Some observations on partial differential equations in Barron and multi-layer spaces

12/02/2020

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We use explicit representation formulas to show that solutions to certain partial differential equations can be represented efficiently using artificial neural networks, even in high dimension. Conversely, we present examples in which the solution fails to lie in the function space associated to a neural network under consideration.

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Some observations on partial differential equations in Barron and multi-layer spaces

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Some observations on partial differential equations in Barron and multi-layer spaces

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