Tuesday at 10:3011:30 AM in Cockins Hall (CH) Room 240 (unless otherwise noted).
For questions, contact Dr. Yulong Xing, Email: xing dot 205@osu.edu
DATE and TIME  SPEAKER  TITLE 
September 3
Tuesday, 1pm 
Ruchi Guo
(OSU) 
Immersed Finite Element Methods and The Applications in Interface Inverse Problems 
September 10
Tuesday, 1pm 
No Seminar


September 17
Tuesday, 1pm 
Tong Qin
(OSU) 
Learning Dynamics with Neural Networks 
September 24
Tuesday, 3pm 
Daniel Tartakovsky
(Stanford University) 
Method of Distributions for Hyperbolic Conservation Laws with Random Inputs 
October 1
Tuesday, 1pm 
No Seminar


October 8
Tuesday, 1pm 
No Seminar


October 15
Tuesday, 1pm 
No Seminar


October 22
Tuesday, 1pm 
No Seminar


October 29
Tuesday, 1pm 
Ohannes Karakashian
(University of Tennessee) 
Finite Element Methods for a System of Nonlinear Equations 
November 5
Tuesday, 1pm 
No Seminar


November 12
Tuesday, 1pm 
No Seminar


November 19
Tuesday, 1pm 
No Seminar


November 26
Tuesday, 1pm 
No Seminar


December 3
Tuesday, 1pm 
Victor Churchill
(Dartmouth College) 
High order total variation Bayesian learning via synthesis 
January 7
Tuesday, 11am 
No Seminar


January 14
Tuesday, 10:30am 
No Seminar


January 21
Tuesday, 10:30am 
No Seminar


January 28
Tuesday, 10:30am 
No Seminar


February 4
Tuesday, 10:30am 
No Seminar


February 11
Tuesday, 10:30am 
Yang Yang
(Michigan Technological Univ) 
Thirdorder conservative signpreserving and steadystatepreserving time integrations and applications in stiff multispecies and multireaction detonations 
February 18
Tuesday, 10:30am 
No Seminar


February 25
Tuesday, 10:30am 
No Seminar


March 3
Tuesday, 10:30am 
Michael Neilan
(University of Pittsburgh) 
Divergencefree finite elements for the Stokes problem in three dimensions 
March 10
Tuesday, 10:30am 
No Seminar


March 17
Tuesday, 10:30am 
No Seminar


March 24
Tuesday, 10:30am 
No Seminar


March 31
Tuesday, 10:30am 
No Seminar


April 7
Tuesday, 10:30am 
Jianxian Qiu
(Xiamen University) 
CANCELLED 
April 14
Tuesday, 10:30am 
Cory Hauck
(Oak Ridge National Laboratory) 
CANCELLED 
April 21
Tuesday, 10:30am 
No Seminar

Interface problems and the related inverse problems widely appear in many engineering applications. These problems in general involve multiple materials coupled through interfaces which cause challenges to numerical methods. The basic idea of immersed finite element (IFE) methods is to solve interface problems on unfitted meshes which circumvents the burden of mesh regeneration. In this talk, I will firstly review our recent works on developing and analyzing IFE methods to solve various interface problems on unfitted meshes. Then I will describe a parameterized shape optimization algorithm based on IFE methods to solve a group of interface inverse problems including electrical impedance tomography (EIT) and elastography. A set of numerical experiments are shown to demonstrate the strength and versatility of the proposed method.
Recent years have seen great developments of the machine learning techniques, especially the deep learning, in areas like computer vision, signal processing, and recommendation systems. Such techniques, on the other hand, provides powerful tools for solving problems in traditional physical sciences by leveraging accumulated experimental data. In this talk, I will introduce our recent work on using neural networks to learn dynamics from data. In particular, basing on the onestep integral form of the ODEs, we propose to use the residual network (ResNet) as the basic building block for dynamics recovery. The ResNet block can be considered as an exact onestep integration for autonomous ODE systems. Then two other neural network architectures will be introduced, including the recurrent ResNet (RTResNet) and the recursive ResNet (RSResNet), both of which can be viewed as multistep exact temporal integrations for ODEs. I will first use autonomous dynamical systems to illustrate the general framework. Extensions to dynamical systems with random or timedependent parameters will also be discussed.
Parametric uncertainty, considered broadly to include uncertainty in system parameters and driving forces (source terms and initial and boundary conditions), is ubiquitous in mathematical modeling. The method of distributions, which comprises PDF and CDF methods, quantifies parametric uncertainty by deriving deterministic equations for either probability density function (PDF) or cumulative distribution function (CDF) of model outputs. Since it does not rely on finiteterm approximations (e.g., a truncated KarhunenLoeve transformation) of random parameter fields, the method of distributions does not suffer from the ``curse of dimensionality''. On the contrary, it is exact for a class of nonlinear hyperbolic equations whose coefficients lack spatiotemporal correlation, i.e., exhibit an infinite number of random dimensions. In settings that require a closure approximation, we use of neural networks to learn the coefficients in the CDF equations from a training set of Monte Carlo runs.
We consider systems of nonlinear dispersive equations of KdV type that are coupled through the nonlinear terms. We develop finite element discretizations using continuous elements. Both conservative and dissipative formulations are considered and A priori and a posteriori error estimates are derived. We also present results of some numerical experiments.
We present a sparse Bayesian learning algorithm for inverse problems in signal and image processing with a high order total variation sparsity prior that can provide both accurate estimation as well as uncertainty quantification. Sparse Bayesian learning often produces more accurate estimates than the typical maximum a posteriori Bayesian estimates for sparse signal recovery. In addition, it also provides a full posterior distribution which aids downstream processing and uncertainty quantification. However, sparse Bayesian learning is only available to problems with a direct sparsity prior or those formed via synthesis. We build upon a recent paper to demonstrate how both 1D and 2D problems with a high order total variation sparsity prior can be formulated via synthesis, and develop a synthesisbased total variation Bayesian learning algorithm. Numerical examples are provided to demonstrate how our new technique is effectively employed.
In this talk, we develop thirdorder conservative signpreserving time integrations and seek their applications in multispecies and multireaction chemical reactive flows. In this problem, some unknown variables has special physical bounds, for example, the mass fraction for the ith species, denoted as z_i, 1<=i<=M, should be between 0 and 1, where M is the total number of species. We would like to construct suitable numerical techniques to preserve those physical bounds. There are four main difficulties in constructing highorder boundpreserving techniques. First of all, most of the boundpreserving techniques available are based on Euler forward time integration. Therefore, for problems with stiff source, the time step will be significantly limited. Secondly, the mass fraction does not satisfy a maximumprinciple and hence it is not easy to preserve the upper bound 1. Thirdly, in most of the previous works for gaseous denotation, the algorithm relies on secondorder Strang splitting methods where the flux and stiff source terms can be solved separately, and the extension to highorder time discretization seems to be complicated. Finally, most of the previous ODE solvers for stiff problems cannot preserve the total mass and the positivity of the numerical approximations at the same time. In this talk, we will construct thirdorder conservative signpreserving RugneKutta and multistep methods to overcome all these difficulties. The time integrations do not depend on the Strang splitting. Moreover, the time discretization can handle the stiff source with large time step. Numerical experiments will be given to demonstrate the good performance of the boundpreserving technique and the stability of the scheme for problems with stiff source terms.
Using smooth piecewise polynomial spaces as a guide, we develop several stable divergencefree finite element spaces for the Stokes/NSE problem in three dimensions. These spaces are defined on splits of a simplicial triangulation, which are well known in the field of multivariate splines. We show that the divergencefree Stokes pairs are connected via a smooth discrete de Rham complex. Byproducts of this construction include characterizations of discrete divergencefree subspaces for the Stokes problem, commutative projections, and simple formulas for the dimensions of smooth polynomial spaces.
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