Solving parametric PDE problems with artificial neural networks

Published online

Journal Article

The curse of dimensionality is commonly encountered in numerical partial differential equations (PDE), especially when uncertainties have to be modelled into the equations as random coefficients. However, very often the variability of physical quantities derived from PDE can be captured by a few features on the space of the coefficient fields. Based on such observation, we propose using neural network to parameterise the physical quantity of interest as a function of input coefficients. The representability of such quantity using a neural network can be justified by viewing the neural network as performing time evolution to find the solutions to the PDE. We further demonstrate the simplicity and accuracy of the approach through notable examples of PDEs in engineering and physics.

Full Text

Duke Authors

Cited Authors

  • KHOO, Y; LU, J; YING, L

Published In

Start / End Page

  • 1 - 15

Published By

Electronic International Standard Serial Number (EISSN)

  • 1469-4425

International Standard Serial Number (ISSN)

  • 0956-7925

Digital Object Identifier (DOI)

  • 10.1017/s0956792520000182

Language

  • en