A machine-learning solver for modified diffusion equations

Qianshi Wei; Ying Jiang; Jeff Z. Y. Chen

doi:10.1103/physreve.98.053304

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arXiv · 1808.04519

A machine-learning solver for modified diffusion equations

Qianshi Wei·Ying Jiang·Jeff Z. Y. Chen

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Abstract

A feed-forward neural network has a remarkable property which allows the network itself to be a universal approximator for any functions.Here we present a universal, machine-learning based solver for multi-variable partial differential equations. The algorithm approximates the target functions by neural networks and adjusts the network parameters to approach the desirable solutions.The idea can be easily adopted for dealing with multi-variable, coupled integrodifferential equations, such as those in the self-consistent field theory for predicting polymer microphase-separated structures.

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BibTeX RIS

Qianshi Wei, Ying Jiang, Jeff Z. Y. Chen. 2018-08-14. A machine-learning solver for modified diffusion equations. https://doi.org/10.1103/physreve.98.053304

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