- 2:30pm, Tuesday, September 11th: Dejan Slepčev,
*DNN: An Introduction for Applied Mathematicians* - 2:30pm, Tuesday, September 18th: Hayden Schaeffer,
*An Intro to Convolutional Neural Networks* - 2:30pm, Tuesday, October 2nd: Linan Zhang,
*Residual Network* - 2:30pm, Tuesday, October 9th, Matt Thorpe,
*GAN* - 2:30pm, Thursday, October 18th, Matt Thorpe,
*Wasserstein GAN* - 2:30pm, Tuesday, November 6th, Linan Zhang,
*A Short Tutorial on TensorFlow with an Example on AlexNet*

Handout: Tensor Flow Setup Instructions - 2:30pm, Tuesday, November 13th, Raghavendra Venkatraman,
*Connection between deep neural networks and differential equations* - 2:30pm, Tuesday, December 4th, Yifan Sun,
*Solving High Dimensional PDEs using Deep Learning*

Abstract: We examine how to approximate the solution of semi-linear parabolic PDE with terminal conditions using deep neural network. We will link the solution to a certain SDE, from which we can sample the trajectories, and the terminal condition used in order to define a loss function. The solution is parametrized by Deep Neural Network (DNN). The loss is minimized over sample paths to optimize the parametrization. The talk is based on the paper by Han, Jentzen and E : https://arxiv.org/pdf/1707.02568.pdf. Time permitting, we may also take a look at a related paper on using DL to solve optimal stopping problem: https://arxiv.org/pdf/1804.05394.pdf.

- Higham and Higham
*Deep Learning: An Introduction for Applied Mathematicians*arxiv.org/pdf/1801.05894.pdf - Y. LeCun, L. Bottou, Y. Bengio, and P. Haffner
*Gradient-based learning applied to document recognition.*https://ieeexplore.ieee.org/abstract/document/726791/ - Szegedy et al.
*Going Deeper with Convolutions.*https://arxiv.org/abs/1409.4842 - A. Krizhevsky, I. Sutskever, and G. E. Hinton
*ImageNet Classification with Deep Convolutional Neural Networks.*Link - Kaiming He, Xiangyu Zhang, Shaoqing Ren, and Jian Sun,
*Deep residual learning for image recognition.*In Proceedings of the IEEE conference on computer vision and pattern recognition, pp. 770-778. 2016. - Kaiming He, Xiangyu Zhang, Shaoqing Ren, and Jian Sun,
*Identity mappings in deep residual networks*In European conference on computer vision, pp. 630-645. Springer, Cham, 2016 - Martin Arjovsky, Soumith Chintala, Léon Bottou,
*Wasserstein GAN* -
I. J. Goodfellow, J. Pouget-Abadie, M. Mirza, B. Xu, D. Warde-Farley, S. Ozair, A. Courville and Y. Bengio,
*Generative Adversarial Nets*, arXiv:1406.2661 -
I. Goodfellow,
*NIPS 2016 Tutorial: Generative Adversarial Networks,*arXiv:1701.00160 -
S. Lunz, O. Oktem and C.-B. Schoenlieb,
*Adversarial Regularizers in Inverse Problems,*arXiv:1805.11572 -
D. Sussillo and L. F. Abbott,
*Random Walk Initialization for Training Very Deep Feedforward Networks,*arXiv:1412.6558 -
S. Mendonca,
*Splitting, parallel gradient and Bakry-Emery Ricci curvature},*arXiv:1502.00185 -
Y. Jia, E. Shelhamer, J. Donahue, S. Karayev, J. Long, R. Girshick, S. Guadarrama, and
T. Darrell
*Caffe: Convolutional Architecture for Fast Feature Embedding,*arXiv:1408.5093 -
D. P. Kingma and J. Ba,
*Adam: A Method for Stochastic Optimization,*arXiv:1412.6980 -
L. Ruthotto and E. Haber,
*Deep Neural Networks motivated by Partial Differential Equations,*arXiv:1804.04272 -
L. Ruthotto and E. Haber,
*Stable Architectures for Deep Neural Networks,*arXiv:1705.03341