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Deep neural network approximations for Monte Carlo algorithms

, , и . (2019)cite arxiv:1908.10828Comment: 45 pages.

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Arnulf Jentzen

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Richard Jentzen

 

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Convergence Rates for the Stochastic Gradient Descent Method for Non-Convex Objective Functions., , и . J. Mach. Learn. Res., (2020)Deep neural network approximations for Monte Carlo algorithms, , и . (2019)cite arxiv:1908.10828Comment: 45 pages.Algorithms for Solving High Dimensional PDEs: From Nonlinear Monte Carlo to Machine Learning., , и . CoRR, (2020)Galerkin Approximations for the Stochastic Burgers Equation., и . SIAM J. Numerical Analysis, 51 (1): 694-715 (2013)Overcoming the curse of dimensionality in the numerical approximation of Allen-Cahn partial differential equations via truncated full-history recursive multilevel Picard approximations., , , , и . J. Num. Math., 28 (4): 197-222 (2020)Deep learning approximations for non-local nonlinear PDEs with Neumann boundary conditions., , , , и . CoRR, (2022)Deep splitting method for parabolic PDEs., , , , и . CoRR, (2019)Existence, uniqueness, and convergence rates for gradient flows in the training of artificial neural networks with ReLU activation., , , и . CoRR, (2021)Gradient descent provably escapes saddle points in the training of shallow ReLU networks., , и . CoRR, (2022)Solving the Kolmogorov PDE by Means of Deep Learning., , , , и . J. Sci. Comput., 88 (3): 73 (2021)