| Solving high-dimensional partial differential equations using deep learning J Han, A Jentzen, W E Proceedings of the National Academy of Sciences 115 (34), 8505-8510, 2018 | 1239 | 2018 |
| Deep learning-based numerical methods for high-dimensional parabolic partial differential equations and backward stochastic differential equations W E, J Han, A Jentzen https://arxiv.org/abs/1706.04702, 2017 | 532* | 2017 |
| Strong and weak divergence in finite time of Euler's method for stochastic differential equations with non-globally Lipschitz continuous coefficients M Hutzenthaler, A Jentzen, PE Kloeden Proceedings of the Royal Society A: Mathematical, Physical and Engineering …, 2011 | 407 | 2011 |
| Strong convergence of an explicit numerical method for SDEs with nonglobally Lipschitz continuous coefficients M Hutzenthaler, A Jentzen, PE Kloeden | 397 | 2012 |
| Numerical approximations of stochastic differential equations with non-globally Lipschitz continuous coefficients M Hutzenthaler, A Jentzen American Mathematical Soc., 2015 | 247 | 2015 |
| Deep optimal stopping S Becker, P Cheridito, A Jentzen The Journal of Machine Learning Research 20 (1), 2712-2736, 2019 | 194 | 2019 |
| Machine learning approximation algorithms for high-dimensional fully nonlinear partial differential equations and second-order backward stochastic differential equations C Beck, W E, A Jentzen Journal of Nonlinear Science 29, 1563-1619, 2019 | 189 | 2019 |
| A proof that artificial neural networks overcome the curse of dimensionality in the numerical approximation of Black-Scholes partial differential equations P Grohs, F Hornung, A Jentzen, P Von Wurstemberger arXiv preprint arXiv:1809.02362, 2018 | 187 | 2018 |
| Overcoming the order barrier in the numerical approximation of stochastic partial differential equations with additive space–time noise A Jentzen, PE Kloeden Proceedings of the Royal Society A: Mathematical, Physical and Engineering …, 2009 | 177 | 2009 |
| Taylor approximations for stochastic partial differential equations A Jentzen, PE Kloeden Society for Industrial and Applied Mathematics, 2011 | 164 | 2011 |
| The numerical approximation of stochastic partial differential equations A Jentzen, PE Kloeden Milan Journal of Mathematics 77, 205-244, 2009 | 164 | 2009 |
| Analysis of the generalization error: Empirical risk minimization over deep artificial neural networks overcomes the curse of dimensionality in the numerical approximation of … J Berner, P Grohs, A Jentzen SIAM Journal on Mathematics of Data Science 2 (3), 631-657, 2020 | 156 | 2020 |
| A proof that rectified deep neural networks overcome the curse of dimensionality in the numerical approximation of semilinear heat equations M Hutzenthaler, A Jentzen, T Kruse, TA Nguyen SN partial differential equations and applications 1, 1-34, 2020 | 140 | 2020 |
| On a perturbation theory and on strong convergence rates for stochastic ordinary and partial differential equations with nonglobally monotone coefficients M Hutzenthaler, A Jentzen | 116 | 2020 |
| Solving stochastic differential equations and Kolmogorov equations by means of deep learning C Beck, S Becker, P Grohs, N Jaafari, A Jentzen arXiv preprint arXiv:1806.00421 1 (1), 2018 | 111 | 2018 |
| A proof that deep artificial neural networks overcome the curse of dimensionality in the numerical approximation of Kolmogorov partial differential equations with constant … A Jentzen, D Salimova, T Welti arXiv preprint arXiv:1809.07321, 2018 | 110 | 2018 |
| Loss of regularity for Kolmogorov equations M Hairer, M Hutzenthaler, A Jentzen | 102 | 2015 |
| Galerkin approximations for the stochastic Burgers equation D Blomker, A Jentzen SIAM Journal on Numerical Analysis 51 (1), 694-715, 2013 | 98* | 2013 |
| DNN expression rate analysis of high-dimensional PDEs: application to option pricing D Elbrächter, P Grohs, A Jentzen, C Schwab Constructive Approximation 55 (1), 3-71, 2022 | 96 | 2022 |
| Overcoming the curse of dimensionality in the numerical approximation of semilinear parabolic partial differential equations M Hutzenthaler, A Jentzen, T Kruse, T Anh Nguyen, P von Wurstemberger Proceedings of the Royal Society A 476 (2244), 20190630, 2020 | 93 | 2020 |
Martin HutzenthalerUniversity of Duisburg-Essen, MathematicsVerified email at uni-due.de
