Advances in Computational Mathematics最新文献_第5页

A reduced-order model for advection-dominated problems based on the Radon Cumulative Distribution Transform 基于Radon累积分布变换的平流占优问题降阶模型

IF 1.7 3区数学

Advances in Computational Mathematics Pub Date : 2025-01-03 DOI: 10.1007/s10444-024-10209-5

Tobias Long, Robert Barnett, Richard Jefferson-Loveday, Giovanni Stabile, Matteo Icardi

引用次数: 0

On convergence of the generalized Lanczos trust-region method for trust-region subproblems 广义Lanczos信赖域方法在信赖域子问题上的收敛性

IF 1.7 3区数学

Advances in Computational Mathematics Pub Date : 2025-01-02 DOI: 10.1007/s10444-024-10217-5

Bo Feng, Gang Wu

引用次数: 0

Unfitted finite element method for the quad-curl interface problem 四旋度界面问题的非拟合有限元法

IF 1.7 3区数学

Advances in Computational Mathematics Pub Date : 2024-12-27 DOI: 10.1007/s10444-024-10213-9

Hailong Guo, Mingyan Zhang, Qian Zhang, Zhimin Zhang

引用次数: 0

A nonsingular-kernel Dirichlet-to-Dirichlet mapping method for the exterior Stokes problem 外部Stokes问题的非奇核Dirichlet-to-Dirichlet映射方法

IF 1.7 3区数学

Advances in Computational Mathematics Pub Date : 2024-12-18 DOI: 10.1007/s10444-024-10216-6

Xiaojuan Liu, Maojun Li, Tao Yin, Shangyou Zhang

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Discretisation of an Oldroyd-B viscoelastic fluid flow using a Lie derivative formulation 利用列导数公式实现奥尔德罗伊德-B 粘弹性流体流动的离散化

IF 1.7 3区数学

Advances in Computational Mathematics Pub Date : 2024-12-17 DOI: 10.1007/s10444-024-10211-x

Ben S. Ashby, Tristan Pryer

引用次数: 0

A posteriori error control for a discontinuous Galerkin approximation of a Keller-Segel model Keller-Segel模型的不连续Galerkin近似的后验误差控制

IF 1.7 3区数学

Advances in Computational Mathematics Pub Date : 2024-12-13 DOI: 10.1007/s10444-024-10212-w

Jan Giesselmann, Kiwoong Kwon

引用次数: 0

Efficient iterative methods for hyperparameter estimation in large-scale linear inverse problems 大规模线性反问题超参数估计的有效迭代方法

IF 1.7 3区数学

Advances in Computational Mathematics Pub Date : 2024-12-09 DOI: 10.1007/s10444-024-10208-6

Khalil A. Hall-Hooper, Arvind K. Saibaba, Julianne Chung, Scot M. Miller

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引用次数: 0

Analysis of a time filtered finite element method for the unsteady inductionless MHD equations 非定常无感应MHD方程的时间滤波有限元分析

IF 1.7 3区数学

Advances in Computational Mathematics Pub Date : 2024-12-09 DOI: 10.1007/s10444-024-10215-7

Xiaodi Zhang, Jialin Xie, Xianzhu Li

引用次数: 0

On the recovery of initial status for linearized shallow-water wave equation by data assimilation with error analysis 用数据同化法恢复线性化浅水波动方程初始状态及误差分析

IF 1.7 3区数学

Advances in Computational Mathematics Pub Date : 2024-12-05 DOI: 10.1007/s10444-024-10210-y

Jun-Liang Fu, Jijun Liu

{"title":"On the recovery of initial status for linearized shallow-water wave equation by data assimilation with error analysis","authors":"Jun-Liang Fu, Jijun Liu","doi":"10.1007/s10444-024-10210-y","DOIUrl":"10.1007/s10444-024-10210-y","url":null,"abstract":"<div><p>We recover the initial status of an evolution system governed by linearized shallow-water wave equations in a 2-dimensional bounded domain by data assimilation technique, with the aim of determining the initial wave height from the measurement of wave distribution in an interior domain. Since we specify only one component of the solution to the governed system and the observation is only measured in part of the interior domain, taking into consideration of the engineering restriction on the measurement process, this problem is ill-posed. Based on the known well-posedness result of the forward problem, this inverse problem is reformulated as an optimizing problem with data-fit term and the penalty term involving the background of the wave amplitude as <i>a-prior</i> information. We establish the Euler-Lagrange equation for the optimal solution in terms of its adjoint system. The unique solvability of this Euler-Lagrange equation is rigorously proven. Then the optimal approximation error of the regularizing solution to the exact solution is established in terms of the noise level of measurement data and the <i>a-prior</i> background distribution, based on the Lax-Milgram theorem. Finally, we propose an iterative algorithm to realize this process, with several numerical examples to validate the efficacy of our proposed method.</p></div>","PeriodicalId":50869,"journal":{"name":"Advances in Computational Mathematics","volume":"50 6","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142776455","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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

Inverting the fundamental diagram and forecasting boundary conditions: how machine learning can improve macroscopic models for traffic flow 反转基本图和预测边界条件：机器学习如何改善交通流的宏观模型

IF 1.7 3区数学

Advances in Computational Mathematics Pub Date : 2024-12-04 DOI: 10.1007/s10444-024-10206-8

Maya Briani, Emiliano Cristiani, Elia Onofri

{"title":"Inverting the fundamental diagram and forecasting boundary conditions: how machine learning can improve macroscopic models for traffic flow","authors":"Maya Briani, Emiliano Cristiani, Elia Onofri","doi":"10.1007/s10444-024-10206-8","DOIUrl":"10.1007/s10444-024-10206-8","url":null,"abstract":"<div><p>In this paper, we develop new methods to join machine learning techniques and macroscopic differential models, aimed at estimate and forecast vehicular traffic. This is done to complement respective advantages of data-driven and model-driven approaches. We consider here a dataset with flux and velocity data of vehicles moving on a highway, collected by fixed sensors and classified by lane and by class of vehicle. By means of a machine learning model based on an LSTM recursive neural network, we extrapolate two important pieces of information: (1) if congestion is appearing under the sensor, and (2) the total amount of vehicles which is going to pass under the sensor in the next future (30 min). These pieces of information are then used to improve the accuracy of an LWR-based first-order multi-class model describing the dynamics of traffic flow between sensors. The first piece of information is used to invert the (concave) fundamental diagram, thus recovering the density of vehicles from the flux data, and then inject directly the density datum in the model. This allows one to better approximate the dynamics between sensors, especially if an accident/bottleneck happens in a not monitored stretch of the road. The second piece of information is used instead as boundary conditions for the equations underlying the traffic model, to better predict the total amount of vehicles on the road at any future time. Some examples motivated by real scenarios will be discussed. Real data are provided by the Italian motorway company Autovie Venete S.p.A.</p></div>","PeriodicalId":50869,"journal":{"name":"Advances in Computational Mathematics","volume":"50 6","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-12-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142761986","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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