East Asian Journal on Applied Mathematics最新文献_第2页

Multivariate Feedback Particle Filter Rederived from the Splitting-Up Scheme 从拆分方案再衍生出的多元反馈粒子滤波器

IF 1.2 4区数学

East Asian Journal on Applied Mathematics Pub Date : 2024-04-01 DOI: 10.4208/eajam.2022-184.030823

Huimin Miao, Xue Luo

{"title":"Multivariate Feedback Particle Filter Rederived from the Splitting-Up Scheme","authors":"Huimin Miao, Xue Luo","doi":"10.4208/eajam.2022-184.030823","DOIUrl":"https://doi.org/10.4208/eajam.2022-184.030823","url":null,"abstract":"The multivariate feedback particle filter (FPF) is formulated from the viewpoint of splitting-up methods. The essential difference between this formulation and\u0000the formal derivation is that instead of one-time control at a discrete time instant, we\u0000consider the updating stage as a stochastic flow of particles in each time interval. This allows to easily obtain a consistent stochastic flow by comparing the Kolmogorov forward\u0000equation of particles and the updating part of the Kushner’s equation in the splitting-up\u0000method. Moreover, if an optimal stochastic flow exists, the convergence of the splitting-up method can be studied by passing to an FPF with a continuous time. To guarantee the\u0000existence of a stochastic flow, we validate the Poincaré inequality for the alternating distributions, given the time discretization and the observation path, under mild conditions\u0000on the nonlinear filtering system and the initial state. Besides, re-examining the original\u0000derivation of the FPF, we show that the optimal transport map between the prior and\u0000the posterior is an $f$-divergence invariant in the abstract Bayesian inference framework.","PeriodicalId":48932,"journal":{"name":"East Asian Journal on Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140564659","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Partitioned Dashnic-Zusmanovich Type Matric with Applications 分区达什尼奇-祖斯玛诺维奇类型矩阵及其应用

IF 1.2 4区数学

East Asian Journal on Applied Mathematics Pub Date : 2024-04-01 DOI: 10.4208/eajam.2023-019.100823

Wenlong Zeng, Jianzhou Liu

引用次数: 0

Advection-Pressure Splitting Schemes for the Equations of Blood Flow Conservative and Non-Conservative Forms 血流方程保守和非保守形式的对流-压力分割方案

IF 1.2 4区数学

East Asian Journal on Applied Mathematics Pub Date : 2024-04-01 DOI: 10.4208/eajam.2023-045.090523

Eleuterio F. Toro,Annunziato Siviglia,Alessandra Spilimbergo, Lucas O. Müller

{"title":"Advection-Pressure Splitting Schemes for the Equations of Blood Flow Conservative and Non-Conservative Forms","authors":"Eleuterio F. Toro,Annunziato Siviglia,Alessandra Spilimbergo, Lucas O. Müller","doi":"10.4208/eajam.2023-045.090523","DOIUrl":"https://doi.org/10.4208/eajam.2023-045.090523","url":null,"abstract":"We present a class of simple advection-pressure splitting numerical methods\u0000to solve the blood flow equations in compliant arterial vessels. The schemes are inspired\u0000by the TV flux vector splitting approach for conservative systems, proposed by Toro and\u0000Vázquez [30]. But the reformulated TV-type splitting schemes of this paper have a wider\u0000range of applicability, including systems of equations in non-conservative form. The\u0000spatial differential operator is split into advection terms, which may be in conservative form, from pressure terms in conservative or non-conservative form. Additionally,\u0000unlike the original TV scheme, the reformulated splitting of this paper fully preserves\u0000the continuity equation as part of the pressure system. This last feature is consistent\u0000with zero-dimensional models for blood flow that are based on neglecting the inertial\u0000term in the momentum equation. The schemes are also well suited for systems in which\u0000geometric and biomechanical parameters of the problem vary discontinuously. The splitting schemes of this paper are systematically assessed on a carefully designed suite of\u0000test problems and compared with several existing, mainstream methods. Overall, the\u0000proposed numerical methods perform very satisfactorily and suggest themselves as attractive computational tools for modelling the dynamics of bodily fluids under realistic\u0000conditions.","PeriodicalId":48932,"journal":{"name":"East Asian Journal on Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140564663","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

On Pricing Options Under Two Stochastic Volatility Processes 论两种随机波动过程下的期权定价

IF 1.2 4区数学

East Asian Journal on Applied Mathematics Pub Date : 2024-04-01 DOI: 10.4208/eajam.2022-356.180923

Wenjia Xie, Zhongyi Huang

引用次数: 0

Two-Grid Methods for Maxwell’s Equations in a Cole-Cole Dispersive Medium 科尔-科尔色散介质中麦克斯韦方程的双网格法

IF 1.2 4区数学

East Asian Journal on Applied Mathematics Pub Date : 2024-03-01 DOI: 10.4208/eajam.2022-293.010923

Nuodi Liu, Yanping Chen and Yunqing Huang

引用次数: 0

Multiple Poles Solutions of the Hirota Equation Under Nonzero Boundary Conditions by Inverse Scattering Method 用反向散射法求解非零边界条件下的广田方程多极解

IF 1.2 4区数学

East Asian Journal on Applied Mathematics Pub Date : 2024-02-01 DOI: 10.4208/eajam.2023-001.030523

Guixian Wang, Xiu-Bin Wang and Bo Han

引用次数: 0

Iterative Method with Inertia for Variational Inequalities on Hadamard Manifolds with Lower Bounded Curvature 具有下限曲率的哈达玛德曲面上变分不等式的惯性迭代法

IF 1.2 4区数学

East Asian Journal on Applied Mathematics Pub Date : 2024-01-01 DOI: 10.4208/eajam.2023-093.130723

Teng-Teng Yao,Xiao-Qing Jin, Zhi Zhao

引用次数: 0

A Diagonalization-Based Parallel-in-Time Algorithm for Crank-Nicolson’s Discretization of the Viscoelastic Equation 基于对角线化的时间并行算法，用于粘弹性方程的克兰克-尼科尔森离散化

IF 1.2 4区数学

East Asian Journal on Applied Mathematics Pub Date : 2024-01-01 DOI: 10.4208/eajam.2022-304.070323

Fu Li, Yingxiang Xu

{"title":"A Diagonalization-Based Parallel-in-Time Algorithm for Crank-Nicolson’s Discretization of the Viscoelastic Equation","authors":"Fu Li, Yingxiang Xu","doi":"10.4208/eajam.2022-304.070323","DOIUrl":"https://doi.org/10.4208/eajam.2022-304.070323","url":null,"abstract":"In this paper, we extend a diagonalization-based parallel-in-time (PinT) algorithm to the viscoelastic equation. The central difference method is used for spatial discretization, while for temporal discretization, we use the Crank-Nicolson scheme. Then an all-at-once system collecting all the solutions at each time level is formed and solved using a fixed point iteration preconditioned by an $α$-circulant matrix in parallel. Via a rigorous analysis, we find that the spectral radius of the iteration matrix is uniformly bounded by $α/(1 − α),$ independent of the model parameters (the damping coefficient $varepsilon$ and the wave velocity $sqrt{gamma}$) and the discretization parameters (the time step $tau$ and the spatial mesh size $h$). Unlike the classical wave equation with Dirichlet boundary condition where the upper bound $α/(1 − α)$ is very sharp, we find that the occurrence of the damping term $−varepsilon∆y_t,$ as well as the large final time $T,$ leads to even faster convergence of the algorithm, especially when $α$ is not very small. We illustrate our theoretical findings with several numerical examples.","PeriodicalId":48932,"journal":{"name":"East Asian Journal on Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139082096","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Multi-Breather, Rogue Wave and Multi-Bright-Dark Soliton Interaction of the (2+1)-Dimensional Nonlocal Fokas System (2+1)-Dimensional Nonlocal Fokas System 的多呼吸器、流波和多亮暗孤子相互作用

IF 1.2 4区数学

East Asian Journal on Applied Mathematics Pub Date : 2024-01-01 DOI: 10.4208/eajam.2022-258.300123

Xue-Wei Yan,Yong Chen,Shou-Fu Tian, Xiu-Bin Wang

{"title":"Multi-Breather, Rogue Wave and Multi-Bright-Dark Soliton Interaction of the (2+1)-Dimensional Nonlocal Fokas System","authors":"Xue-Wei Yan,Yong Chen,Shou-Fu Tian, Xiu-Bin Wang","doi":"10.4208/eajam.2022-258.300123","DOIUrl":"https://doi.org/10.4208/eajam.2022-258.300123","url":null,"abstract":"We study the (2+1)-dimensional nonlocal Fokas system by using the Hirota’s\u0000bilinear method. Firstly, a general tau-function of Kadomtsev-Petviashvili (KP) hierarchy satisfied with the bilinear equation under nonzero boundary condition is derived by\u0000considering differential relations and a variable transformation. Secondly, two Gramtype solutions are utilized to the construction of multi-breather, high-order rogue wave,\u0000and multi-bright-dark soliton solutions. Then the corresponding parameter restrictions\u0000of these solutions are given to satisfy with the complex conjugation symmetry. Furthermore, we find that if the parameter $p_{iI}$ takes different values, the rogue wave solution\u0000can be classified as three types of states, such as dark-dark, four-peak and bright-bright\u0000high-order rogue wave. If the parameter $c_i$ takes different values, the soliton solution\u0000can be classified as three type of states, including the multi-dark, multi-bright-dark and\u0000multi-bright solitons. By considering third-type of reduced tau-function to the Hirota’s\u0000bilinear equations, we give the collisions between the high-order rogue wave and the\u0000multi-bright-dark solitons on constant ($N$ is positive even) or periodic background ($N$ is\u0000positive odd). In order to understand the dynamics behaviors of the obtained solutions\u0000better, the various rich patterns are theoretically and graphically analyzed in detail.","PeriodicalId":48932,"journal":{"name":"East Asian Journal on Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139082673","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Less Emphasis on Hard Regions: Curriculum Learning of PINNs for Singularly Perturbed Convection-Diffusion-Reaction Problems 减少对困难区域的重视：奇异扰动对流-扩散-反作用问题的 PINNs 课程学习

IF 1.2 4区数学

East Asian Journal on Applied Mathematics Pub Date : 2024-01-01 DOI: 10.4208/eajam.2023-062.170523

Yufeng Wang,Cong Xu,Min Yang, Jin Zhang

{"title":"Less Emphasis on Hard Regions: Curriculum Learning of PINNs for Singularly Perturbed Convection-Diffusion-Reaction Problems","authors":"Yufeng Wang,Cong Xu,Min Yang, Jin Zhang","doi":"10.4208/eajam.2023-062.170523","DOIUrl":"https://doi.org/10.4208/eajam.2023-062.170523","url":null,"abstract":"Although physics-informed neural networks (PINNs) have been successfully\u0000applied in a wide variety of science and engineering fields, they can fail to accurately predict the underlying solution in slightly challenging convection-diffusion-reaction problems. In this paper, we investigate the reason of this failure from a domain distribution perspective, and identify that learning multi-scale fields simultaneously makes the\u0000network unable to advance its training and easily get stuck in poor local minima. We\u0000show that the widespread experience of sampling more collocation points in high-loss\u0000regions hardly help optimize and may even worsen the results. These findings motivate\u0000the development of a novel curriculum learning method that encourages neural networks to prioritize learning on easier non-layer regions while downplaying learning on\u0000harder regions. The proposed method helps PINNs automatically adjust the learning emphasis and thereby facilitates the optimization procedure. Numerical results on typical\u0000benchmark equations show that the proposed curriculum learning approach mitigates\u0000the failure modes of PINNs and can produce accurate results for very sharp boundary\u0000and interior layers. Our work reveals that for equations whose solutions have large\u0000scale differences, paying less attention to high-loss regions can be an effective strategy\u0000for learning them accurately.","PeriodicalId":48932,"journal":{"name":"East Asian Journal on Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139082297","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0