ALOP invited guest Ratna Khatri with George Mason University will speak during the research seminar on October 21, 2020 at 17:00.

She will speak on the following topic:

 

Role of Nonlocal Operators in Inverse and Deep Learning Problems

 

Abstract:

In this talk, we will discuss the applications of nonlocal operators in two kinds of problems. The first problem is motivated by imaging science where we propose to use the fractional Laplacian as a regularizer. In addition, we create a bilevel optimization neural network (BONNet) to learn the optimal regularization parameters, like the strength of regularization and the fractional exponent. As our model problem, we consider tomographic reconstruction and show an improvement in the reconstruction quality, especially for limited data. In the second problem, we introduce a novel fractional deep neural network (fractional-DNN), with a rigorous mathematical framework. Fractional-DNN, can be viewed as a time-discretization of a fractional in time nonlinear ordinary differential equation (ODE). The learning problem then is a minimization problem subject to that fractional ODE as constraints. We test our network on datasets for classification problems. The key advantage of the fractional-DNN is a significant improvement to the vanishing gradient issue, due to the memory effect.

Please join us via ZOOM at 17:00. The link will be distributed via email.