邮箱 English

往期活动

Uncertainty quantification of deep neural networks

Abstract

I will first give a mathematical introduction to deep learning. Then I will talk about recent work on uncertainty quantification (UQ) of deep learning. In our UQ for deep neural networks (DNN) framework, the DNN architecture is the neural-ODE which formulates the evolution of potentially huge hidden layers in the DNN as a discretized ODE system. To characterize the randomness caused by the uncertainty of models and noises of data, we add a multiplicative Brownian motion noise to the ODE as a stochastic diffusion term, where the drift parameters serve as the prediction of the network, and the stochastic diffusion governs the randomness of network output.


Biography
Prof. Yanzhao Cao is currently the Don Logan Endowed Chair in Mathematics at Auburn University. He received both his BA and MA degrees in mathematics from Jilin University and Ph.D. in mathematics from Virginia Tech. He is an associate editor of SIAM Journal in Numerical Analysis and Journal of Integral Equations and Applications, and a managing editor of Communications in Mathematical Research. He is also serving as the President of SIAM Southeast and Atlantic Section. His expertise is in numerical methods for PDEs and stochastic computing.