Iowa State University

Conference Schedule

Saturday, April 29, 2023
07:45 - 08:15 Registration 205 Carver Hall
08:15 - 08:30 Opening remarks 205 Carver Hall
08:30 - 09:15 Plenary Talk #1

Hongkai Zhao, Duke University
How much can one learn a PDE from a single solution data?

In this presentation, we discuss a few basic questions for PDE learning from observed solution data. Using various types of PDEs as examples, we show (1) how large the data space spanned by all snapshots along a solution trajectory is, (2) if one can construct an arbitrary solution by superposition of snapshots of a single solution, and (3) identifiability of a differential operator from a single solution data on local patches.

205 Carver Hall
09:15 - 9:45 Coffee Break 205 Carver Hall
09:45 - 11:15 Contributed Talks #1
09:45 - 10:00 Dexuan Xie, U. Wisconsin-Milwaukee
An effective Poisson-Nernst-Planck ion channel finite element solver
10:00 - 10:15 Mahboub Baccouch, U. Nebraska at Omaha
A superconvergent ultra-weak discontinuous Galerkin method for two-dimensional elliptic problems on Cartesian grids
10:15 - 10:30 Yang Yang, Michigan Technological U.
Provable convergence of blow-up time of numerical approximations for a class of convection-diffusion equations
10:30 - 10:45 Kunlun Qi, U. Minnesota-Twin Cities
Stability and convergence analysis of the Fourier-Galerkin spectral method for the Boltzmann equation
10:45 - 11:00 Fangyao Zhu, Michigan Technological U.
Well-balanced positivity preserving discontinuous Galerkin methods for Euler equations with gravitation
11:00 - 11:15 James Rossmanith, Iowa State U.
Maximum-Taylor discontinuous Galerkin (MTDG) schemes for solving linear hyperbolic systems
202 Carver Hall
Contributed Talks #2
09:45 - 10:00 Hailiang Liu, Iowa State U.
Some mathematical aspects of deep learning and optimal control
10:00 - 10:15 David Stewart, U. Iowa
Approximation by ridge functions and neural networks
10:15 - 10:30 Xuping Tian, Iowa State U.
Anderson acceleration of gradient methods with energy for optimization problems
10:30 - 10:45 Juntao Huang, Texas Tech U.
Structure-preserving machine learning moment closures for the radiative transfer equation
10:45 - 11:00 Andrew Pensoneault, U. Iowa
Efficient approximate Bayesian physics informed neural networks for inverse problems via ensemble Kalman inversion
11:00 - 11:15 Jue Yan, Iowa State U.
Cell-average based neural network method for time dependent partial differential equations
204 Carver Hall
11:30 - 12:15 Plenary Talk #2

Ann Almgren, Lawrence Berkeley National Lab
Adaptive mesh refinement: algorithms and applications

Adaptive mesh refinement (AMR) is one of several techniques for adapting the spatial resolution of a simulation in particular regions of the spatial domain. Block-structured AMR specifically refines the mesh by defining locally structured regions with finer spatial, and possibly temporal, resolution. This combination of locally structured meshes within an irregular global hierarchy is in some sense the best of both worlds in that it enables regular local data access while enabling greater flexibility in the overall computation.

Originally, block-structured AMR was designed for solving hyperbolic conservation laws with explicit time-stepping; in this case the changes to solution methodology in transforming a single-level solver to an AMR-based solver are relatively straightforward. AMR has come a long way, however, and the more complex the simulation, the more complex the changes to effectively use AMR. One can even consider whether to use different physical models at different levels of resolution. In this talk I will give an overview of block-structured AMR and focus on a few key exemplars for how to think about adaptivity for multiphysics simulations.

205 Carver Hall
12:15 - 13:45 Lunch on your own
13:45 - 14:30 Plenary Talk #3

William J. Layton, University of Pittsburgh
The challenge of accurate prediction of fluid motion

Over the last 40 years there have been great advances in computer hardware, solvers (methods for solving Ax=b), meshing algorithms, time stepping methods, adaptivity and so on. Yet accurate prediction of fluid motion (for settings where this is needed) is still elusive. This talk will review three major hurdles that remain: ensemble simulations, time accuracy and model stagnation. Three recent ideas where numerical analysis can help push forward the boundary between what can be done and what can't be done will be described. This talk is based on joint work with Catalin Trenchea, Ming Chen, Michael McLaughlin, Kiera Kean, Wenlong Pei, Nan Jiang, Joe Fiordelino, Ali Pakzad, Victor DeCaria, Yao Rong, Yi Li, Li Qin, Haiyun Zhao, Yong Li, Ahmet Guzel, Songul Kaya-Merdan, Michael Schneier and ….

205 Carver Hall
14:45 - 16:15 Contributed Talks #3
14:45 - 15:00 Xiaoming He, Missouri U. Science and Technology
A fully decoupled iterative method with 3D anisotropic immersed finite elements of non-homogeneous flux jump for Kaufman-type discharge problems
15:00 - 15:15 Preeti Sar, Iowa State U.
Asymptotic-preserving schemes for multidimensional Boltzmann-BGK
15:15 - 15:30 Tianxiang Gao, Iowa State U.
Wide neural networks are Gaussian processes, even they have infinitely many layers and shared weights
15:30 - 15:45 Zhen Chao, U. Michigan
Integral equation method for the 1D steady-state Poisson-Nernst-Planck equations

Songting Luo, Iowa State U.
Semiclassical approximations for fractional Schrödinger equations
15:45 - 16:00 Yindong Chen, Illinois Institute of Technology
A deterministic sampling method via maximum mean discrepancy flow with adaptive kernel
16:00 - 16:15 Michelle Michelle, Purdue U.
Wavelet Galerkin method for an electromagnetic scattering problem
202 Carver Hall
Contributed Talks #4
14:45 - 15:00 Shuwang Li, Illinois Institute of Technology
Kernel free boundary integral method (KFBIM) with linear regression model
15:00 - 15:15 Laurent Jay, U. Iowa
Solving initial value problems with constant step sizes and time-rescaling
15:15 - 15:30 Youxin Yuan, Missouri U. Science and Technology
Decoupled finite element method for a phase field model of two-phase ferrofluid flows
15:30 - 15:45 Ming Zhong, Illinois Institute of Technology
Computational discovery of collective behaviors from observation
15:45 - 16:00 Xiaokai Huo, Iowa State U.
Structure preserving numerical scheme for a quantum diffusion equation
16:00 - 16:15 Shuhao Cao, U. Missouri-Kansas City
Transformer meets boundary value inverse problems
204 Carver Hall
16:15 - 17:30 Poster Session and Coffee Break
1 Yuanxing Cheng, Illinois Institute of Technology
Energetic variational Gaussian process regression for computer experiments
2 Olivia Johnson, Iowa State U.
Dirichlet eigenvalue computation with deep neural networks
3 Heather Junk, Iowa State U.
Dirichlet eigenvalue computation with deep neural networks
4 Walker Wilcoxon, Iowa State U.
Solving Dirichlet eigenvalue problem with neural networks
5 Minshen Xu, Illinois Institute of Technology
Dimension reduction for Gaussian process models via convex combination of kernels
205 Carver Hall
18:30 - 20:30 Conference Dinner

Reiman Gardens
(Garden Room)

1407 University Blvd
Ames, IA 50011
Phone: 515.294.2710
Reiman Gardens (Garden Room)

Coordinated by
Iowa State University