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Connections between deep learning and partial differential equations

Published online by Cambridge University Press:  06 May 2021

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, GA 30322, USA email: lruthotto@emory.edu
S. J. OSHER
Affiliation:
UCLA, Department of Mathematics, 520 Portola Plaza, Los Angeles, CA 90095, USA email: sjo@math.ucla.edu
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Abstract

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Type
Editorial Announcement
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, 470514.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, 397420.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, 515539.Google Scholar
Khoo, Y., Lu, J. % Ying, L. (2021) Solving parametric PDE problems with artificial neural networks. European Journal of Applied Mathematics, 32, 421435.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, 436469.Google Scholar
Savarino, F. & Schnörr, C. (2021) Continuous-domain assignment flows. European Journal of Applied Mathematics, 32, 570597.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, 540569.Google Scholar
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