Search Results for author: Kaj Nyström

Found 4 papers, 2 papers with code

Neural ODEs as the Deep Limit of ResNets with constant weights

2 code implementations arXiv 2019 Benny Avelin, Kaj Nyström

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

1 code implementation31 Aug 2018 Jens Berg, Kaj Nyström

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.

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Neural network augmented inverse problems for PDEs

no code implementations27 Dec 2017 Jens Berg, Kaj Nyström

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

no code implementations17 Nov 2017 Jens Berg, Kaj Nyström

In this paper we use deep feedforward artificial neural networks to approximate solutions to partial differential equations in complex geometries.

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