Department Colloquium

2023-2024 Colloquium

Unless indicated otherwise (*), the talks will be held 12-12:50 p.m. Tuesday in 372 MSC, with refreshment and conversation from 11:30 a.m. - noon in 368 MSC.

November 7, Krzysztof Fidkowski (University of Michigan) Output-Adaptive Hybridized Discontinuous Finite Elements for Efficient Flow Computations

Discontinuous Galerkin (DG) methods have enabled accurate computations of complex flowfields, yet their memory footprint and computational costs are large. Hybridized discontinuous Galerkin (HDG/EDG) methods reduce the number of globally-coupled degrees of freedom by decoupling elements and stitching the unknowns together through equations of weak flux continuity. An adjoint-weighted residual provides the error estimate in a chosen output, and localized to elements, this error indicator is used to optimize the computational mesh. The mesh optimization includes order (p) refinement and remeshing (h). Both steady and unsteady problems are considered, with the latter requiring attribution of the error to the spatial and temporal discretizations. The applications of interest include external aerodynamics with compressible flows at high Reynolds numbers.

November 2*, Huong Tran (Oakland University) Graphical Assessment of Univariate and Multivariate Normality and Other Probability Distributions

The assumption of normality plays an important role in numerous statistical analyses, and making an accurate assessment of this assumption is vital. Due to the complexity of high dimensional data, most of the existing hypothesis testing-based techniques have low power and fail to give much insight as the decision is just reduced to one number and corresponding p-value. Graphical methods, although more informal, shed more insight into the extent of departure from normality. With visual representations, one can gain deeper insights into the characteristics of the distribution of the data.

In this work, we introduce certain graphical tools to assess univariate and multivariate normality based on the derivatives of the cumulant generating functions. These enable us to assess the departures due to the skewness of the data and the thickness of the distribution towards the tails. In the case of univariate data, the method can also be extended to test other distributional assumptions for the data.

October 31, Tamás Horváth (Oakland University) Embedded or Hybridized Discontinuous Galerkin Methods? Maybe both?

Discontinuous Galerkin methods have been developed for many applications but are usually criticized for the larger number of unknowns compared to continuous Galerkin discretizations. The Hybridizable DG method overcame this issue by introducing additional facet unknowns and reducing the problem to the facet unknowns using static condensation. The Embedded DG methods further reduced the number of unknowns by using continuous basis functions for the facet unknowns. However, in certain applications, such as incompressible fluids, one can consider using different trace functions for the different variables, which leads to the Embedded-Hybridizable DG methods. This talk will present some applications of these methods and discuss the advantages and disadvantages.

October 24, Giselle Sosa Jones (Oakland University) Numerical simulation of multiphase flow in porous media

Modeling the flow of liquid, aqueous, and vapor phases through porous media is a complex and challenging task that requires solving nonlinear coupled partial differential equations. In this talk, we propose a second-order accurate and energy-stable time discretization method for the two-phase flow problem in porous media. We prove the convergence of the linearization scheme and demonstrate the energy-stability property. Our spatial discretization uses an interior penalty discontinuous Galerkin method, and we establish the well-posedness of the discrete problem and provide error estimates under certain conditions on the data. We validate our method through numerical simulations, which show that our approach achieves the theoretical convergence rates. Furthermore, the numerical examples highlight the advantages of our time discretization over other second-order approximations.

October 17, Susan Strong, Theo Cauc, Greg Antoine (Altair) Meet Altair and learn about your path to success!

Altair is global leader in computational science and AI, converging software, and cloud solutions in simulation, HPC, and data analytics.

October 10, Chen Liu, (Purdue University) Recent Progress on Positivity-preserving High-order Accurate Implicit-explicit Algorithm for Compressible Flow Simulations

In many demanding gas dynamics applications such as hypersonic flow simulation, the compressible Navier–Stokes equations form one of the most popular and important models. In this talk, we propose a fully discrete implicit-explicit scheme for solving the compressible Navier–Stokes equations within the operator splitting framework. In our approach, the compressible model is split into a hyperbolic subproblem and a parabolic subproblem, which represent two asymptotic regimes: the vanishing viscosity limit and the dominant of diffusive terms. We utilize the Runge–Kutta discontinuous Galerkin method and interior penalty discontinuous Galerkin method to discrete the hyperbolic subproblem and the parabolic subproblem, respectively.

Our proposed scheme preserves conservations of arbitrary high order in space. The positive-preserving property for up to Q3 space discretization is rigorously provable via using the monotonicity of the system matrix. For even higher order Qk (k ≥ 4) space discretization, the numerical schemes can be rendered bound-preserving without losing conservation and accuracy, by a post-processing procedure of solving a constrained minimization in each time step. Such a constrained optimization can be formulated as a nonsmooth convex minimization problem, which can be efficiently solved by Douglas–Rachford method if using the optimal algorithm parameters. By analyzing the asymptotic linear convergence rate of the generalized Douglas–Rachford splitting method, optimal algorithm parameters can be approximately expressed as a simple function of the numerical solutions. For each time step, the computational cost for the Douglas–Rachford splitting to enforce bounds and conservation up to the round-off error is of order O(N), where N denotes the total number of mesh cells. Our scheme enjoys the standard hyperbolic CFL on time step size upper bound selection. Numerical experiments suggest that our scheme produces satisfactory non-oscillatory solutions when physical diffusion is accurately resolved. Therefore, it is highly preferred and well-suited for simulating realistic physical and engineering problems.

October 5, Peter Shi (Oakland University) A rigorous justification of buy-low and sell-high for stocks

The author proves that a novel formulation of the Efficient Market Hypothesis (EMH) leads to a rigorous justification of the old market adage: buy-low and sell-high. In particular, the benchmarks for "low and high" are established through a min-max operation on the Bayes's error. This explicit connection between the EMH and Statistical Arbitrage represents a novel contribution to  quantitative trading. The resulting system is extensively back-tested using historical data to support the theoretical findings.

September 26, Huan Lei (Michigan State University) A machine-learning based non-Newtonian hydrodynamic model with molecular fidelity

A long standing problem in the modeling of non-Newtonian hydrodynamics of polymeric flows is the availability of reliable and interpretable hydrodynamic models that faithfully encode the underlying micro-scale polymer dynamics. The main complication arises from the long polymer relaxation time, the complex molecular structure and heterogeneous interaction. We developed a deep learning-based non-Newtonian hydrodynamic model, DeePN$^2$, that enables us to systematically pass the micro-scale structural mechanics information to the macro-scale hydrodynamics for polymer suspensions. The model retains a multi-scaled nature with clear physical interpretation, and strictly preserves the frame-indifference constraints. We show that DeePN$^2$ can faithfully capture the broadly overlooked viscoelastic differences arising from the specific molecular structural mechanics without human intervention.

September 7, Aycil Cesmelioglu (Oakland University), Numerical study of the Stokes/Darcy model and related problems

The coupling of free flow and porous media flow, which is governed by the Stokes/Darcy model, arises in a wide range of physical processes such as the transport of contaminants via surface/subsurface flow. In this talk, we will look at this problem and a couple of other related problems from a numerical perspective using the hybridizable discontinuous Galerkin (HDG) method. We will discuss the properties and well-posedness of the numerical schemes and their a priori error estimates. Supporting numerical experiments will be presented.

2022-2023 Colloquium

Unless indicated otherwise (*), the talks will be held 12-12:50 p.m. Tuesday in 372 MSC, with refreshment and conversation from 11:30 a.m. - noon in 368 MSC.

April 18, Yaser Samadi (Southern Illinois University), Dimension Reduction for Multivariate Autoregressive Models

The issue of overparameterization poses a significant challenge for standard vector autoregressive (VAR) models, particularly when dealing with high-dimensional time series data, as it limits the number of variables and lags that can be effectively incorporated into the model. Existing statistical methods, such as the reduced-rank model for multivariate time series and the Envelope VAR model, offer partial solutions for dimension reduction of the parameter space in VAR models. However, these methods have limitations, such as inefficiency in extracting relevant information from complex data or neglecting the rank deficiency problem. In this talk, we introduce a novel approach that combines the strengths of envelope models with the reduced-rank VAR model to address these challenges, resulting in a new parsimonious version of the classical VAR model called the reduced-rank envelope VAR model (REVAR). The REVAR model aims to achieve both efficiency and accuracy by leveraging the advantages of reduced-rank VAR and envelope VAR models. We will discuss the asymptotic properties of the proposed estimators and conduct simulation studies and real data analysis to evaluate and illustrate the effectiveness of our method. Our results demonstrate significant improvements in efficiency and accuracy compared to existing methods, as shown through simulation studies and real data analysis.

April 11, Michael Meitzner (General Motors), Data Science and Analytics at General Motors

Mike Meitzner is a Data Science Manager in the Advanced Analytics Center of Expertise (AACE) at General Motors. The AACE team works on projects that span the enterprise, with the aim to deliver value to key business stakeholders using both proven techniques as well as researching new and novel approaches. Mike will provide an overview of data science and analytics in the automotive and transportation sector in general, as well as provide some examples of applications specific to General Motors.

April 4, Gary McDonald, Disparity testing when there is uncertainty in data sources.

This colloquia talk centers on a new class of statistical inference problems arising from disparity assessments in the financial, insurance, and related industries where individual information is incomplete with respect to race/ethnicity. The evolution of such problems will be discussed along with the formulation of the statistical model and strategies for relevant parameter estimation. Both frequentist and Bayesian approaches will be formulated and computational methods given to permit implementation with real-world problems involving both small sample and large sample cases. This work has taken place over the past five years with the contributions of three Dept. of Math & Stat students. The talk should be of interest to a "general" audience as well as to "technical specialists".

March 21, Ebrahim Sarabi, Miami University, Twice Epi-Differentiability: Past, Present, and Future

In this talk, we discuss various aspects of twice epi-differentiablity of extended-real-valued functions and its remarkable applications in parametric optimization, second-order variational analysis, and local convergence analysis of the Newton method. We begin with presenting the history of this concept and then proceed with its evolution in the last three decades. In particular, we demonstrate that this property often holds for various classes of functions, important for applications to optimization problems. Finally, we discuss how a generalization of this concept leads us to achieve a characterization of continuous differentiability of the projection mapping for a large class of sets.

March 14, Loic Cappanera (University of Houston), Robust and efficient numerical methods for incompressible flows with variable density.

The modeling and approximation of incompressible flows with variable density are important for a large range of applications in biology, engineering and geophysics. Our main goal here is to develop and analyze numerical methods that use time-independent stiffness matrices and that can be used with high order finite element and spectral methods. First, we introduce a semi-implicit scheme based on projection methods and the use of the momentum, equal to the density times the velocity, as primary unknown. We analyze the stability and convergence properties of the method and establish a priori error estimates. A fully explicit version of the scheme is then proposed. Its robustness and convergence properties are studied with a pseudo spectral code over various setups involving large ratio of density, gravity and surface tension effects, or manufactured solutions. Applications to magnetohydrodynamics instabilities in industrial setups such as liquid metal batteries will be presented shortly. Eventually, a novel method based on artificial compressibility techniques is introduced and its performances are compared to our projection-based method.

Feb 14, Santosh Kottalgi (Ansys), Understanding the increasing role of numerical simulation to address product design challenges using Ansys software

Product design process has changed significantly in the last 20 years because of increasing use of simulation technologies, improved IT hardware offering and pressure to reduce time and cost. A simulation that was used as a failure analysis tool during the service life stage is now used almost in all stages of the product life cycle, from design to manufacturing to servicing to recycling. The strength of simulation is improved by added focus from researchers on accurate and comprehensive numerical methods to represent real-world physics as closely as possible. It is no wonder that simulation models are used as Digital twins of physical models in many cases. Ansys as a market leader in simulation solution providers is working on addressing these complex challenges and the talk will discuss some of the market trends and technologies. The author will also provide guidance to students to find their career paths as simulation analysts, developers, researchers, and educators.

The talk is from noon - 12:50 p.m. in MSC 372.

Santosh Kottalgi's talk will be also live on Zoom.

Nov 8 Matthew Toeniskoetter (Oakland University) Overrings of a 2-Dimensional RLR

Given a two-dimensional regular local ring D, there is a rich classical theory of the regular local rings birationally dominating it (between it and its field of fractions). These rings are in one-to- one correspondence with the divisorial valuation rings birationally dominating D, and they form a tree structure called the quadratic tree through the process of blowing-up. Much less is known about the non-Noetherian rings between D and its field of fractions. In this talk, we work towards a classification of the integrally closed rings between D and its field of fractions. We consider subspaces of the Zariski-Riemann space of valuation rings dominating D, and we relate the topological properties of the subspace with the ring-theoretic properties of the ring it produces. We give a new construction of a type of ring first proved by Nagata: a 1-dimensional integrally closed local ring birationally dominating D that's not integrally closed. We also describe new examples of one- and two-dimensional vacant domains (domains with a unique Kronecker function ring) that are not Prüfer. This is joint work with B. Heinzer, A. Loper, and
B. Olberding.

(*) The talk is from 11:30 a.m. - 12:20 p.m. in MSC 372.

Matthew Toeniskoetter's talk will be also live on Zoom.

Oct 25 Jun Hu (Oakland University) A general sequential learning procedure with illustrations

Sequential learning builds sampling schemes in which the required sample size is not fixed in advance and instead, observations are collected successively according to some predefined stopping rule. In this talk, we propose a broad and general sequential learning procedure, which incorporates four different types of sampling schemes: (i) the classic Anscombe-Chow-Robbins purely sequential sampling scheme; (ii) the ordinary accelerated sequential sampling scheme; (iii) the relatively new k-at-a-time sequential sampling scheme; and (iv) the new k-at-a-time improved accelerated sequential sampling scheme. The second-order efficiency of this general sequential learning procedure is fully investigated.

We will implement this sequential learning procedure to handle three fundamental statistical inference problems as possible illustrations, namely, (i) minimum risk point estimation, (ii) bounded variance point estimation, and (iii) point estimation in linear regression. An extensive set of simulations are presented to validate our theoretical findings. And real data analyses are included to highlight its practical applicability.

Jun Hu's talk will be also live on Zoom.

Oct 18 Yongjin Lu (Oakland University) Large time behavior of nonlinear partial differential equations subject to external force

In this presentation, we address the problem of long-time behavior and the associated stabilization of solutions to nonlinear partial differential equations (PDE) when they are subject to external force. The equations under study include a system of nonlinear PDEs that couples Navier-Stokes equation with wave equation to describe the interaction between a solid submerged in surrounding fluid and its constitutive equation: the Navier-Stokes equation. We study the technically interesting and practically realistic problem of stabilizing the coupled dynamics of FSI to a non-trivial equilibrium driven by a time-independent external force. To achieve this goal, feedback control mechanisms that depend on the equilibrium and applied to the fluid and solid domains are proposed. A natural problem to study next is the large-time behavior of the solution when the system is subject to a time dependent external force. In this direction, we established the existence of pullback attractor for the constitutive equation, the Navier-Stokes equation, of FSI, when it is subject to a time dependent external force with relaxed compactness assumption. We also showed that the pullback attractor has a finite fractal dimension using the trace formula.

Yongjin Lu's talk will be also live via Zoom.

Oct 11 Hon Yiu So (Oakland University) Semiparametric inference in one-shot device with competing risks

One-shot devices mean one-time products. Typical one-shot devices include airbags, fire-extinguishers, missiles, etc. Those devices' observations are either successes or failures at the time of test/use. So, there is usually a considerable loss of information, as we cannot observe the exact failure time. In addition, those one-shot devices contain multiple components. For example, airbags contain crash sensors and air inflation chemicals, and missiles have accelerators and explosives. Malfunctioning in any element will result in device failures. Then, engineers will inspect the failed devices to identify the specific cause of failure. With such complexity, estimating those life characteristics becomes a complex problem.

This talk will focus on the estimation problem of One-shot devices under constant stress accelerated life-test. To avoid model misspecification, we proposed a semiparametric method. It can analyze the relationship between the lifetime of the parts and the stress level without any assumption about the component's lifetime. A link function relating to stress levels and lifetime is then applied to extrapolate the lifetimes of units from accelerated conditions to normal operating conditions.

Hon Yiu So's talk will be also live via Zoom.

Sep 27 Gary McDonald (Oakland University) Approaches to the problem of ranking populations (or choosing the "best")

The subject area of statistical ranking and selection procedures will be introduced. The so-called “indifference-zone” procedures and “subset selection” procedures will be described and their properties presented. These methodologies are applicable in comparing two or more populations with the goal of selecting (or isolating) the “best” population with a user specified level of confidence. In this context “best” is based on the ordering of a parameter characterizing each of the populations. For example, the “best” population could be defined as that one possessing the largest mean. Parametric, nonparametric (distribution-free), and Bayesian methods will be included. An analysis of motor vehicle traffic fatality rates will be given illustrating the use of a distribution-free subset selection procedure in a two-way block design context. The analysis of the traffic fatality rates will also be addressed from a Bayesian perspective.
Time permitting, some discussion will be given to research issues still remaining with one or more of these methodologies.

Gary McDonald's talk will be also live via Zoom.
Room: 910 1377 8430
Passcode: 894238

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