Hostname: page-component-848d4c4894-pjpqr Total loading time: 0 Render date: 2024-06-21T17:50:11.876Z Has data issue: false hasContentIssue false
  • English
  • Français

Connections between deep learning and partial differential equations

Published online by Cambridge University Press:  06 May 2021

M. BURGER ,
W. E ,
L. RUTHOTTO  and
S. J. OSHER
M. BURGER
Affiliation:
Department Mathematik, Friedrich-Alexander Universität Erlangen-Nürnberg, Cauerstrasse 11, 91058 Erlangen, Germany email: martin.burger@fau.de
W. E
Affiliation:
Princeton University, Department of Mathematics, Princeton, NJ 08544-1000, USA email: weinan@math.princeton.edu
L. RUTHOTTO
Affiliation:
Emory University, Mathematics and Computer Science, 400 Dowman Drive, Atlanta, GA30322, USA email: lruthotto@emory.edu
S. J. OSHER
Affiliation:
UCLA, Department of Mathematics, 520 Portola Plaza, Los Angeles, CA90095, USA email: sjo@math.ucla.edu
Rights & Permissions [Opens in a new window]

Abstract

An abstract is not available for this content so a preview has been provided. As you have access to this content, a full PDF is available via the ‘Save PDF’ action button.
Image of the first page of this content. For PDF version, please use the ‘Save PDF’ preceeding this image.'
Type
Editorial Announcement
Information
European Journal of Applied Mathematics , Volume 32 , Special Issue 3: Connections between Deep learning and Partial Differential Equations , June 2021 , pp. 395 - 396
Check for updates
Copyright
© The Author(s), 2021. Published by Cambridge University Press

References

Becker, S., Cheridito, P., Jentzen, A. & Welti, T. (2021) Solving high-dimensional optimal stopping problems using deep learning. European Journal of Applied Mathematics, 32, 470–514.Google Scholar
Chen, X., Duan, J. & Karniadakis, G. E. (2021) Learning and meta-learning of stochastic advection-diffusion-reaction systems from sparse measurements. European Journal of Applied Mathematics, 32, 397–420.Google Scholar
Gin, C., Lusch, B., Brunton, S. C. & Kutz, J. N. (2021) Deep learning models for global coordinate transformations that linearize PDEs. European Journal of Applied Mathematics, 32, 515–539.Google Scholar
Khoo, Y., Lu, J. % Ying, L. (2021) Solving parametric PDE problems with artificial neural networks. European Journal of Applied Mathematics, 32, 421–435.Google Scholar
Lye, K. O., Mishra, S. & Molinaro, R. (2021) A Multi-level procedure for enhancing accuracy of machine learning algorithms. European Journal of Applied Mathematics, 32, 436–469.Google Scholar
Savarino, F. & Schnörr, C. (2021) Continuous-domain assignment flows. European Journal of Applied Mathematics, 32, 570–597.Google Scholar
Wang, B. & Osher, S. J. (2021) Graph interpolating activation improves both natural and robust accuracies in data- efficient deep learning. European Journal of Applied Mathematics, 32, 540–569.Google Scholar