Mathematics

Schedule

Abstracts (PDF)

Friday, March 21, 2025

1:15 — 1:30 pm Opening Remarks

Vasileios Maroulas (Associate Vice Chancellor of Research, Director of AI Tennessee Initiative, University of Tennessee Knoxville)
Walters Academic building room M309

1:00 — 5:00 pm Registration
Ayres Hall room 227

1:30 — 2:30 pm Plenary Talk

Robert B. Gramacy (Virginia Tech), “A surrogate modeling journey through Gaussian processes modeling for computer simulation experiments”
Walters Academic building room M309

Abstract

This talk begins with an overview of Gaussian process (GP) surrogate modeling, and my favorite application: active learning for the (Bayesian) optimization of a blackbox function.  I shall then survey some important, recent methodological developments targeting specific situations that increasingly arise in practice: large simulation campaigns, noisy observations/stochastic simulation, nonstationary modeling, and the calibration of computer models to field data.  The presentation concludes with an in-depth description of a recent application: contour location for reliability in an airfoil simulation experiment using deep GPs.   Throughout, there will be reproducible visuals and demos supported by code, both run live and embedded in the slides.  These are biased toward my own work, in part because I understand that code best.  But along the way I shall also endeavour to provide an otherwise balanced discussion of myriad alternatives that can be found elsewhere in this fast-moving literature. 

2:35 — 2:50 pm Coffee Break
Ayres Hall 1st floor

3:00 — 5:00 pm Mini-symposia Talks

Applications and Algorithms for Diff. Eq. in Modelling and Engineering (session 1 of 2)
Organizer: Johannes Krotz (University of Notre Dame)
Ayres Hall room 112

  • 3:00-3:25 pm — Tingao Lucy Jiang (University of Tennessee, Knoxville), “Intravascular Stent Drug Release and Transport-Model, Analysis, and Simulation”
  • 3:30-3:55 pm — Maggie Sullen (NSF APPEX Postdoctoral Researcher University of Tennessee, Knoxville), “Conceptualizing Contagion: Modeling Complex Contagion Transmission with Differential Equations”
  • 4:00-4:25 pm — Maruf Lawal (University of Tennessee, Knoxville), “Optimal Sustainable Management of the Horse Mackerel Harvesting in the Southern Black Sea Coast”
  • 4:30-4:55 pm — Johannes Krotz (University of Notre Dame), “Minimizing Uncertainty in Transport Problems through Dynamic Likelihood Filtering”

Early Careers in Mathematical Biology (session 1 of 2)
Organizer: Leah LeJeune (Virginia Tech) and Omar Saucedo (Virginia Tech)
Ayres Hall room 123

  • 3:00-3:25 pm — Omar Saucedo (Virginia Tech), “Exploring the identifiability of an avian influenza model.”
  • 3:30-3:55 pm — Madison Pratt (University of Tennessee, Knoxville), “Refining SIR Parameter Estimation: ALFFI for Comprehensive Uncertainty Analysis”
  • 4:00-4:25 pm — Megan Grey (Virginia Tech), “Group size and environmental obstacles drive acoustic call properties for wild gray bats in flight: a data-driven analysis”
  • 4:30-4:55 pm — Keoni Castellano (Virginia Tech), “Spatial Heterogeneity and its Effect on Infectious Disease Spread”

Mathematical and Statistical Models in Biological Modeling: Advances and Applications
Organizers: Masud Rana (Kennesaw State University) and Duc Nguyen (University of Tennessee at Knoxville)
Ayres Hall room 120

  • 3:00-3:25 pm — Tania Hazra (Department of Mathematics, University of South Carolina, Sumter), “Unconditionally Stable Locally One Dimensional (LOD) Method for Pseudo-time Coupled Nonlinear Solvation Analysis”
  • 3:30-3:55 pm — David Murrugarra (Department of Mathematics, University of Kentucky), “When does additional information improve accuracy of RNA secondary structure prediction?”
  • 4:00-4:25 pm — Thien Le (Department of Mathematics, University of Tennessee, Chattanooga), “Temporal Configuration Model: Statistical Inference and Spreading Processes”
  • 4:30-4:55 pm — Masud Rana (Department of Mathematics, Kennesaw State University), “Mathematical Representations of Molecules and Machine Learning for Drug Design”

Modeling and Analysis of Complex Systems (session 1 of 2)
Organizer: Miroslav Stoyanov (Oak Ridge National Laboratory)
Ayres Hall room 124

  • 3:00-3:25 pm — Eirik Endeve (Oak Ridge National Laboratory), “Conservative Discontinuous Galerkin Method for a Mul0-Species Vlasov-Fokker-Planck Model”
  • 3:30-3:55 pm — Evan Butterworth (Clemson University), “Accurate Temporal Integration Schemes for Nonlinear Adsorption Problems”
  • 4:00-4:25 pm — Yanzhi Zhang (Missouri University of Science and Technology), “Numerical Studies of Anomalous Diffusion in Heterogeneous Media”
  • 4:30-4:55 pm — John Lagergren (Oak Ridge National Laboratory), “Toward Foundation Models for Advanced Plant Phenotyping”

Optimal Control and Optimization with Math Biology Applications (session 1 of 2)
Organizers: Suzanne Lenhart (University of Tennessee at Knoxville) and Olivia Feldman (University of Tennessee at Knoxville)
Ayres Hall room 111

  • 3:00-3:25 pm — Rachel Leander (Middle Tennessee State University), “Optimal Control and Modeling of West Nile Virus”
  • 3:30-3:55 pm — Summer Atkins (University of Alabama in Huntsville), “A Switch Point Algorithm Applied to a Harvesting Problem”
  • 4:00-4:25 pm — Ebenezer Acquah (University of Tennessee, Knoxville), “Modeling the Effect of HIV/AIDS Stigma on HIV Infection Dynamics in Kenya with Optimal Control”

Recent Advances in Data-Driven Methods for Complex Dynamical Systems: From Data Assimilation to Reduced-Order Modeling (session 1 of 2)
Organizers: Zezhong Zhang (Oak Ridge National Laboratory) and Yanfang Liu (Middle Tennessee State University)
Ayres Hall room 121

  • 3:00-3:25 pm — Yanxiang Zhao (George Washington University), “Synchronized Optimal Transport”
  • 3:30-3:55 pm — Yuwei Geng (University of South Carolina), “Gradient Preserving Operator Inference: Data-driven Reduced-order Models for Equations with Gradient Structure”
  • 4:00-4:25 pm — Duygu Vargun (Oak Ridge National Lab), “Advancing Nonlinear Iterative Solvers for Navier-Stokes Equations through Data-driven Assimilation Strategies”

Recent Progress in Numerical PDEs and Applications (session 1 of 3)
Organizers: Xiaobing Feng (University of Tennessee at Knoxville) and Chunmei Wang (University of Florida)
Ayres Hall room 122

  • 3:00-3:25 pm — Leo Rebeholz (Clemson University), “Approximating a branch of solutions to the Navier–Stokes equations by reduced-order modeling”
  • 3:30-3:55 pm — Jichun Li (University of Nevada Las Vegas), “A novel finite element method for simulating graphene sheets”
  • 4:00-4:25 pm — Stefan Schnake (Oak Ridge National Lab), “Sparse-grid Discontinuous Galerkin Methods for the Vlasov-Poisson-Lenard-Bernstein Model”
  • 4:30-4:55 pm — Hong Wang (University of South Carolina), “Modeling, Analysis, and Discretization of Anomalously Diffusive Transport”

Uncertainty Quantification for Machine Learning
Organizer: Tianshi Xu (Emory University)
Ayres Hall room 110

  • 3:00-3:25 pm — Nicole Yang (Emory University, Department of Mathematics), “Generative modeling with partial observations”
  • 3:30-3:55 pm — Difeng Cai (Southern Methodist University, Department of Mathematics), “Posterior Covariance Structures in Gaussian Processes”
  • 4:00-4:25 pm — Huan He (Auburn University, Department of Mathematics and Statistics), “Sensitivity Analysis for Neural Network based Causal Inference”
  • 4:30-4:55 pm — Tianshi Xu (Emory University, Department of Mathematics), “HiGP: Data-Driven Hierarchical Matrix-Based Gaussian Process”

3:00 — 5:15 pm Contributed Talks
Ayres Hall room 405

  • 3:00-3:15 pm — Ben Atawiah (The University of Alabama), “On the two-stage filtered Runge-Kutta discontinuous Galerkin method and its variant: Fourier analysis and local time marching”
  • 3:25-3:40 pm — Yiming Ren (The University of Alabama), “High-order Finite Difference Methods and Their Hybridization with Neural Networks for Elliptic Interface Problems”
  • 3:50-4:05 pm — Idowu Ijaodoro (The University of Alabama), “On generalizing the induced surface charge method to heterogeneous Poisson-Boltzmann models for electrostatic free energy calculation”
  • 4:15-4:30 pm — Nick Arustamyan (University of Central Florida), “Curriculum Learning for Inverse Scattering Problems”
  • 4:40-4:55 pm — Grace Mowery (Clemson University), “Numerical Discrepancies in Single Precision Calculations Between CPU and GPU”

5:30 — 6:30 pm Plenary Talk

Christine Heitsch (Georgia Tech), “How can discrete mathematics improve RNA folding predictions?”
Walters Academic building room M309

Abstract

Understanding the folding of RNA sequences into three-dimensional structures — such as a viral genome inside its protein capsid —  is a fundamental scientific challenge.  Branching is a critical characteristic of RNA folding, yet too often poorly predicted under the standard thermodynamic objective function.  By formulating this discrete optimization problem as a linear program, methods from geometric combinatorics (convex polytopes and their normal fans) can fully characterize the optimal branching configurations.  This parametric analysis illuminates the optimization geometry.  The insights gained significantly improve the prediction accuracy while also revealing why the general problem is so difficult. 

Saturday, March 22, 2025

7:30 — 2:00 pm Registration
Ayres Hall room 227

8:00 — 8:30 pm Breakfast Refreshments
Walters Academic building room M309

8:30 — 9:30 am Plenary Talk

Guowei Wei (Michigan State), “Topological deep learning on graphs, manifolds, and curves”
Walters Academic building room M309

Abstract

In the past few years, topological deep learning (TDL), a term coined by us in 2017, has become an emerging paradigm in artificial intelligence (AI) and data science. TDL is built on persistent homology (PH), a vital tool in topological data analysis (TDA) that bridges the gap between complex geometry and abstract topology through multiscale analysis. While TDA has made huge strides in a wide variety of scientific and engineering disciplines, it has many limitations. I will discuss our recent effort in extending the scope of TDA from graphs to manifolds and curves, through new formulations from algebraic topology, geometric topology, and differential topology. I will also discuss how TDL achieved its victories in worldwide annual competitions in computer-aided drug design, discovered SARS-CoV-2 evolutionary mechanism, and accurately predicted emerging dominant viral variants. 

10:00 — 12:00 pm Mini-symposia Talks

Advances in Data Analysis Across Scales (session 1 of 2)
Organizers: Alina Peluso (Oak Ridge National Laboratory) and Ioannis Sgouralis (University of Tennessee at Knoxville)
Ayres Hall room 110

  • 10:00-10:25 am — Seung-Hwan Lim (Oak Ridge National Laboratory), “Attention for Causal Relationship Discovery from Biological Neural Dynamics”
  • 10:30-10:55 am — Sharmin Afrose (Oak Ridge National Laboratory), “Efficient Communication in Federated Learning with Dynamical Sketching”
  • 11:00-11:25 am — Paul Laiu (Oak Ridge National Laboratory), “Streaming scientific data compression using weak-SINDy surrogate models”
  • 11:30-11:55 am — Viswadeep Lebakula (Oak Ridge National Laboratory), “High resolution gridded population estimates for the globe with machine learning”

Applied Algebra and Geometry
Organizer: Dustin Cartwright (University of Tennessee at Knoxville)
Ayres Hall room 123

  • 10:00-10:25 am — Michael Byrd (Clemson University), “Certified algebraic curve projections by path tracking”
  • 10:30-10:55 am — Ian Tan (Auburn University), “Tensor decompositions with applications to LU and SLOCC equivalence of multipartite pure states”
  • 11:00-11:25 am — Julianne Barnhart (Clemson University), “Trace Tests and Monodromy Groups”
  • 11:30-11:55 am — Luke Oeding (Auburn University), “Tensors and Phylogenetic Networks”

Dynamical Systems in Biology (session 1 of 2)
Organizers: Christopher Strickland (University of Tennessee at Knoxville) and Xinyue Zhao (University of Tennessee at Knoxville)
Ayres Hall room 120

  • 10:00-10:25 am — Bei Hu (University of Notre Dame), “Periodic Solution for a Free-boundary Tumor Model – Asymptotic Behavior”
  • 10:30-10:55 am — Patrick Shipman (University of Arizona), “Dynamical Systems Applied to Optimal Packing Problems in Biology”
  • 10:30-10:55 am — Zhisheng Shuai (Central Florida University), “A Tale of Two Incidence Functions in Epidemiological Models” “
  • 11:00-11:25 am — Yixiang Wu (Middle Tennessee State University), “Global Dynamics of Epidemic Network Models via Construction of Lyapunov Functions”

Early Careers in Mathematical Biology (session 2 of 2)
Organizer: Leah LeJeune (Virginia Tech) and Omar Saucedo (Virginia Tech)
Ayres Hall room 124

  • 10:00-10:25 am — Leah LeJeune (Virginia Tech), “The role of testing in epidemic dynamics: a human behavior approach”
  • 10:00-10:25 am — Quiyana Murphy (Virginia Tech), “Antibody magnitude and durability following vaccination against SARS-CoV-2”
  • 10:30-10:55 am — Jordan Pellett (University of Tennessee, Knoxville), “Using Integral Projection Models to Understand How Amphibian Defense Strategies Against a Virulent Fungus Vary Among Host Life Stages”

Mathematics of Quantum Computing (session 1 of 2)
Organizers: Sarah Chehade (Oak Ridge National Laboratory) and Elaine Wong (Oak Ridge National Laboratory)
Ayres Hall room 111

  • 10:00-10:25 am — Joseph Wang (Oak Ridge National Laboratory), “Ancilla-entangling Floquet kicks for accelerating quantum algorithms”
  • 10:30-10:55 am — Zhenhua Wang (Alabama A&M University), “Generalized Trotter Product Formulas via the Jordan Product with Associated Error Estimates”
  • 11:00-11:25 am — Bojko Bakalov (North Carolina State University), “Dynamical Lie Algebras in Quantum Computing”
  • 11:30-11:55 am — Shuchen Zhu (Duke University), “Synthesis of Single Qutrit Circuits from Clifford+R gates”

Modeling and Analysis of Complex Systems (session 2 of 2)
Organizer: Miroslav Stoyanov (Oak Ridge National Laboratory)
Ayres Hall room 121

  • 10:00-10:25 am — Auroni Hashim (North Carolina State University), “Latent-Consistent Variational Autoencoder for Diversifying Generation”
  • 10:30-10:55 am — Deepanshu Verma (Clemson University), “Neural Network Approaches for High-Dimensional Optimal Control and Transport Problems”
  • 11:00-11:25 am — Ben Plumridge (UT-Knoxville), “Neural Network-Based Adaptive Filtering of the Spherical Harmonic Method”

On the Nexus of Data, Models, and Computing
Organizer: Antigoni Georgiadou (Oak Ridge National Laboratory), Colter Richardson (University of Tennessee, Knoxville), and Khadiza Begham (Oak Ridge National Laboratory)
Ayres Hall room 122

  • 10:00-10:25 am — Jack Marquez (Min H. Kao Department of Electrical Engineering and Computer Science, UTK), “Increasing the Efficiency of Ensemble Molecular Dynamics Simulations with Termination of Unproductive Trajectories Identified at Runtime”
  • 10:30-10:55 am — Khadiza Begam (Oak Ridge National Lab), “Virtual instrumentation of dynamic nuclear polarization to locate the hydrogen atoms in biomolecular crystals.”
  • 11:00-11:25 am — Van A. Ngo (Oak Ridge National Lab), “Tales of how two tails play key roles in protein functions”
  • 11:30-11:55 am — Samuel Fagbemi (Oak Ridge National Lab), “Electro-Thermal modeling for Alkane Dehydrogenation in Fibrous Media at the Pore scale”

Recent Advances in Data-Driven Methods for Complex Dynamical Systems: From Data Assimilation to Reduced-Order Modeling (session 2 of 2)
Organizers: Zezhong Zhang (Oak Ridge National Laboratory) and Yanfang Liu (Middle Tennessee State University)
Ayres Hall room G004

  • 10:00-10:25 am — Siming Liang (Florida State University), “Ensemble Score Filter with Image Inpainting for Data Assimilation in Tracking Surface QuasiGeostrophic Dynamics with Partial Observations”
  • 10:30-10:55 am — Phillip Si (Georgia Tech), “Latent-EnSF: A Latent Ensemble Score Filter for High-Dimensional Data Assimilation with Sparse Observation Data”
  • 11:00 – 11:25 am — Toan Phuoc Huynh (Florida State University), “Joint State-Parameter Estimation for the Reduced Fracture Model via the United Filter.”

Recent advances in machine learning theory and applications (session 1 of 2)
Organizers: Qiang Wu (University of Tennessee at Knoxville) and Yunlong Feng (University of Albany)
Ayres Hall room 113

  • 10:00-10:25 am — Yunlong Feng (University at Albany), “Machine Learning Based Computational Approaches for Biological Spectral Imaging”
  • 10:30-10:55 am — Yanfang Liu (Middle Tennessee State University), “Training-free Conditional Diffusion Model for Stochastic Dynamical Systems Learning”
  • 11:00-11:25 am — Viktor Reshniak (Oak Ridge National Laboratory), “Integrated Edge-to-Exascale Workflow for Real-Time Steering in Neutron Scattering Experiments”
  • 11:30-11:55 am — Zeya Wang (University of Kentucky), “How to Validate Clustering in Deep Learning: Challenges and Solutions”

Recent Progress in Numerical PDEs and Applications (session 2 of 3)
Organizers: Xiaobing Feng (University of Tennessee at Knoxville) and Chunmei Wang (University of Florida)
Ayres Hall room G003

  • 10:00-10:25 am — Yingjie Liu (Georgia Institute of Technology), “Neural Networks with Local Converging Inputs (NNLCI) for Solving Conservation Laws with Orders of Magnitude Reduction in Complexity and Minimal Training Data Requirement”
  • 10:30-10:55 am — Tao Lin (Virginia Tech), “Differential Geometry-Based Construction of Immersed Finite Element Functions”
  • 11:00-11:25 am — Slimane Adjerid (Virginia Tech), “An Immersed HDG method for Elliptic Interface Problems”
  • 11:30-11:55 am — Yi Zhang (University of North Carolina at Greensboro), “Dual-Wind Discontinuous Galerkin Methods for An Elliptic Optimal Control Problem”

Topological Data Analysis in Biosciences
Organizers: Zixuan Cang (North Carolina State University) and and Jiahui Chen (University of Arkansas)
Ayres Hall room 112

  • 10:00-10:25 am — Fox Zach (Oak Ridge National Lab), “Integrating Discrete and Equivariant Diffusion Models for 3D Molecule Generation”
  • 10:30-10:55 am — Rui Wang (New York University), “Topological Deep Learning for RNA, Protein Interactions, and COVID-19 Variant Prediction”
  • 11:00-11:25 am — Dong Chen (Michigan State University), “Multiscale Topology-enabled Artificial Intelligence for Drug Discovery”
  • 11:30-11:55 am — Travis Johnson (Indiana University), “Topological approaches to spatial transcriptomics analysis”

10:00 — 12:15 pm Contributed Talks
Ayres Hall room 405

  • 10:00-10:15 am — Krishna Gahatraj (University of Tennessee, Knoxville), “A Mathematical Model for the Dynamics of Spruce Budworm Population Under Predation and Insecticide”
  • 10:25-10:40 am — John Alford (Sam Houston State University), “Assessing Southern Pine Beetle Infestation Risks Using Agent-Based Modeling”
  • 10:50-11:05 am — Jonathan Engle (Florida State University), “The dynamics of strategic voting: pathways to consensus and gridlock”
  • 11:15-11:30 am — Zhaiming Shen (Georgia Institute of Technology), “Transformers for Learning on Noisy and Task-Level Manifolds: Approximation and Generalization Insights.”
  • 11:40-11:55 am — Sarah Cornell (Clemson University), “Continuous Data Assimilation of Burger’s and Navier-Stokes Equations”

10:00 — 12:15 pm Contributed Talks
Ayres Hall room 401

  • 10:00-10:15 am — Anna Davis (Middle Tennessee State University) and Morgan Chappell (Middle Tennessee State University), “Modeling Asymmetric Cell Division for Comparison to Florescent Confocal Microscopy Data”
  • 10:25-10:40 am — Paul Klockenkemper (Middle Tennessee State University), “Modeling the impact of host heterogeneity on the risk and dynamics of a West Nile virus epidemic”

12:30 — 2:00 pm Lunch
Walters Academic building room M309

2:00 — 3:00 am Plenary Talk

Mark Ainsworth (Brown University), “Galerkin Neural Network Approximation of Variational Problems with Error Control”
Walters Academic building room M309

Abstract

Recent years have seen an unprecedented surge of interest in applying neural networks to a very wide range of areas including non-scientific applications and artificial intelligence. In principle, neural networks offer benefits for scientific applications including the approximate solution of differential equations. However, if such methods are to be accepted then it is important that they are set on a firm theoretical foundation and ideally include quantitative measures on the reliability of the results that are obtained. 

We present an overview of some of our recent work in this direction on what we call Extended Galerkin Neural Networks (xGNN) where we aim to provide variational framework for approximating general boundary value problems (BVPs) with error control. The main contributions of this work are (1) a rigorous theory guiding the construction of weighted least squares variational formulations suitable for use in neural network approximation of general BVPs (2) an “extended’ feedforward network architecture which incorporates and is even capable of learning singular solution structures, thus offering the potential to greatly improve the efficiency for singular solutions. 

This is joint work with Justin Dong, Lawrence Livermore National Laboratory, USA. 

3:00 — 3:15 pm Coffee Break
Ayres Hall 1st floor

3:30 — 5:30 pm Mini-symposia Talks

Addressing Intractability in Optimal control
Organizers: Deepanshu Verma (Clemson University) and Guannan Zhang (Oak Ridge National Laboratory)
Ayres Hall room 110

  • 3:30-3:55 pm — Zezhong Zhang (Oak Ridge National Lab), “Reducing Structural Errors in Score Estimation of the Ensemble Score Filter for Nonlinear Data Assimilation with Partial Observation”
  • 4:00-4:25 pm — Konstantin Pieper (Oak Ridge National Lab), “Nonuniform derivative-based random weight initialization for neural network optimization”
  • 4:30-4:55 pm — Yijie Jin (Georgia Tech), “Parametrized Wasserstein Gradient Flow with Application in Porous-Medium Equation”
  • 5:00-525 pm — Hongjiang Qian (Auburn University), “Numerical approximations for optimal control of stochastic partial differential equations with partial observation”

Advances in Data Analysis Across Scales (session 2 of 2)
Organizers: Alina Peluso (Oak Ridge National Laboratory) and Ioannis Sgouralis (University of Tennessee at Knoxville)
Ayres Hall room G003

  • 3:30-3:55 pm — Daniel McBride (University of Tennessee, Knoxville), “Hamiltonian Monte Carlo methods for spectroscopy data analysis”
  • 4:00-4:25 pm — Steffen Schotthoefer (Oak Ridge National Laboratory), “Geometric integration for parameter efficient fine-tuning of neural networks”
  • 4:30-4:55 pm — Chiara Mattamira (University of Tennessee, Knoxville), “Bayesian analysis and efficient MCMC samplers for single-molecule fluorescence data and step counting”
  • 5:00-525 pm — Hoang Tran (Oak Ridge National Laboratory), “Diffusion-based generative models for efficient sampling of high-dimensional multi-modal distributions”

Applications and Algorithms for Diff. Eq. in Modelling and Engineering (session 2 of 2)
Organizer: Johannes Krotz (University of Notre Dame)
Ayres Hall room 123

  • 3:30-3:55 pm — Charlotte Beckford (University of Tennessee, Knoxville), “A Comparison of Dual Ion Conductor Electrolyte and Single Ion Conductor Electrolyte Battery Models”
  • 4:00-4:25 pm — Ziyao Xu (University of Notre Dame), “Stability and Time-Step Constraints of Exponential Time Differencing Runge-Kutta Discontinuous Galerkin Methods for Advection-Diffusion Equations”
  • 4:30-4:55 pm — Maddison Phelps (Oregon State University), “Nonlinear Solvers for Permafrost Problems”

Computational Methods for Partial Differential Equations (session 1 of 2)
Organizer: Miroslav Stoyanov (Oak Ridge National Laboratory)
Ayres Hall room 120

  • 3:30-3:55 pm — Yichen Guo (Virginia Tech), “Mixed Precision Sparse Approximate Inverse Smoothers for GPU-Accelerated Matrix-Free High-Order Finite Element Poisson Solvers”
  • 4:00-4:25 pm — Ping-Hsuan Tsai (Virginia Tech Traian Iliescu, Virginia Tech), “Data-Driven Regularized Reduced-Order Models for Turbulent Flows”
  • 4:30-4:55 pm — Jeff Borggaard and Ali Bouland (Virginia Tech), “Nonlinear Feedback Control of the Fluidic Pinball”
  • 5:00-525 pm — Hamza Adjerid (Virginia Tech), “Nonlinear balanced truncation and Nonlinear feedback control for Stokes-type DAEs”

Optimal Control and Optimization with Math Biology Applications (session 2 of 2)
Organizers: Suzanne Lenhart (University of Tennessee at Knoxville) and Olivia Feldman (University of Tennessee at Knoxville)
Ayres Hall room G004

  • 3:30-3:55 pm — Hem R Joshi (Xavier University), “Controlling Rabies Transmission”
  • 4:00-4:25 pm — Lakmali Weerasena (University of Tennessee at Chattanooga), “Compactness in Conservation: A Multiobjective Framework for Ecological Reserve Design”
  • 4:30-4:55 pm — Lida Rabiei (Pennsylvania State University), “Data-Driven Modeling of Amyloid-Beta Aggregation and Optimal Treatments of Anti-Abeta Therapies”
  • 5:00-525 pm — David Garber (University of Tennessee, Knoxville), “Optimal Control of Coupled Oscillator Networks with Higher Order Interactions”

Recent advances in mathematical biology: Modeling life across scales (session 1 of 2)
Organizer: Yuta Hozumi (Georgia Institute of Technology)
Ayres Hall room 124

  • 3:30-3:55 pm — Yuta Hozumi (Georgia Institute of Technology, School of Mathematics), “Revealing the Shape of Genome Space via K-mer Topology”
  • 4:00-4:25 pm — Laszlo A. Szekely (University of South Carolina, Department of Mathematics), “New distances between phylogenetic trees”
  • 4:30-4:55 pm — Eleni Panagiotou (Arizona State University, School of Mathematical and Statistical Sciences), “Novel topological metrics of biopolymer structure and the topological and dynamical landscape of proteins”
  • 5:00-525 pm — Daniela Genova (University of North Florida, Department of Mathematics and Statistics), “Functions and Structures of Reaction Systems”

Recent Advances in Phase-Field Modeling
Organizers: Toai Luong (University of Tennessee at Knoxville) and Abba Ramadan (The University of Alabama)
Ayres Hall room 111

  • 3:30-3:55 pm — Shuwang Li (Illinois Institute of Technology), “A simple model for simulating vesicle growth and shrinkage”
  • 4:00-4:25 pm — Shibin Dai (The University of Alabama), “Gamma Convergence for the De Gennes-Cahn-Hilliard Energy”
  • 4:30-4:55 pm — Natasha Sharma (The University of Texas at El Paso), “A Second Order Numerical Scheme for a Sixth-Order Cahn-Hilliard Type Equation modeling Microemulsions”
  • 5:00-525 pm — Abba Ramadan (The University of Alabama), “Minimizers for the de Gennes-Cahn-Hilliard energy under strong anchoring conditions”

Recent Developments in Machine Learning for Computational Mathematics (session 1 of 2)
Organizers: Yiping Lu (Northwestern University) and Chunmei Wang (University of Florida)
Ayres Hall room 121

  • 3:30-3:55 pm — Rick Archibald (DOE), “Federated Machine Learning for Experimental Facilities”
  • 4:00-4:25 pm — Yulong Lu (University of Minnesota), “Provable in-context learning of PDEs”
  • 4:30-4:55 pm — Yiping Lu (Northwestern University), “Two Tales, One Resolution: Physics-Informed Test Time Scaling and Precondition”
  • 5:00-525 pm — Jiahui Chen (University of Arkansas), “Poisson-Boltzmann-based machine learning model for electrostatic analysis”

Recent Progress in Numerical PDEs and Applications (session 3 of 3)
Organizers: Xiaobing Feng (University of Tennessee at Knoxville) and Chunmei Wang (University of Florida)
Ayres Hall room 122

  • 3:30-3:55 pm — Tom Lewis (University of North Carolina at Greensboro), “A high order correction to the Lax-Friedrich’s method for approximating stationary Hamilton-Jacobi equations”
  • 4:00-4:25 pm — Qingguo Hong (Missouri University of Science and Technology), “Title: Generalized Korn’s inequalities for piecewise H1 and H2 vector fields”
  • 4:30-4:55 pm — Yiming Chen (Affiliation: Ohio State University), “Analysis of Fully Discrete Discontinuous Galerkin Method for Nonlinear Stochastic Convection-Diffusion Equations”
  • 5:00-525 pm — Toai Luong (University of Tennessee at Knoxville), “Gamma-Convergence and Asymptotic Analysis for a Diffuse Domain Problem with Transmission Boundary Conditions: Part 1, Theoretical Analysis”

Structure-Preserving Numerical Methods for Partial Differential Equations (session 1 of 2)
Organizers: Jia Zhao (The University of Alabama), Zheng Sun (The University of Alabama), and Yiran Wang (The University of Alabama)
Ayres Hall room 112

  • 3:30-3:55 pm — Calvin Wong (The University of Tennessee, Knoxville, Department of Mathematics), “Gamma-Convergence and Asymptotic Analysis for a Diffuse Domain Problem with Transmission Boundary Conditions: Part 2, Numerical Confirmation”
  • 4:00-4:25 pm — Jia Zhao (The University of Alabama, Department of Mathematics), “General Numerical Framework for Structure-Preserving Reduced Order Models of Thermodynamically Consistent Reversible-Irreversible PDEs”
  • 4:30-4:55 pm — Zheng Sun (The University of Alabama, Department of Mathematics), “A bound-preserving Runge-Kutta discontinuous Galerkin method with compact stencils for hyperbolic conservation laws”
  • 5:00-525 pm — Qifan Chen (The Ohio State University, Department of Mathematics), “Compact Runge-Kutta Flux Reconstruction for Hyperbolic Conservation Laws with admissibility preservation”

Theory, Computation, and Machine Learning in Geometric and Topological Problems
Organizer: Sathya Rengaswami (Army Research Laboratory)
Ayres Hall room 113

  • 3:30-3:55 pm — Sathya Rengaswami (Army Research Lab), “On the Relation between Graph Ricci Curvature and Community Structure”
  • 4:00-4:25 pm — Nicole Feng (Carnegie Mellon University), “Generalized Signed Distance”
  • 4:30-4:55 pm — Hayden Everett (University of Tennessee, Knoxville), “Bayesian Topological Convolutional Neural Networks for Image Classification.”
  • 5:00-525 pm — Sarah Harkins (University of Tennessee), “Bayesian Topological Convolutional Neural Networks”

3:30 — 6:00 pm Contributed Talks
Ayres Hall room 405

  • 3:30-3:45 pm —  Aniekan Ebiefung (University of Tennessee, Chattanooga), “Vertical Block 𝑷−matric Classes: A review.”
  • 3:55-4:10 pm — Chimezie Izuazu (University of Louisiana at Lafayette), “Stochastic Analysis of Interplay Among Drug Mode of Action, Nutrient Availability, and Antibiotic Resistance”
  • 4:20-4:35 pm — Andrew Deas (Oak Ridge National Laboratory), “Integrating Data Analysis and Machine Learning to Investigate the Relationship Between Social Vulnerability and Opioid-Related Mortality”
  • 4:45-5:00 pm — Achille Kakeu (The University of Pretoria), “Modeling and Asymptotic Analysis of Alzheimer’s Disease in a Thin Heterogeneous Domain”
  • 5:10-5:25 pm — Le Gong (Vanderbilt University), “Source Recovery Through Dynamical Sampling”

7:30 — 9:00 pm Banquet Dinner
Hilton Knoxville (Directions)

Sunday, March 23, 2025

8:00 — 8:30 pm Breakfast Refreshments
Walters Academic building room M309

8:30 — 9:30 am Plenary Talk

Yingda Cheng (Virginia Tech), “Low rank Anderson Acceleration”
Walters Academic building room M309

Abstract

In this talk, we present the low rank Anderson Acceleration (lrAA), a numerical method that directly computes low rank solutions to nonlinear equations. In many applications (e.g. nonlinear diffusion), the approximate solution, when represented as a matrix, is approximately low rank. It is challenging to design a numerical scheme for nonlinear equations that work directly with low rank. A principal challenge is that if nonlinearities are evaluated element-wise for all matrix elements then the computational savings, from quadratic to linear in the grid points per dimension, is lost. 

We propose lrAA, which is based on Anderson Acceleration (AA), a well known technique for accelerating Picard iteration for fixed point problems. We couple AA with low rank truncation and cross approximations. We develop a new method for matrix cross approximation, Cross-DEIM, that uses the discrete empirical interpolation method (DEIM) based index selection with adaptive error control to achieve effective cross approximations throughout the iterations. We show that lrAA works well for benchmark problems, such as Bratu problem and Allen-Cahn equations. This is joint work with Daniel Appelo (VT). 

10:00 — 12:00 pm Mini-symposia Talks

Computational Methods for Partial Differential Equations (session 2 of 2)
Organizer: Miroslav Stoyanov (Oak Ridge National Laboratory)
Ayres Hall room 123

  • 10:00-10:25 am — Miroslav Stoyanov (Oak Ridge National Laboratory), “High-Dimensional Sparse Tensor Kronecker Operations”
  • 10:30-10:55 am — Evan Habbershaw (University of Tennessee), “Numerical Methods for Multi-Species Kinetic Models with Moment Dependent Collision Frequencies”
  • 11:00-11:25 am — Jiuhua Hu (Virginia Tech), “High-order, low-rank CPTP scheme for the Lindblad equation with time-dependent Hamiltonians”
  • 11:30-11:55 am — Xiaoming He (Missouri University of Science and Technology), “Variational data assimilation with finite element discretization for second order parabolic interface equation”

Dynamical Systems in Biology (session 2 of 2)
Organizers: Christopher Strickland (University of Tennessee at Knoxville) and Xinyue Zhao (University of Tennessee at Knoxville)
Ayres Hall room 120

  • 10:00-10:25 am — Xiunan Wang (University of Tennessee at Chattanooga), “Impact of Water Flow on Schistosomiasis Transmission: Insights from a Reaction-Advection-Diffusion Model”
  • 10:30-10:55 am — Kimberlyn Eversman (University of Tennessee, Knoxville), “A Multiscale Mixed Modeling Framework for Analyzing Parasitoid Wasp Dispersal and Host Interactions”
  • 11:00-11:25 am — Ryan Campbell (University of Tennessee, Knoxville), “Intermittent Search Strategies and Some Applications”
  • 11:30-11:55 am — Jingyi Liu (University of Notre Dame), “Stability of Periodic Solution for a Free Boundary Problem Modeling Small Plaques.”

Federated Learning and Data Mining in Distributed Environments
Organizers: Steffen Schotthöfer (Oak Ridge National Laboratory) and Paul Laiu (Oak Ridge National Laboratory)
Ayres Hall room 124

  • 10:00-10:25 am — Jiayi Wang (Oak Ridge National Laboratory), “CAFE AU LAIT: Compute-Aware Federated Augmented Low-rank AI Training”
  • 10:30-10:55 am — Joyce Ho (Emory University), “Bridging Multimodal Healthcare Data Across Institutions Using Federated Learning”
  • 11:00-11:25 am — Steffen Schotthöfer (Oak Ridge National Laboratory), “Federated Dynamical Low-Rank Training with Global Loss Convergence Guarantees”
  • 11:30-11:55 am — Hoang Tran (Oak Ridge National Laboratory), “An exponential mechanism approach for fine-tuning classification model with privacy guarantee.”

Mathematics of Quantum Computing (session 2 of 2)
Organizers: Sarah Chehade (Oak Ridge National Laboratory) and Elaine Wong (Oak Ridge National Laboratory)
Ayres Hall room 111

  • 10:00-10:25 am — Eugene Dumitrescu (Oak Ridge National Laboratory), “Symmetrizing Arithmetic Quantum Computations”
  • 10:30-10:55 am — Dong Ye (Middle Tennessee State University), “Clustering Algorithms for Social Signed Networks”
  • 11:00-11:25 am — Rebekah Herrman (University of Tennessee, Knoxville), “Combinatorics methods in deterministic quantum state preparation”
  • 11:30-11:55 am — “Open Discussion: Integration of Quantum Computing in Mathematics Education” Moderated by Sarah Chehade and Elaine Wong

Recent advances in machine learning theory and applications (session 2 of 2)
Organizers: Qiang Wu (University of Tennessee at Knoxville) and Yunlong Feng (University of Albany)
Ayres Hall room 110

  • 10:00-10:25 am — Ramchandra Rimal (Middle Tennessee State University), “Unraveling Market Mysteries: Deep Learning in Business Cycle Forecasting”
  • 10:30-10:55 am — Xingyi Guo (Vanderbilt University), “Machine learning and omics analyses for drug discovery in cancer prevention and intervention”
  • 11:00-11:25 am — Qiang Wu (University of Tennessee, Knoxville), “Fast and efficient toolkit for rare variants association testing”

Recent advances in mathematical biology: Modeling life across scales (session 2 of 2)
Organizer: Yuta Hozumi (Georgia Institute of Technology)
Ayres Hall room 121

  • 10:00-10:25 am — Zixuan Cang (North Carolina state University, Department of Mathematics), “Modeling Single-cell and Spatial Transcriptomics Data Using Optimal Transport”
  • 10:30-10:55 am — Idowu Ijaodoro (University of Alabama, Department of Mathematics), “On generalizing the induced surface charge method to heterogeneous Poisson-Boltzmann models for electrostatic free energy calculation”
  • 11:00-11:25 am — Leah LeJeune (Virginia Polytechnic Institute and State University, Department of Mathematics), “Mathematical analysis of simple behavioral epidemic models”
  • 11:30-11:55 am — Sung Ha Kang (Georgia Institute of Technology, School of Mathematics), “StemP: A fast and deterministic Stem-graph approach for RNA folding prediction”

Recent Developments in Machine Learning for Computational Mathematics (session 2 of 2)
Organizers: Yiping Lu (Northwestern University) and Chunmei Wang (University of Florida)
Ayres Hall room 122

  • 10:00-10:25 am — Di Qi (Purdue University), “Data-driven strategies for reduced-order closure models in turbulent systems”
  • 10:30-10:55 am — Wei Zhu (Georgia Tech), “Data-driven discovery of conservation laws, Lax pairs, and system integrability”
  • 11:00-11:25 am — Sifan Wang (Yale University), “Gradient Alignment in Physics-informed Neural Networks: A Second-Order Optimization Perspective”
  • 11:30-11:55 am — Chunmei Wang (University of Florida), “The Finite Expression Method as a Symbolic Approach for Scientific Machine Learning”

Structure-Preserving Numerical Methods for Partial Differential Equations (session 2 of 2)
Organizers: Jia Zhao (The University of Alabama), Zheng Sun (The University of Alabama), and Yiran Wang (The University of Alabama)
Ayres Hall room 112

  • 10:00-10:25 am — Yalchin Efendiev (Texas A&M Universtiy, Department of Mathematics), “Multicontinuum homogenization and applications.”
  • 10:30-10:55 am — Yiran Wang (The University of Alabama, Department of Mathematics), “Physics-preserving IMPES based multiscale methods for immiscible two-phase flow in highly heterogeneous porous media”
  • 11:00-11:25 am — Xuelong Gu (University of South Carolina, Department of Mathematics), “Parallel and energy-preserving schemes based on the partitioned averaged vector field method”
  • 11:30-11:55 am — Cory Hauck (University of Tennessee, Knoxville Math/ Oak Ridge National Lab), “A data-driven strategy for entropy-based moment closures.”

10:00 — 11:25 am Contributed Talks
Ayres Hall room 405

  • 10:00-10:15 am — Preeti Sar (Oak Ridge National Laboratory), “Asymptotic preserving micro-macro decomposition scheme for the kinetic Boltzmann-ES-BGK equation”
  • 10:25-10:40 am — Edward Fuselier (High Point University), “Locally supported, quasi-interpolatory bases for the approximation of functions on graphs”
  • 10:50-11:05 am — Matthias Dogbatsey (The University of Alabama), “Numerical Solution to the 3D p-Laplace Operator.”
  • 11:15-11:30 am — Dingsen Zhang (The Ohio State University), “On the Effects of Quadrature Rules with Insufficient Accuracy in Discontinuous Galerkin Methods”
  • 11:40 – 11:55 am — Kevin Slote (Georgia State University), “How advocacy groups on Twitter and media coverage can drive U.S. firearm acquisition: a causal study.”