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04/04/2022
Deep learning, stochastic gradient descent and diffusion maps
Stochastic gradient descent (SGD) is widely used in deep learning due to...
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10/07/2021
Solving the Dirichlet problem for the Monge-Ampère equation using neural networks
The Monge-Ampère equation is a fully nonlinear partial differential equa...
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06/28/2019
Neural ODEs as the Deep Limit of ResNets with constant weights
In this paper we prove that, in the deep limit, the stochastic gradient ...
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08/31/2018
Data-driven discovery of PDEs in complex datasets
Many processes in science and engineering can be described by partial di...
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12/27/2017
Neural network augmented inverse problems for PDEs
In this paper we show how to augment classical methods for inverse probl...
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11/17/2017