Advances in Computational Mathematics最新文献_第3页

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

{"title":"Efficient iterative methods for hyperparameter estimation in large-scale linear inverse problems","authors":"Khalil A. Hall-Hooper, Arvind K. Saibaba, Julianne Chung, Scot M. Miller","doi":"10.1007/s10444-024-10208-6","DOIUrl":"10.1007/s10444-024-10208-6","url":null,"abstract":"<div>We study Bayesian methods for large-scale linear inverse problems, focusing on the challenging task of hyperparameter estimation. Typical hierarchical Bayesian formulations that follow a Markov Chain Monte Carlo approach are possible for small problems but are not computationally feasible for problems with a very large number of unknown inverse parameters. In this work, we describe an empirical Bayes (EB) method to estimate hyperparameters that maximize the marginal posterior, i.e., the probability density of the hyperparameters conditioned on the data, and then we use the estimated hyperparameters to compute the posterior of the unknown inverse parameters. For problems where the computation of the square root and inverse of prior covariance matrices are not feasible, we describe an approach based on the generalized Golub-Kahan bidiagonalization to approximate the marginal posterior and seek hyperparameters that minimize the approximate marginal posterior. Numerical results from seismic and atmospheric tomography demonstrate the accuracy, robustness, and potential benefits of the proposed approach.</div>","PeriodicalId":50869,"journal":{"name":"Advances in Computational Mathematics","volume":"50 6","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-12-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142793849","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

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>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 a-prior 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 a-prior 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.</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>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.</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

Solving the quadratic eigenvalue problem expressed in non-monomial bases by the tropical scaling 用热带标度法求解非一元基表示的二次特征值问题

IF 1.7 3区数学

Advances in Computational Mathematics Pub Date : 2024-12-03 DOI: 10.1007/s10444-024-10214-8

Hongjia Chen, Teng Wang, Chun-Hua Zhang, Xiang Wang

引用次数: 0

Discontinuous Galerkin schemes for Stokes flow with Tresca boundary condition: iterative a posteriori error analysis 具有 Tresca 边界条件的斯托克斯流的非连续 Galerkin 方案：迭代后验误差分析

IF 1.7 3区数学

Advances in Computational Mathematics Pub Date : 2024-11-25 DOI: 10.1007/s10444-024-10207-7

J.K. Djoko, T. Sayah

引用次数: 0

Helmholtz FEM solutions are locally quasi-optimal modulo low frequencies 亥姆霍兹有限元求解在低频局部准最优

IF 1.7 3区数学

Advances in Computational Mathematics Pub Date : 2024-11-18 DOI: 10.1007/s10444-024-10193-w

M. Averseng, J. Galkowski, E. A. Spence

{"title":"Helmholtz FEM solutions are locally quasi-optimal modulo low frequencies","authors":"M. Averseng, J. Galkowski, E. A. Spence","doi":"10.1007/s10444-024-10193-w","DOIUrl":"10.1007/s10444-024-10193-w","url":null,"abstract":"<div>For h-FEM discretisations of the Helmholtz equation with wavenumber k, we obtain k-explicit analogues of the classic local FEM error bounds of Nitsche and Schatz (Math. Comput. 28(128), 937–958 1974), Wahlbin (1991, §9), Demlow et al.(Math. Comput. 80(273), 1–9 2011), showing that these bounds hold with constants independent of k, provided one works in Sobolev norms weighted with k in the natural way. We prove two main results: (i) a bound on the local (H^1) error by the best approximation error plus the (L^2) error, both on a slightly larger set, and (ii) the bound in (i) but now with the (L^2) error replaced by the error in a negative Sobolev norm. The result (i) is valid for shape-regular triangulations, and is the k-explicit analogue of the main result of Demlow et al. (Math. Comput. 80(273), 1–9 2011). The result (ii) is valid when the mesh is locally quasi-uniform on the scale of the wavelength (i.e., on the scale of (k^{-1})) and is the k-explicit analogue of the results of Nitsche and Schatz (Math. Comput. 28(128), 937–958 1974), Wahlbin (1991, §9). Since our Sobolev spaces are weighted with k in the natural way, the result (ii) indicates that the Helmholtz FEM solution is locally quasi-optimal modulo low frequencies (i.e., frequencies (lesssim k)). Numerical experiments confirm this property, and also highlight interesting propagation phenomena in the Helmholtz FEM error.</div>","PeriodicalId":50869,"journal":{"name":"Advances in Computational Mathematics","volume":"50 6","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-11-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10444-024-10193-w.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142664470","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Higher-order iterative decoupling for poroelasticity 孔弹性的高阶迭代解耦

IF 1.7 3区数学

Advances in Computational Mathematics Pub Date : 2024-11-15 DOI: 10.1007/s10444-024-10200-0

Robert Altmann, Abdullah Mujahid, Benjamin Unger

引用次数: 0

Adaptive quarklet tree approximation 自适应夸克树近似法

IF 1.7 3区数学

Advances in Computational Mathematics Pub Date : 2024-10-31 DOI: 10.1007/s10444-024-10205-9

Stephan Dahlke, Marc Hovemann, Thorsten Raasch, Dorian Vogel

引用次数: 0