The Deep Ritz Method: A Deep Learning-Based Numerical Algorithm for Solving Variational Problems

Goodfellow, I., Bengio, Y., Courville, A.: Deep Learning. MIT Press, Cambridge (2016)

E, W.: A proposal for machine learning via dynamical systems. Commun. Math. Stat. 5(1), 1–11 (2017)

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

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

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

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

Zhang, L., Han, J.Q., Wang, H., Car, R., E, W.: Deep potential molecular dynamics: a scalable model with the accuracy of quantum mechanics, submitted, arXiv:1707.09571

Evans, L.C.: Partial Differential Equations, 2nd edn. American Mathematical Society, Providence (2010)

He, K.M., Zhang, X.Y., Ren, S.Q., Sun, J.: Deep residual learning for image recognition. In: 2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pp. 770–778 (2016). https://doi.org/10.1109/CVPR.2016.90

Kingma, D.P., Ba, J.: Adam: a method for stochastic optimization. arXiv preprint. arXiv:1412.6980 , (2014)

Strang, G., Fix, G.: An Analysis of the Finite Element Method. Prentice-Hall, Upper Saddle River (1973)

Huang, G., Liu, Z., Weinberger, K.Q., Laurens, V.D.M.: Densely connected convolutional networks. arXiv preprint. arXiv:1608.06993 , (2016)