Tuesday at 10:30-11:30 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
|
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| 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
|
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| October 8
Tuesday, 1pm |
No Seminar
|
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| October 15
Tuesday, 1pm |
No Seminar
|
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| October 22
Tuesday, 1pm |
No Seminar
|
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| October 29
Tuesday, 1pm |
Ohannes Karakashian
(University of Tennessee) |
Finite Element Methods for a System of Nonlinear Equations |
| November 5
Tuesday, 1pm |
No Seminar
|
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| November 12
Tuesday, 1pm |
No Seminar
|
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| November 19
Tuesday, 1pm |
No Seminar
|
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| November 26
Tuesday, 1pm |
No Seminar
|
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| December 3
Tuesday, 1pm |
Victor Churchill
(Dartmouth College) |
High order total variation Bayesian learning via synthesis |
| January 7
Tuesday, 11am |
No Seminar
|
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| January 14
Tuesday, 10:30am |
No Seminar
|
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| January 21
Tuesday, 10:30am |
No Seminar
|
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| January 28
Tuesday, 10:30am |
No Seminar
|
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| February 4
Tuesday, 10:30am |
No Seminar
|
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| February 11
Tuesday, 10:30am |
Yang Yang
(Michigan Technological Univ) |
Third-order conservative sign-preserving and steady-state-preserving time integrations and applications in stiff multispecies and multireaction detonations |
| February 18
Tuesday, 10:30am |
No Seminar
|
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| February 25
Tuesday, 10:30am |
No Seminar
|
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| March 3
Tuesday, 10:30am |
Michael Neilan
(University of Pittsburgh) |
Divergence-free finite elements for the Stokes problem in three dimensions |
| March 10
Tuesday, 10:30am |
No Seminar
|
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| March 17
Tuesday, 10:30am |
No Seminar
|
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| March 24
Tuesday, 10:30am |
No Seminar
|
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| March 31
Tuesday, 10:30am |
No Seminar
|
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| 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 one-step 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 one-step integration for autonomous ODE systems. Then two other neural network architectures will be introduced, including the recurrent ResNet (RT-ResNet) and the recursive ResNet (RS-ResNet), both of which can be viewed as multi-step exact temporal integrations for ODEs. I will first use autonomous dynamical systems to illustrate the general framework. Extensions to dynamical systems with random or time-dependent 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 finite-term approximations (e.g., a truncated Karhunen-Loeve 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 spatio-temporal 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 synthesis-based total variation Bayesian learning algorithm. Numerical examples are provided to demonstrate how our new technique is effectively employed.
In this talk, we develop third-order conservative sign-preserving 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 high-order bound-preserving techniques. First of all, most of the bound-preserving 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 maximum-principle 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 second-order Strang splitting methods where the flux and stiff source terms can be solved separately, and the extension to high-order 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 third-order conservative sign-preserving Rugne-Kutta 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 bound-preserving 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 divergence--free 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 multi-variate splines. We show that the divergence--free Stokes pairs are connected via a smooth discrete de Rham complex. Byproducts of this construction include characterizations of discrete divergence-free subspaces for the Stokes problem, commutative projections, and simple formulas for the dimensions of smooth polynomial spaces.
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