Arnulf Jentzen

Solving high-dimensional partial differential equations using deep learning

Jiequn Han, Arnulf Jentzen, E Weinan · Proceedings of the National Academy of Sciences · 2018 · 1.7K citations · Full text

Computing, Computer Science, Physics +12

Deep Learning-Based Numerical Methods for High-Dimensional Parabolic Partial Differential Equations and Backward Stochastic Differential Equations

E Weinan, Jiequn Han, Arnulf Jentzen · Communications in Mathematics and Statistics · 2017 · 828 citations · Full text

Natural Sciences, Mathematics, Physics +16

Strong convergence of an explicit numerical method for SDEs with nonglobally Lipschitz continuous coefficients

Martin Hutzenthaler, Arnulf Jentzen, Peter E. Kloeden · The Annals of Applied Probability · 2012 · 439 citations · Full text

Engineering, Computational Engineering, Differential Equations +14

Strong and weak divergence in finite time of Euler's method for stochastic differential equations with non-globally Lipschitz continuous coefficients

Martin Hutzenthaler, Arnulf Jentzen, Peter E. Kloeden · Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences · 2010 · 432 citations · Full text

Natural Sciences, Mathematics, Differential Equations +16

Machine Learning Approximation Algorithms for High-Dimensional Fully Nonlinear Partial Differential Equations and Second-order Backward Stochastic Differential Equations

Christian Beck, E Weinan, Arnulf Jentzen · Journal of Nonlinear Science · 2019 · 314 citations · Full text

Computing, Computer Science, Machine Learning +13