2.3k citations · 2.3k across the 9 of their papers we have counts for
4 papers · 1 filter
DPM: A deep learning PDE augmentation method (with application to large-eddy simulation)
Jonathan B. Freund, Jonathan F. MacArt, Justin Sirignano
Machine learning for scientific applications faces the challenge of limited data. We propose a framework that leverages a priori known physics to reduce overfitting when training o…
Asymptotics of Reinforcement Learning with Neural Networks
Justin Sirignano, Konstantinos Spiliopoulos
We prove that a single-layer neural network trained with the Q-learning algorithm converges in distribution to a random ordinary differential equation as the size of the model and…
Scaling Limit of Neural Networks with the Xavier Initialization and Convergence to a Global Minimum
Justin Sirignano, Konstantinos Spiliopoulos
We analyze single-layer neural networks with the Xavier initialization in the asymptotic regime of large numbers of hidden units and large numbers of stochastic gradient descent tr…
Mean Field Analysis of Deep Neural Networks
Justin Sirignano, Konstantinos Spiliopoulos
We analyze multi-layer neural networks in the asymptotic regime of simultaneously (A) large network sizes and (B) large numbers of stochastic gradient descent training iterations.…