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12/17/2021
On the existence of global minima and convergence analyses for gradient descent methods in the training of deep neural networks
In this article we study fully-connected feedforward deep ReLU ANNs with...
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10/15/2021
Strong L^p-error analysis of nonlinear Monte Carlo approximations for high-dimensional semilinear partial differential equations
Full-history recursive multilevel Picard (MLP) approximation schemes hav...
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03/19/2021
Landscape analysis for shallow ReLU neural networks: complete classification of critical points for affine target functions
In this paper, we analyze the landscape of the true loss of a ReLU neura...
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12/22/2020
An overview on deep learning-based approximation methods for partial differential equations
It is one of the most challenging problems in applied mathematics to app...
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08/31/2020
