Skip to main content
Journal cover image

Variational training of neural network approximations of solution maps for physical models

Publication ,  Journal Article
Li, Y; Lu, J; Mao, A
Published in: Journal of Computational Physics
May 15, 2020

A novel solve-training framework is proposed to train neural network in representing low dimensional solution maps of physical models. Solve-training framework uses the neural network as the ansatz of the solution map and trains the network variationally via loss functions from the underlying physical models. Solve-training framework avoids expensive data preparation in the traditional supervised training procedure, which prepares labels for input data, and still achieves effective representation of the solution map adapted to the input data distribution. The efficiency of solve-training framework is demonstrated through obtaining solution maps for linear and nonlinear elliptic equations, and maps from potentials to ground states of linear and nonlinear Schrödinger equations.

Duke Scholars

Altmetric Attention Stats
Dimensions Citation Stats

Published In

Journal of Computational Physics

DOI

EISSN

1090-2716

ISSN

0021-9991

Publication Date

May 15, 2020

Volume

409

Related Subject Headings

  • Applied Mathematics
  • 51 Physical sciences
  • 49 Mathematical sciences
  • 40 Engineering
  • 09 Engineering
  • 02 Physical Sciences
  • 01 Mathematical Sciences
 

Citation

APA
Chicago
ICMJE
MLA
NLM
Li, Y., Lu, J., & Mao, A. (2020). Variational training of neural network approximations of solution maps for physical models. Journal of Computational Physics, 409. https://doi.org/10.1016/j.jcp.2020.109338
Li, Y., J. Lu, and A. Mao. “Variational training of neural network approximations of solution maps for physical models.” Journal of Computational Physics 409 (May 15, 2020). https://doi.org/10.1016/j.jcp.2020.109338.
Li Y, Lu J, Mao A. Variational training of neural network approximations of solution maps for physical models. Journal of Computational Physics. 2020 May 15;409.
Li, Y., et al. “Variational training of neural network approximations of solution maps for physical models.” Journal of Computational Physics, vol. 409, May 2020. Scopus, doi:10.1016/j.jcp.2020.109338.
Li Y, Lu J, Mao A. Variational training of neural network approximations of solution maps for physical models. Journal of Computational Physics. 2020 May 15;409.
Journal cover image

Published In

Journal of Computational Physics

DOI

EISSN

1090-2716

ISSN

0021-9991

Publication Date

May 15, 2020

Volume

409

Related Subject Headings

  • Applied Mathematics
  • 51 Physical sciences
  • 49 Mathematical sciences
  • 40 Engineering
  • 09 Engineering
  • 02 Physical Sciences
  • 01 Mathematical Sciences