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Found 6 papers, 2 papers with code
Neural ODEs as the Deep Limit of ResNets with constant weights
In this paper we prove that, in the deep limit, the stochastic gradient descent on a ResNet type deep neural network, where each layer shares the same weight matrix, converges to the stochastic gradient descent for a Neural ODE and that the corresponding value/loss functions converge.
Data-driven discovery of PDEs in complex datasets
A different approach is to measure the quantities of interest and use deep learning to reverse engineer the PDEs which are describing the physical process.
Neural network augmented inverse problems for PDEs
In this paper we show how to augment classical methods for inverse problems with artificial neural networks.
A unified deep artificial neural network approach to partial differential equations in complex geometries
In this paper we use deep feedforward artificial neural networks to approximate solutions to partial differential equations in complex geometries.
Solving the Dirichlet problem for the Monge-Ampère equation using neural networks
The Monge-Amp\`ere equation is a fully nonlinear partial differential equation (PDE) of fundamental importance in analysis, geometry and in the applied sciences.
Deep learning, stochastic gradient descent and diffusion maps
Stochastic gradient descent (SGD) is widely used in deep learning due to its computational efficiency, but a complete understanding of why SGD performs so well remains a major challenge.
