 (2023; Zbl 07652560) Full Text: DOI arXiv
Gao, Wenhan; Wang, Chunmei Active learning based sampling for high-dimensional nonlinear partial differential equations. (English) Zbl 07649269 J. Comput. Phys. 475, Article ID 111848, 20 p. (2023). MSC: 68Txx 65Mxx 65Nxx PDFBibTeX XMLCite \textit{W. Gao} and \textit{C. Wang}, J. Comput. Phys. 475, Article ID 111848, 20 p. (2023; Zbl 07649269) Full Text: DOI arXiv
Bersetche, Francisco M.; Borthagaray, Juan Pablo A deep first-order system least squares method for solving elliptic PDEs. (English) Zbl 1524.65756 Comput. Math. Appl. 129, 136-150 (2023). MSC: 65N30 65N12 65N99 65K10 35J15 68T07 65C05 PDFBibTeX XMLCite \textit{F. M. Bersetche} and \textit{J. P. Borthagaray}, Comput. Math. Appl. 129, 136--150 (2023; Zbl 1524.65756) Full Text: DOI arXiv
Owhadi, Houman Do ideas have shape? Idea registration as the continuous limit of artificial neural networks. (English) Zbl 07642857 Physica D 444, Article ID 133592, 41 p. (2023). MSC: 68-XX 65-XX PDFBibTeX XMLCite \textit{H. Owhadi}, Physica D 444, Article ID 133592, 41 p. (2023; Zbl 07642857) Full Text: DOI arXiv
Hashemi, Abolfazl; Schaeffer, Hayden; Shi, Robert; Topcu, Ufuk; Tran, Giang; Ward, Rachel Generalization bounds for sparse random feature expansions. (English) Zbl 1505.65039 Appl. Comput. Harmon. Anal. 62, 310-330 (2023). MSC: 65D15 68Q32 46N10 PDFBibTeX XMLCite \textit{A. Hashemi} et al., Appl. Comput. Harmon. Anal. 62, 310--330 (2023; Zbl 1505.65039) Full Text: DOI arXiv
Bartolucci, Francesca; De Vito, Ernesto; Rosasco, Lorenzo; Vigogna, Stefano Understanding neural networks with reproducing kernel Banach spaces. (English) Zbl 1511.46015 Appl. Comput. Harmon. Anal. 62, 194-236 (2023). MSC: 46E22 68T07 PDFBibTeX XMLCite \textit{F. Bartolucci} et al., Appl. Comput. Harmon. Anal. 62, 194--236 (2023; Zbl 1511.46015) Full Text: DOI arXiv
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
Sudakow, Ivan; Vakulenko, Sergey A.; Grigoriev, Dima Excitable media store and transfer complicated information via topological defect motion. (English) Zbl 1501.35133 Commun. Nonlinear Sci. Numer. Simul. 116, Article ID 106844, 11 p. (2023). MSC: 35G61 35B41 35C07 35Q56 PDFBibTeX XMLCite \textit{I. Sudakow} et al., Commun. Nonlinear Sci. Numer. Simul. 116, Article ID 106844, 11 p. (2023; Zbl 1501.35133) Full Text: DOI
Kohler, Michael; Langer, Sophie; Reif, Ulrich Estimation of a regression function on a manifold by fully connected deep neural networks. (English) Zbl 1495.62031 J. Stat. Plann. Inference 222, 160-181 (2023). MSC: 62G08 62G05 62G20 68T07 PDFBibTeX XMLCite \textit{M. Kohler} et al., J. Stat. Plann. Inference 222, 160--181 (2023; Zbl 1495.62031) Full Text: DOI arXiv
Goebbels, Steffen On sharpness of error bounds for multivariate neural network approximation. (English) Zbl 07771830 Ric. Mat. 71, No. 2, 633-653 (2022). MSC: 41A25 41A50 62M45 PDFBibTeX XMLCite \textit{S. Goebbels}, Ric. Mat. 71, No. 2, 633--653 (2022; Zbl 07771830) Full Text: DOI arXiv
Wang, Guoshun; Yu, Dansheng; Zhou, Ping Neural network interpolation operators optimized by Lagrange polynomial. (English) Zbl 1523.41008 Neural Netw. 153, 179-191 (2022). MSC: 41A30 41A63 PDFBibTeX XMLCite \textit{G. Wang} et al., Neural Netw. 153, 179--191 (2022; Zbl 1523.41008) Full Text: DOI
Lu, Jianfeng; Lu, Yulong A priori generalization error analysis of two-layer neural networks for solving high dimensional Schrödinger eigenvalue problems. (English) Zbl 07750988 Commun. Am. Math. Soc. 2, 1-21 (2022). MSC: 65-XX 35P15 65N25 68T07 35Q40 PDFBibTeX XMLCite \textit{J. Lu} and \textit{Y. Lu}, Commun. Am. Math. Soc. 2, 1--21 (2022; Zbl 07750988) Full Text: DOI arXiv
Yang, Yunfei; Li, Zhen; Wang, Yang On the capacity of deep generative networks for approximating distributions. (English) Zbl 1521.68207 Neural Netw. 145, 144-154 (2022). MSC: 68T07 60E05 PDFBibTeX XMLCite \textit{Y. Yang} et al., Neural Netw. 145, 144--154 (2022; Zbl 1521.68207) Full Text: DOI arXiv
Wang, Ming-Xi; Qu, Yang Approximation capabilities of neural networks on unbounded domains. (English) Zbl 1521.68166 Neural Netw. 145, 56-67 (2022). MSC: 68T05 41A30 91G20 PDFBibTeX XMLCite \textit{M.-X. Wang} and \textit{Y. Qu}, Neural Netw. 145, 56--67 (2022; Zbl 1521.68166) Full Text: DOI arXiv
Meng, Yan; Ming, Pingbing A new function space from Barron class and application to neural network approximation. (English) Zbl 1505.65294 Commun. Comput. Phys. 32, No. 5, 1361-1400 (2022). MSC: 65N30 65M12 35J25 41A46 68T07 PDFBibTeX XMLCite \textit{Y. Meng} and \textit{P. Ming}, Commun. Comput. Phys. 32, No. 5, 1361--1400 (2022; Zbl 1505.65294) Full Text: DOI
Korolev, Yury Two-layer neural networks with values in a Banach space. (English) Zbl 07632464 SIAM J. Math. Anal. 54, No. 6, 6358-6389 (2022). MSC: 68Q32 68T07 46E40 41A65 65J22 PDFBibTeX XMLCite \textit{Y. Korolev}, SIAM J. Math. Anal. 54, No. 6, 6358--6389 (2022; Zbl 07632464) Full Text: DOI arXiv
Ma, Xiaoyu; Sardy, Sylvain; Hengartner, Nick; Bobenko, Nikolai; Lin, Yen Ting A phase transition for finding needles in nonlinear haystacks with LASSO artificial neural networks. (English) Zbl 1499.62026 Stat. Comput. 32, No. 6, Paper No. 99, 18 p. (2022). MSC: 62-08 62J07 68T07 PDFBibTeX XMLCite \textit{X. Ma} et al., Stat. Comput. 32, No. 6, Paper No. 99, 18 p. (2022; Zbl 1499.62026) Full Text: DOI arXiv
Kaltenbacher, Barbara; Nguyen, Tram Thi Ngoc Discretization of parameter identification in PDEs using neural networks. (English) Zbl 1512.65197 Inverse Probl. 38, No. 12, Article ID 124007, 35 p. (2022). Reviewer: Temur A. Jangveladze (Tbilisi) MSC: 65M32 65M30 65J20 65M12 65M15 65K10 68T07 35R30 35R25 35R60 PDFBibTeX XMLCite \textit{B. Kaltenbacher} and \textit{T. T. N. Nguyen}, Inverse Probl. 38, No. 12, Article ID 124007, 35 p. (2022; Zbl 1512.65197) Full Text: DOI arXiv
Costarelli, Danilo Density results by deep neural network operators with integer weights. (English) Zbl 1524.68314 Math. Model. Anal. 27, No. 4, 547-560 (2022). MSC: 68T07 41A25 PDFBibTeX XMLCite \textit{D. Costarelli}, Math. Model. Anal. 27, No. 4, 547--560 (2022; Zbl 1524.68314) Full Text: DOI
Pei, Eddie; Fokoué, Ernest On some similarities and differences between deep neural networks and kernel learning machines. (English) Zbl 1524.68325 Math. Appl., Brno 11, No. 1, 75-106 (2022). MSC: 68T07 46E22 68T05 PDFBibTeX XMLCite \textit{E. Pei} and \textit{E. Fokoué}, Math. Appl., Brno 11, No. 1, 75--106 (2022; Zbl 1524.68325) Full Text: DOI
Li, Lingfeng; Tai, Xue-Cheng; Yang, Jiang Generalization error analysis of neural networks with gradient based regularization. (English) Zbl 07612898 Commun. Comput. Phys. 32, No. 4, 1007-1038 (2022). MSC: 68T07 PDFBibTeX XMLCite \textit{L. Li} et al., Commun. Comput. Phys. 32, No. 4, 1007--1038 (2022; Zbl 07612898) Full Text: DOI arXiv
Chen, Hengjie; Yu, Dansheng; Li, Zhong The construction and approximation of ReLU neural network operators. (English) Zbl 07607176 J. Funct. Spaces 2022, Article ID 1713912, 10 p. (2022). MSC: 68-XX PDFBibTeX XMLCite \textit{H. Chen} et al., J. Funct. Spaces 2022, Article ID 1713912, 10 p. (2022; Zbl 07607176) Full Text: DOI
De Ryck, Tim; Mishra, Siddhartha; Ray, Deep On the approximation of rough functions with deep neural networks. (English) Zbl 1524.65052 S\(\vec{\text{e}}\)MA J. 79, No. 3, 399-440 (2022). MSC: 65D05 65D15 65G99 68T07 PDFBibTeX XMLCite \textit{T. De Ryck} et al., S\(\vec{\text{e}}\)MA J. 79, No. 3, 399--440 (2022; Zbl 1524.65052) Full Text: DOI arXiv
Gu, Yiqi; Ng, Michael K. Deep adaptive basis Galerkin method for high-dimensional evolution equations with oscillatory solutions. (English) Zbl 1506.65154 SIAM J. Sci. Comput. 44, No. 5, A3130-A3157 (2022). Reviewer: Yinhua Xia (Hefei) MSC: 65M60 65M70 65M20 65M15 68T07 41A25 42C10 35B05 PDFBibTeX XMLCite \textit{Y. Gu} and \textit{M. K. Ng}, SIAM J. Sci. Comput. 44, No. 5, A3130--A3157 (2022; Zbl 1506.65154) Full Text: DOI arXiv
Zeglaoui, Anis; Ben Mabrouk, Anouar; Kravchenko, Oleg V. Wavelet neural networks functional approximation and application. (English) Zbl 1500.42020 Int. J. Wavelets Multiresolut. Inf. Process. 20, No. 4, Article ID 2150060, 31 p. (2022). Reviewer: Mehdi Rashidi-Kouchi (Kerman) MSC: 42C40 68T07 41A30 PDFBibTeX XMLCite \textit{A. Zeglaoui} et al., Int. J. Wavelets Multiresolut. Inf. Process. 20, No. 4, Article ID 2150060, 31 p. (2022; Zbl 1500.42020) Full Text: DOI
Chen, Hengjie; Li, Zhong A note on the applications of one primary function in deep neural networks. (English) Zbl 1517.41006 Int. J. Wavelets Multiresolut. Inf. Process. 20, No. 4, Article ID 2150058, 18 p. (2022). MSC: 41A30 41A25 68T07 82C32 92B20 PDFBibTeX XMLCite \textit{H. Chen} and \textit{Z. Li}, Int. J. Wavelets Multiresolut. Inf. Process. 20, No. 4, Article ID 2150058, 18 p. (2022; Zbl 1517.41006) Full Text: DOI
Pieper, Konstantin; Petrosyan, Armenak Nonconvex regularization for sparse neural networks. (English) Zbl 07576440 Appl. Comput. Harmon. Anal. 61, 25-56 (2022). MSC: 68-XX 92-XX PDFBibTeX XMLCite \textit{K. Pieper} and \textit{A. Petrosyan}, Appl. Comput. Harmon. Anal. 61, 25--56 (2022; Zbl 07576440) Full Text: DOI arXiv
Gu, Yiqi; Ng, Michael K. Deep Ritz method for the spectral fractional Laplacian equation using the Caffarelli-Silvestre extension. (English) Zbl 1492.65309 SIAM J. Sci. Comput. 44, No. 4, A2018-A2036 (2022). MSC: 65N30 65N15 65C05 68T07 41A25 PDFBibTeX XMLCite \textit{Y. Gu} and \textit{M. K. Ng}, SIAM J. Sci. Comput. 44, No. 4, A2018--A2036 (2022; Zbl 1492.65309) Full Text: DOI arXiv
Cheng, Fangxiong; Xu, Hui; Feng, Xinlong Retracted: Model order reduction method based on machine learning for parameterized time-dependent partial differential equations. (English) Zbl 07568384 J. Sci. Comput. 92, No. 2, Paper No. 64, 25 p. (2022); retraction note ibid. 93, No. 3, Paper No. 71, 1 p. (2022). MSC: 68Txx 65Mxx 65Nxx PDFBibTeX XMLCite \textit{F. Cheng} et al., J. Sci. Comput. 92, No. 2, Paper No. 64, 25 p. (2022; Zbl 07568384) Full Text: DOI
He, Juncai; Li, Lin; Xu, Jinchao ReLU deep neural networks from the hierarchical basis perspective. (English) Zbl 1524.68317 Comput. Math. Appl. 120, 105-114 (2022). MSC: 68T07 41A25 41A30 65D15 65N30 PDFBibTeX XMLCite \textit{J. He} et al., Comput. Math. Appl. 120, 105--114 (2022; Zbl 1524.68317) Full Text: DOI arXiv
Ma, Limin; Siegel, Jonathan W.; Xu, Jinchao Uniform approximation rates and metric entropy of shallow neural networks. (English) Zbl 1514.41011 Res. Math. Sci. 9, No. 3, Paper No. 46, 21 p. (2022). MSC: 41A30 62B10 65N30 PDFBibTeX XMLCite \textit{L. Ma} et al., Res. Math. Sci. 9, No. 3, Paper No. 46, 21 p. (2022; Zbl 1514.41011) Full Text: DOI
He, Juncai; Li, Lin; Xu, Jinchao Approximation properties of deep ReLU CNNs. (English) Zbl 1514.41009 Res. Math. Sci. 9, No. 3, Paper No. 38, 24 p. (2022). MSC: 41A30 65D40 68T07 PDFBibTeX XMLCite \textit{J. He} et al., Res. Math. Sci. 9, No. 3, Paper No. 38, 24 p. (2022; Zbl 1514.41009) Full Text: DOI arXiv
Kadak, Uğur Multivariate neural network interpolation operators. (English) Zbl 07553114 J. Comput. Appl. Math. 414, Article ID 114426, 13 p. (2022). MSC: 68Txx 41A35 65D05 68T05 94A08 26A33 PDFBibTeX XMLCite \textit{U. Kadak}, J. Comput. Appl. Math. 414, Article ID 114426, 13 p. (2022; Zbl 07553114) Full Text: DOI
Galaris, Evangelos; Fabiani, Gianluca; Gallos, Ioannis; Kevrekidis, Ioannis; Siettos, Constantinos Numerical bifurcation analysis of PDEs from lattice Boltzmann model simulations: a parsimonious machine learning approach. (English) Zbl 1490.65184 J. Sci. Comput. 92, No. 2, Paper No. 34, 30 p. (2022). MSC: 65M32 35R30 68T05 76M28 PDFBibTeX XMLCite \textit{E. Galaris} et al., J. Sci. Comput. 92, No. 2, Paper No. 34, 30 p. (2022; Zbl 1490.65184) 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
Zhong, Qixian; Mueller, Jonas; Wang, Jane-Ling Deep learning for the partially linear Cox model. (English) Zbl 07547933 Ann. Stat. 50, No. 3, 1348-1375 (2022). MSC: 62N02 62G20 62C20 62G08 PDFBibTeX XMLCite \textit{Q. Zhong} et al., Ann. Stat. 50, No. 3, 1348--1375 (2022; Zbl 07547933) Full Text: DOI
Kim, Garam; Kim, Hyun-Min Deep learning approach for solving a quadratic matrix equation. (English) Zbl 1492.65102 East Asian Math. J. 38, No. 1, 95-105 (2022). MSC: 65F45 15A24 65H10 68T07 PDFBibTeX XMLCite \textit{G. Kim} and \textit{H.-M. Kim}, East Asian Math. J. 38, No. 1, 95--105 (2022; Zbl 1492.65102) Full Text: DOI
Qian, Yunyou; Yu, Dansheng Neural network interpolation operators activated by smooth ramp functions. (English) Zbl 1494.41007 Anal. Appl., Singap. 20, No. 4, 791-813 (2022). Reviewer: D. K. Ugulava (Tbilisi) MSC: 41A25 41A05 41A27 41A28 PDFBibTeX XMLCite \textit{Y. Qian} and \textit{D. Yu}, Anal. Appl., Singap. 20, No. 4, 791--813 (2022; Zbl 1494.41007) Full Text: DOI
Beck, Christian; Jentzen, Arnulf; Kuckuck, Benno Full error analysis for the training of deep neural networks. (English) Zbl 1492.65132 Infin. Dimens. Anal. Quantum Probab. Relat. Top. 25, No. 2, Article ID 2150020, 76 p. (2022). MSC: 65G99 68T07 PDFBibTeX XMLCite \textit{C. Beck} et al., Infin. Dimens. Anal. Quantum Probab. Relat. Top. 25, No. 2, Article ID 2150020, 76 p. (2022; Zbl 1492.65132) Full Text: DOI arXiv
Guan, Yu; Fang, Tingting; Zhang, Diankun; Jin, Congming Solving Fredholm integral equations using deep learning. (English) Zbl 1492.65359 Int. J. Appl. Comput. Math. 8, No. 2, Paper No. 87, 10 p. (2022). MSC: 65R20 45B05 68T07 PDFBibTeX XMLCite \textit{Y. Guan} et al., Int. J. Appl. Comput. Math. 8, No. 2, Paper No. 87, 10 p. (2022; Zbl 1492.65359) Full Text: DOI
Huang, Jianguo; Wang, Chunmei; Wang, Haoqin A deep learning method for elliptic hemivariational inequalities. (English) Zbl 1485.65070 East Asian J. Appl. Math. 12, No. 3, 487-502 (2022). MSC: 65K15 68T07 68U99 PDFBibTeX XMLCite \textit{J. Huang} et al., East Asian J. Appl. Math. 12, No. 3, 487--502 (2022; Zbl 1485.65070) Full Text: DOI
Siegel, Jonathan W.; Xu, Jinchao High-order approximation rates for shallow neural networks with cosine and \(\mathrm{ReLU}^k\) activation functions. (English) Zbl 1501.41006 Appl. Comput. Harmon. Anal. 58, 1-26 (2022). MSC: 41A30 42C40 46E35 65D05 PDFBibTeX XMLCite \textit{J. W. Siegel} and \textit{J. Xu}, Appl. Comput. Harmon. Anal. 58, 1--26 (2022; Zbl 1501.41006) Full Text: DOI arXiv
E, Weinan; Ma, Chao; Wu, Lei The Barron space and the flow-induced function spaces for neural network models. (English) Zbl 1490.65020 Constr. Approx. 55, No. 1, 369-406 (2022). MSC: 65D15 68T07 PDFBibTeX XMLCite \textit{W. E} et al., Constr. Approx. 55, No. 1, 369--406 (2022; Zbl 1490.65020) Full Text: DOI arXiv
Gribonval, Rémi; Kutyniok, Gitta; Nielsen, Morten; Voigtlaender, Felix Approximation spaces of deep neural networks. (English) Zbl 1491.82017 Constr. Approx. 55, No. 1, 259-367 (2022). Reviewer: Claudia Simionescu-Badea (Wien) MSC: 82C32 41A65 68T05 41A46 42C40 PDFBibTeX XMLCite \textit{R. Gribonval} et al., Constr. Approx. 55, No. 1, 259--367 (2022; Zbl 1491.82017) Full Text: DOI arXiv
Safran, Itay; Eldan, Ronen; Shamir, Ohad Depth separations in neural networks: what is actually being separated? (English) Zbl 1504.41023 Constr. Approx. 55, No. 1, 225-257 (2022). Reviewer: Alexei Lukashov (Moskva) MSC: 41A30 41A10 65D15 68T07 PDFBibTeX XMLCite \textit{I. Safran} et al., Constr. Approx. 55, No. 1, 225--257 (2022; Zbl 1504.41023) Full Text: DOI arXiv