The Deep Ritz method: A deep learning-based numerical algorithm for solving variational problems

G. Strang and G. Fix, An Analysis of the Finite Element Method

1973

Earlier work this paper cites.

L. C. Evans, Partial Differential Equations, 2nd ed

2010

Earlier work this paper cites.

D. P. Kingma, and J. Ba. “Adam: A method for stochastic optimization.” arXiv preprint arXiv:1412.6980

Original

2014

Earlier work this paper cites.

I. Goodfellow, Y. Bengio and A. Courville, Deep Learning

2016

Cited alongside, same era.

K. M. He, X. Y. Zhang, S. Q. Ren, J. Sun, “Deep residual learning for image recognition”, 2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR)

2016

Cited alongside, same era.

J. Q. Han, A. Jentzen and W. E, “Overcoming the curse of dimensionality: Solving high-dimensional partial differential equations using deep learning”, submitted, arXiv:1707.02568

Original

Cited in the paper.

W. E, J. Q. Han and A. Jentzen, “Deep learning-based numerical methods for high-dimensional parabolic partial differential equations and backward stochastic differential equations”, submitted, arXiv:1706.04702

Original

Cited in the paper.

C. Beck, W. E and Arnulf Jentzen, “Machine learning approximation algorithms for high-dimensional fully nonlinear partial differential equations and second-order backward stochastic differential equations”, submitted. arXiv:1709.05963

Original

Cited in the paper.

J. Q. Han, L. Zhang, R. Car and W. E, “Deep Potential: A general and “first-principle” representation of the potential energy”, submitted, arXiv:1707.01478

Original

Cited in the paper.

L. Zhang, J.Q. Han, H. Wang, R. Car and W.E, “Deep Potential Molecular Dynamics: A scalable model with the accuracy of quantum mechanics”, submitted, arXiv:1707.09571

Original

Cited in the paper.

G. Huang, Z. Liu, K. Q. Weinberger, V. D. M. Laurens, “Densely connected convolutional networks.”, arXiv preprint arXiv:1608.06993

Original

2016

Later among the works it cites.

W. E, “A proposal for machine learning via dynamical systems”, Communications in Mathematics and Statistics

2017

Closest in time.