Abstract : Complex partial differential equations have been widely applied to different areas to understand the spatiotemporal dynamics of multiple interactive components, such as reaction-diffusion equations for modeling diffusive molecules in biology, Navier-Stokes equations for modeling fluid dynamics. Traditional numerical approaches may fail when applied to PDE models in applications due to specific features of application problems. In this minisymposium, we will focus on the recent development of new numerical approaches and applications of different PDE systems. The goal of this session is to bring together researchers in numerical PDEs and mathematical models to exchange ideas and explore collaborations.
[04291] A learned conservative semi-Lagrangian finite volume scheme for transport simulations
Format : Talk at Waseda University
Author(s) :
Wei Guo (Texas Tech University)
Yongsheng Chen (Zhejiang University)
Xinghui Zhong (Zhejiang University)
Abstract : Semi-Lagrangian (SL) schemes are known as a major numerical tool for solving transport equations with many. In this talk, we introduce a novel machine learning-assisted approach to accelerate the conventional SL finite volume schemes. The proposed scheme avoids the expensive tracking of upstream cells but attempts to learn the SL discretization from the data by incorporating specific inductive biases in the neural network, significantly simplifying the algorithm implementation and leading to improved efficiency.
[03990] A new type of simplified inverse Lax-Wendroff boundary treatment for hyperbolic conservation laws
Format : Talk at Waseda University
Author(s) :
Shihao Liu (University of Science and Technology of China)
Tingting Li (Henan University)
Ziqiang Cheng (Hefei University of Technology)
Yan Jiang (University of Science and Technology of China)
Chi-Wang Shu (Brown University)
Mengping Zhang (University of Science and Technology of China)
Abstract : In this talk, we will introduce a new kind of high order inverse Lax-Wendroff (ILW) boundary treatment for solving hyperbolic conservation laws with finite difference method on a Cartesian mesh, in which both scalar equations and systems are considered. This new ILW method decomposes the construction of ghost points into two steps: interpolation and extrapolation. At first, we approximate some special points value through interpolation polynomial given the interior points near boundary. Then, we will construct a Hermite extrapolation polynomial based on those special point values and spatial derivatives at boundary obtained through ILW process. This extrapolation polynomial will give us the approximation of the the ghost points value. Eigenvalue analysis shows that the new method can improve the computational efficiency on the premise of maintaining accuracy and stability. Numerical tests for one- and two-dimensional problems indicate that our method has high order accuracy for smooth solutions and non-oscillatory property for shock solution near boundary.
[02713] Transmission Dynamics of Tuberculosis with Age-specific Disease Progression
Format : Talk at Waseda University
Author(s) :
Wing-Cheong Lo (City University of Hong Kong)
Abstract : In this talk, we develop a system of delay partial differential equations to model tuberculosis transmission in a heterogeneous population. The system considers demographic structure coupling with the continuous development of the disease stage. We determine the basic reproduction number and several numerical simulations are used to investigate the influence of various progression rates on tuberculosis dynamics. This is joint work with Yu Mu, Tsz-Lik Chan, and Hsiang-Yu Yuan.
[02985] Extended-release Pre-Exposure Prophylaxis and Drug Resistant HIV
Format : Talk at Waseda University
Author(s) :
Yanping Ma (Loyola Marymount University)
Yeona Kang (Howard University)
Angelica Davenport (Florida State University)
Jennifer Aduamah (University of Delaware)
Kathryn Link (Pfzier)
Katharine Gurski (Howard University)
Abstract : We present a within-host, mechanistic Differential Equation model of the HIV latency and infection cycle in CD4+ T-cells to investigate drug-resistant mutations. We develop a pharmacokinetic/pharmacodynamic model for long-acting cabotegravir (CAB-LA, injectable PrEP) to relate the inhibitory drug response to the drug concentration in plasma and rectal, cervical, and vaginal fluids and tissue. And we will report some of our important findings in the talk.
[04493] A Level-Set Framework for Implicit Solvation
Format : Talk at Waseda University
Author(s) :
Li-Tien Cheng (UC San Diego)
Abstract : Implicit solvation involves the study of the effects solute atoms have on a surrounding solvent, which can be particularly important in, for example, the process of protein docking. An implicit treatment of the solvent gives rise to an interface between solute and solvent. We introduce a level-set framework applied to a variational free-energy setup for constructing such an interface, and consider efficient and accurate solvers in the presence of curvature, electrostatic, and mechanical effects.
[04909] Adaptive ANOVA and reduced basis methods to anisotropic stochastic PDEs
Format : Talk at Waseda University
Author(s) :
Heyrim Cho (University of California Riverside)
Bedřich Sousedík (University of Maryland, Baltimore County)
Howard Elman (University of Maryland, College Park)
Abstract : The combination of reduced basis and collocation methods enables efficient and accurate evaluation of the solutions to parameterized PDEs. We study the stochastic collocation methods that can be combined with reduced basis methods to solve high-dimensional parameterized stochastic PDEs. We also propose an adaptive algorithm using a probabilistic collocation method (PCM) and ANOVA decomposition. This procedure involves two stages. First, the method employs an ANOVA decomposition to identify the effective dimensions, i.e., subspaces of the parameter space in which the contributions to the solution are larger, and sort the reduced basis solution in a descending order of error. Then, the adaptive search refines the parametric space by increasing the order of polynomials until the algorithm is terminated by a saturation constraint. We demonstrate the effectiveness of the proposed algorithm for solving a stationary stochastic convection-diffusion equation, a benchmark problem chosen because solutions contain steep boundary layers and anisotropic features. We also solve the Stokes-Brinkman equations that model fluid flow in highly heterogeneous porous media.
[04915] Theoretical Principles of Enhancer-Promoter Communication in Gene Expression
Format : Talk at Waseda University
Author(s) :
Jiajun Zhang (Sun Yat-sen University)
Abstract : Recent experimental evidence strongly supports that long-range enhancer-promoter interactions have important influences on gene-expression dynamics, but it is unclear how the interaction information is translated into gene expression over time. To address this challenge, we develop a general theoretical framework that integrates chromatin dynamics, enhancer-promoter communication, and gene-state switching to study gene expression. Our model and results provide quantitative insight into both spatiotemporal gene-expression determinants and cellular fates during development.
