Events for 01/29/2020 from all calendars

Inverse Problems and Machine Learning

Time: 12:00PM - 1:00PM

Location: BLOC 628

Speaker: Mauricio Tano, Department of Nuclear Engineering, Texas A&M University

Title: Artificial Neural Networks to Accelerate Radiation Transport Sweeps

Abstract: Transport sweeping is a fast and efficient solution technique for solving the Sn (discrete ordinates) first-order transport equation discretized using Discontinuous Finite Elements. In transport sweeps, the angular flux solution is obtained for one angle and one spatial cell at a time by solving a small local system of equations. Gaussian Elimination (GE) is typically invoked to perform this task. However, GE may take up to 50% of the computing time spent in the sweeping routine. Here, we investigate the use of Machine Learning techniques to bypass assembling and solving the local system. In our approach, a shallow feed-forward artificial neural network (ANN) is chosen. The architecture of the ANN is to be optimized in order to reduce the number of operations compared to the Gaussian Elimination solve, while keeping a bounded error in the solution. The resulting ANN consists of an ANN with only one hidden layer. Numerical results show that speedups of a factor 3-4 are attainable by training a shallow artificial neural network.

Groups and Dynamics Seminar

Time: 3:00PM - 4:00PM

Location: BLOC 220

Speaker: Tianyi Zheng, UCSD

Title: Properties and construction of FC-central extensions

Abstract: We discuss a few properties of groups that are preserved under FC-central extensions. Various examples of FC-central extensions of groups constructed via taking diagonal products of marked groups will be explained.

Student/Postdoc Working Geometry Seminar

Time: 4:00PM - 5:00PM

Location: BLOC 624

Speaker: A. Huang, TAMU

Title: Mukai spring 2

Graduate Student Organization Seminar

Time: 4:00PM - 5:00PM

Location: BLOC 628

Speaker: Jiuhua Hu

Title: Homogenization of time-fractional diffusion equations with periodic coefficients

Abstract: In this talk, I will begin with introducing one of the model reduction techniques: homogenization. We shall consider the initial boundary value problem for the time-fractional diffusion equation with a homogeneous Dirichlet boundary condition and an inhomogeneous initial data $a(x)\in L^{2}(D)$ in a bounded domain $D\subset \mathbb{R}^d$ with a sufficiently smooth boundary. We analyze the homogenized solution under the assumption that the diffusion coefficient $\kappa^{\epsilon}(x)$ is smooth and periodic with the period $\epsilon>0$ being sufficiently small. We derive that its first order approximation measured by both pointwise-in-time in $L^2(D)$ and $L^p((\theta,T); H^1(D))$ for $p\in [1,\infty)$ and $\theta\in (0,T)$ has a convergence rate of $\mathcal{O}(\epsilon^{1/2})$ when the dimension $d\leq 2$ and $\mathcal{O}(\epsilon^{1/6})$ when $d=3$. Several numerical tests are presented to demonstrate the performance of the first order approximation. This is joint work with Guanglian Li.