Poster Title and Abstract

Posters are in a random order. Please hang your poster using the assigned number of your poster.

Poster 1 Title: A Multivariate Spline based Collocation Method for Numerical Solution of Partial Differential Equations

Presenter: Jinsil Lee, University of Georgia

Poster Abstract: We propose a collocation method based on multivariate polynomial splines over triangulation or tetrahedralization for numerical solution of partial differential equations.

We start with a detailed explanation of the method for the Poisson equation and

then extend the study to the second order elliptic PDE in non-divergence form, Navier-Stokes equation, Keller-Segel equation.

We shall show that the numerical solution can approximate the exact PDE solution very well.

Then we present a large amount of numerical experimental results to demonstrate

the performance of the method over the 2D and 3D settings.

Poster 2 Title: Modeling the dynamics of Usutu virus infection in birds

Presenter: Nora Heitzman-Breen, Virginia Tech

Poster Abstract: Usutu virus is a mosquito-borne flavivirus maintained in wild bird populations, causing high avian mortality rates and occasional severe neurological disorders in humans. It has been hypothesized that increased Usutu virus replication in birds and/or decreased bird immune competence leads to increased mosquito infection and increased spillover in humans. To provide insight into the intrinsic complexity of host-virus processes in birds, we use within–host mathematical models to characterize the mechanisms responsible for virus expansion and clearance in juvenile chickens challenged with four Usutu virus strains. Several virus strains are co-circulating in the wild, and we find heterogeneity between the virus strains, with the time between cell infection and viral production varying between 16 h and 23 h, the infected cell lifespan varying between 48 min and 9.5 h, and the basic reproductive number varying between 12.05 and 19.49. The strains with high basic reproductive number have short infected cell lifespan, indicative of immune responses. The virus strains with low basic reproductive number have lower viral peaks and longer lasting viremia, due to lower infection rates and high infected cell lifespan. These results can be used to better determine which virus strain is the most likely to spillover in the human population. We also investigate the effect of antibody on virus dynamics by fitting the models to chickens that were genetically engineered to have low and high antibody count; and show that the viral clearance rate is a stronger mitigating factor for USUV viremia than neutralizing antibody response in this avian model.

Poster 3 Title: Topological data analysis of pattern formation of human induced pluripotent stem cell colonies

Presenter: Iryna Hartsock, University of Florida

Poster Abstract: Pluripotent stem cells are able to differentiate into diverse types of cells. We use various concentrations of a chemical called doxycycline to increase the rate of cell differentiation, which induces different pattern formations of stem cell colonies. We apply topological data analysis to images of stem cell colonies with various levels of doxycycline to study and detect changes in the cell pattern formations.

Poster 4 Title: Estimations for operator learning and sketching methods for inverse problems

Presenter: Ke Chen, University of Maryland

Poster Abstract: Machine learning methods have been widely applied to solving inverse problems such as optical tomography, atmospheric remote sensing, and seismic full wave inversion. Although great success has been seen in numerical simulations, theoretical guarantees are less pronounced. This talk will discuss the theoretical results of two popular machine learning methods. For nonlinear problems, we studied the deep neural network surrogate of a nonlinear operator and provided a non-asymptotic upper bound of the generalization error with respect to the sample size. For linear problems, we considered randomized sketching methods and provided a probabilistic estimation of sketching error with respect to the data size. Both methods exploited the low intrinsic dimension of the problem, showing that a fast decay rate can be obtained for inverse problems, especially when many observations are gathered via multiple sources and receivers.

Poster 5 Title: Deterministic-Statistical Approach for an Inverse Acoustic Source Problem using Multiple Frequency Limited Aperture Data

Presenter: Yanfang Liu, The George Washington University

Poster Abstract: We propose a deterministic-statistical method for an inverse source problem using multiple frequency limited aperture far field data. The direct sampling method is used to obtain a disc such that it contains the compact support

of the source. The Dirichlet eigenfunctions of the disc are used to expand the source function. Then the inverse problem is recast as a statistical inference problem for the expansion coefficients and the Bayesian inversion is employed to reconstruct the coefficients. The stability of the statistical inverse problem with respect to the measured data is justified in the sense of Hellinger distance. A preconditioned Crank-Nicolson (pCN) Metropolis-Hastings (MH) algorithm is implemented to explore the posterior density function of the unknowns. Numerical examples show that the proposed method is effective for both smooth and non-smooth sources given limited-aperture data.

Poster 6 Title: Nonlocal effects on a generalized ohta-kawasaki model

Presenter: Wangbo Luo, The George Washington University

Poster Abstract: We propose a nonlocal Ohta-Kawasaki model to study the nonlocal effect on the pattern formation of some binary systems with general long-range interactions. While the nonlocal Ohta-Kawasaki model displays similar bubble patterns as the standard Ohta-Kawasaki model, by performing Fourier analysis, we find that the optimal number of bubbles for the nonlocal model may have an upper bound no matter how large the repulsive strength is. The existence of such an upper bound is characterized by the eigenvalues of the nonlocal kernels. Additionally we explore the conditions under which the nonlocal horizon parameter may promote or demote the bubble splitting, and apply the analysis framework to several case studies for various nonlocal operators.

Poster 7 Title: Transformed Primal-Dual Methods for Non-linear Saddle Point Systems

Presenter: Jingrong Wei, University of California, Irvine

Poster Abstract: I will present a novel transformed primal-dual gradient flow for a class of nonlinear smooth saddle point systems. We then derive several transformed primal-dual iterations by implicit Euler, explicit Euler, and implicit-explicit Euler discretization of the flow, and provide linear convergence even for non-strongly convex-concave cases. We also give a clear convergence analysis with nonlinear inexact inner solvers. We use Cahn-Hillard equations to show the numerical results for the method.

Poster 8 Title: Simulation of cell proliferation in a tissue-engineering scaffold pore

Presenter: Haniyeh Fattahpour, Georgia State University

Poster Abstract: Tissue-engineering scaffolds contain pores lined by cells that allow nutrient-rich culture medium to pass through to encourage cell proliferation. Several factors have significant impacts on the tissue growth, including the nutrient flow rate and concentration in the feed, scaffold elasticity as well as cell properties. Several studies have investigated these effects separately; however, in this work, we examine all of them simultaneously. Our objectives in this work are as follows: (i) the development of a mathematical model describing the nutrient fluid dynamics and concentration, scaffold elasticity and cell proliferation; (ii) solving the model and then simulating the cell proliferation process; (iii) developing a `reverse algorithm' that determines the initial configuration of the scaffold based on the desired geometry of the final tissue.

Poster 9 Title: Chemical absorption in the layers of human skin

Presenter: Jessica Stevens, North Carolina State University

Poster Abstract: Whether from environmental and occupational hazards or topical pharmaceuticals, the human skin comes into contact with various chemicals every day. In vivo experiments not only require large investments of both time and money but also are ethically infeasible due to the potential exposure to toxic chemicals. Comparatively, in vitro experiments offer ethical and financial advantages when combined with prioritization. Due to this, many scientists have chosen to make their in vitro data available publicly. Using publicly available data, we have created a detailed database that can be used in connection with mathematical modeling to predict diffusion, permeability, and partition coefficients. With this database, we present preliminary findings from machine learning techniques that can be drawn upon for future model building and better prediction of chemical absorption in human skin.

Poster 10 Title: Human papillomvirus vaccination strategy: modeling and implications

Presenter: Shasha Gao, University of Florida

Poster Abstract: Human papillomavirus (HPV) infection can spread between regions. What is the impact of disassortative geographical mixing on the dynamics of HPV transmission? How to allocate HPV vaccines between genders within each region and between regions to reduce the total infection? We develop a two-patch two-sex model to address these questions. The reproduction number is obtained and shown to provide a critical threshold for disease elimination. Both analytical and numerical results reveal that disassortative geographical mixing does not affect the reproduction number and only has a minor impact on the disease prevalence in the total population given the vaccine uptake proportional to the population size for each gender in the two patches. When the vaccine uptake is not proportional to the population size, sexual mixing between the two patches can reduce the reproduction number and mitigate the consequence of disproportionate vaccine coverage. Using parameters calibrated from the data of a case study, we find that if the two patches have the same or similar sex ratios, allocating vaccines proportionally according to the new recruits in two patches and giving priority to the gender with a smaller recruit rate within each patch will bring the maximum benefit in reducing the total prevalence.

Poster 11 Title: A Partitioned Method for the Solution of Fluid-Structure Interaction: Methodology and Reduced Order Modeling

Presenter: Amy de Castro, Clemson University

Poster Abstract: Partitioned methods for the solution of fluid-structure interaction (FSI) problems are often the preferred approach as they allow the reuse of existing codes for each subdomain that take into account its unique mathematical and physical properties.

We present a partitioned method for FSI problems based on a monolithic formulation of the problem which employs a Schur complement equation for a Lagrange multiplier. This algorithm eradicates the need for iterations between the fluid and structure subdomains and instead allows them to be decoupled and solved separately at each time step. The Lagrange multiplier, representing an approximation of the interface flux as well as the fluid pressure, serves as a Neumann boundary condition for each sub-problem, allowing for the fluid and structure to be solved independently at each time step.

To reduce computational costs, we consider implementing a reduced order model (ROM) for one or both subdomains. The Schur complement method developed for the original FSI scheme can be utilized to couple a reduced order model with either a full order model or a reduced order model on the other subdomain. We show numerical results demonstrating the method’s capability to capture each type of coupling.

Poster 12 Title: Spatial Pattern Formation Resulting from Invasion Dynamics and Biocontrol Outcomes: A Model Study

Presenter: Yuanming Lu, University of Florida

Poster Abstract: The invasion of an ecosystem by an alien plant species can often strongly alter the vegetation dynamics of the invaded ecosystem, since it may alter basic ecosystem properties once it has become established. In principle, this can cause a regime shift that cannot be easily reversed. Here we use spatially explicit agent-based modeling to simulate the invasion of an introduced tree species to a habitat occupied by a native species. The model is inspired by the invasion of Melaleuca quinquenervia in southern Florida habitats. Biocontrol agents have been introduced to try to control the Melaleuca, which has significantly reduced the invasive’s reproduction rate and increased its mortality rate. These effects are included in the model. We also, consider an increasingly important and far understudied novel aspect of forestry – standing dead – which is considered and tested for its effect on the dynamics, including its influence on the possibility of a regime shift. Our simulations show that added biocontrol will significantly delay the invasion process, and even help native outcompete the invasive in the future; a legacy of standing dead may delay the vegetation shift. Our results show that agent-based modeling is essential for examining fine-scale interactions among trees, predicting trajectories of invaded forest communities, and our findings can inform management and policy focused on preserving invaded plant communities.

Poster 13 Title: Computational Modeling of Cell Migration in Microfluidic Channel

Presenter: Zengyan Zhang, Utah State University

Poster Abstract: Cell migration plays an important role in various biological processes, such as tissue morphogenesis, wound healing and cancer metastasis, etc.. The mechanisms underlying cellular motility involve generating protrusive patches on the moving interfaces and determining moving directions under the guidance of chemotaxis. In our work, we proposed a phase-field model coupled with a reaction-diffusion system to keep track of the morphology changes of the cell membrane and steer the cell by gradients of attractive chemicals. In this talk, I will introduce our phase-field model for the migration of cell through complex channels and some numerical simulation results will be elaborated.

Poster 14 Title: Machine Learning and Computational Methods for Blood Flow in Organs

Presenter: Bilyana Tzolova, Rice University

Poster Abstract: We aim to efficiently and effectively segment the vascular system in the liver organ using deep learning techniques in order to improve on current manual methods. To do this, we propose a 3D DenseNet using PocketNet paradigm with binary classifications that has less parameters to train than the state of the art methods. We explore the impact of various preprocessing techniques on the accuracy of the neural network using the dice score coefficient. We find that successful preprocessing and post-processing filters and neural network parameters are necessary for consistently high dice scores. From the vessel segmentations, the blood vessels are skeletonized and their centerlines are computational domains for reduced 1D models. Using finite element method we model the flow of blood from the vessels into the 3D organ domain.

Poster 15 Title: Greedy Training Algorithms for Neural Networks and Applications to Numerical PDEs

Presenter: Qingguo Hong, The Pennsylvania State University

Poster Abstract: Recently, neural networks have been widely applied for solving partial differential equations. However, with current training algorithms the numerical convergence of neural networks when solving PDEs has not been empirically observed. The primary difficulty lies in solving the highly non-convex optimization problems resulting from the neural network discretization. Theoretically analyzing the optimization process presents significant difficulties and empirical experiments require extensive hyperparameter tuning to achieve acceptable results. In order to conquer this challenge, we develop a novel greedy training algorithm for shallow neural networks in this talk. We also analyze the resulting method and obtain a priori error bounds when solving PDEs from the function class defined by shallow networks. This rigorously establishes the convergence of the method as the network size increases. Finally, we test the algorithm on several benchmark examples, including high dimensional PDEs, to confirm the theoretical convergence rate and to establish its efficiency and robustness. An advantage of this method is its straightforward applicability to high-order equations on general domains.

Poster 16 Title: Mathematical modeling for optimal control of BK virus infection in Renal transplant recipients

Presenter: Dana Droz, North Carolina State University

Poster Abstract: Kidney transplant recipients are put on an immunosuppressant drug regimen to suppress their immune system which prevents allograft rejection. These drugs make the patient susceptible to infections. The opportunistic BK virus (BKV) infection has no effective antiviral treatment. The standard clinical practice to treat BKV is to reduce immunosuppression which in turn increases the risk of rejection. We use a mathematical model to predict the amount of BKV and suggest the optimal adjustment of immunosuppression using a receding horizon control approach. We present the validation of this model using data from the Duke Transplant Center.

Poster 17 Title: CCP: Correlated Clustering and Projection for Dimensionality Reduction

Presenter: Yuta Hozumi, Michigan State University

Poster Abstract: Most dimensionality reduction methods employ frequency domain representations obtained from matrix diagonalization and may not be efficient for large datasets with relatively high intrinsic dimensions. To address this challenge, Correlated Clustering and Projection (CCP) offers a novel data domain strategy that does not need to solve any matrix. CCP partitions high-dimensional features into correlated clusters and then projects correlated features in each cluster into a one-dimensional representation based on sample correlations. Furthermore, we propose Residue-Similarity (R-S) scores for visualizing and validating benchmark datasets associated with various machine learning algorithms.

Poster 18 Title: Using a Cahn-Hilliard equation to model mammal migration

Presenter: Zachary Hilliard, Oregon State University

Poster Abstract: It is possible to use techniques from continuum mechanics to model mammal migration by making the analogy of mammals traveling over some terrain to a fluid flowing through a porous medium. In previous work, it has been shown that a Cahn-Hilliard equation can be used as a model. This model is given by

\begin{equation*}

\begin{cases}

u_t = \nabla\cdot u K\nabla w \\

w = f(u) - \alpha \Delta u + \phi,

\end{cases}

\end{equation*}

where $u$ is the population density, $K$ is the trafficability (diffusion) tensor, $f$ is a nonlinear term which controls aggregation, $\phi$ represents a danger potential, and $\alpha>0$ is a scalar. In this poster, we show that one can obtain qualitatively better results by taking $w = f(u) - \nabla\cdot A \nabla u + \phi$ where $A\propto K^{-1}$.

Poster 19 Title: Mathematical and numerical analysis of a fully coupled Stokes-Biot-transport model

Presenter: Xing Wang, Penn State University

Poster Abstract: We study the coupled system of the flow and transport problem. In this paper, the Stokes equations are adopted to govern the fluid region; for the poroelastic region, the Biot system is utilized; for the transport of species within the fluid, we use an advection-diffusion equation. Equilibrium and kinematic conditions are imposed on the interface between the fluid and poroelastic media. And the continuity of flux on the fluid-structure interface is imposed via a Lagrange multiplier. This model is fully coupled and non-linear due to the convective transport term and the non-linear viscosity. To address the stability and convergence of the coupled system, we first use a Galerkin method and \textit{a priori} estimates to obtain the well-posedness of a linearized formulation. Next, a fixed point iteration procedure is utilized to study the stability and convergence of the original non-linear problem. The error analysis is performed for the semi-discrete continuous-in-time formulation. A series of computational experiments are conducted to confirm the theoretical convergence rate and to explore the feasibility of the method to model the physical flow and transport phenomena.

Poster 20 Title: A Causality-Based Learning Approach for Discovering the Underlying Dynamics of Complex Systems from Partial Observations with Stochastic Parameterization

Presenter: Yinling Zhang, University of Wisconsin Madison

Poster Abstract: Discovering the underlying dynamics of complex systems from data is an important practical topic. Constrained optimization algorithms are widely utilized and lead to many successes. Yet, such purely data-driven methods may bring about incorrect physics in the presence of random noise and cannot easily handle the situation with incomplete data. In this paper, a new iterative learning algorithm for complex turbulent systems with partial observations is developed that alternates between identifying model structures, recovering unobserved variables, and estimating parameters. First, a causality-based learning approach is utilized for the sparse identification of model structures, which takes into account certain physics knowledge that is pre-learned from data. It has unique advantages in coping with indirect coupling between features and is robust to the stochastic noise. A practical algorithm is designed to facilitate the causal inference for high-dimensional systems. Next, a systematic nonlinear stochastic parameterization is built to characterize the time evolution of the unobserved variables. Closed analytic formula via an efficient nonlinear data assimilation is exploited to sample the trajectories of the unobserved variables, which are then treated as synthetic observations to advance a rapid parameter estimation. Furthermore, the localization of the state variable dependence and the physics constraints are incorporated into the learning procedure, which mitigate the curse of dimensionality and prevent the finite time blow-up issue. Numerical experiments show that the new algorithm succeeds in identifying the model structure and providing suitable stochastic parameterizations for many complex nonlinear systems with chaotic dynamics, spatiotemporal multiscale structures, intermittency, and extreme events.

Poster 21 Title: Title: Patient-Specific MRI VR Model Construction and Simulation

Presenter: Jennifer Cremer, University of Florida

Abstract: This research seeks to disambiguate the exploration and discussions surrounding the evaluation of Magnetic Resonance Images (MRI) of colorectal tumors. While image processing and machine learning techniques have made advances in our ability to recognize key structures, they struggle when presented with MRI data and the opportunistically evolved vasculature that feeds the tumors. It is for these complexities that we propose a human-in-the-loop pipeline to develop concrete representations of the pertinent structures. We make use of the intuitive nature and stereoscopic rendering provided by virtual reality (VR) head-mounted displays (HMD) to support the spatial understanding that expert-users already have of anatomy and present the images as a simple 3-dimensional construct. We are working to provide a toolset to augment visualization of the construct to enhance detail isolation without loss of contextual understanding. This construct is then curated by the surgeons and fitted with pre-built generic deformable models using explicit piecewise polynomial surfaces. These models will then be exported into a custom surgical simulator where different surgical plans can be tested and evaluated for feasibility and outcomes.

Poster 22 Title: Best of two worlds: Cartesian sampling and volume computation for high dimensional configuration spaces using Cayley coordinates.

Presenter: Yichi Zhang, University of Florida

Abstract: We give an algorithm that uniformly samples and computes a discrete volume measure of a space of configurations of rigid bodies satisfying a system of distance inequality constraints belonging to a large natural class that occurs in several application scenarios. The algorithm views the configuration space as a branched covering and uses a recent theory of Cayley or distance coordinates to convexify the base space. By employing an on-demand grid traversal datastructure, the algorithm runs in linear time and empirically sublinear space in the number of grid cubes that are used to define the discrete volume measure and that intersect the configuration space. A software implementation and comparison with existing methods is provided.