IMA Journal of Numerical Analysis最新文献

Convergence analysis of three semidiscrete numerical schemes for nonlocal geometric flows including perimeter terms 含周长项的非局部几何流动的三种半离散数值格式的收敛性分析

IF 2.1 2区数学

IMA Journal of Numerical Analysis Pub Date : 2025-05-01 DOI: 10.1093/imanum/draf015

Wei Jiang, Chunmei Su, Ganghui Zhang

引用次数: 0

A backward differential deep learning-based algorithm for solving high-dimensional nonlinear backward stochastic differential equations 一种求解高维非线性后向随机微分方程的后向微分深度学习算法

IF 2.1 2区数学

IMA Journal of Numerical Analysis Pub Date : 2025-04-28 DOI: 10.1093/imanum/draf022

Lorenc Kapllani, Long Teng

{"title":"A backward differential deep learning-based algorithm for solving high-dimensional nonlinear backward stochastic differential equations","authors":"Lorenc Kapllani, Long Teng","doi":"10.1093/imanum/draf022","DOIUrl":"https://doi.org/10.1093/imanum/draf022","url":null,"abstract":"In this work we propose a novel backward differential deep learning-based algorithm for solving high-dimensional nonlinear backward stochastic differential equations (BSDEs), where the deep neural network (DNN) models are trained, not only on the inputs and labels, but also on the differentials of the corresponding labels. This is motivated by the fact that differential deep learning can provide an efficient approximation of the labels and their derivatives with respect to inputs. The BSDEs are reformulated as differential deep learning problems by using Malliavin calculus. The Malliavin derivatives of the BSDE solution themselves satisfy another BSDE, resulting thus in a system of BSDEs. Such formulation requires the estimation of the solution, its gradient and the Hessian matrix, represented by the triple of processes $left (Y, Z, varGamma right ).$ All the integrals within this system are discretized by using the Euler–Maruyama method. Subsequently, DNNs are employed to approximate the triple of these unknown processes. The DNN parameters are backwardly optimized at each time step by minimizing a differential learning type loss function, which is defined as a weighted sum of the dynamics of the discretized BSDE system, with the first term providing the dynamics of the process $Y$ and the other the process $Z$. An error analysis is carried out to show the convergence of the proposed algorithm. Various numerical experiments of up to $50$ dimensions are provided to demonstrate the high efficiency. Both theoretically and numerically, it is demonstrated that our proposed scheme is more efficient in terms of computation time or accuracy compared with other contemporary deep learning-based methodologies.","PeriodicalId":56295,"journal":{"name":"IMA Journal of Numerical Analysis","volume":"39 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2025-04-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143884791","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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

An asymptotic preserving scheme for the defocusing Davey–Stewartson II equation in the semiclassical limit 半经典极限下离焦Davey-Stewartson II方程的渐近保持格式

IF 2.1 2区数学

IMA Journal of Numerical Analysis Pub Date : 2025-04-26 DOI: 10.1093/imanum/draf019

Dandan Wang, Hanquan Wang

引用次数: 0

Spatio-temporal Lie–Poisson discretization for incompressible magnetohydrodynamics on the sphere 球上不可压缩磁流体力学的时空Lie-Poisson离散化

IF 2.1 2区数学

IMA Journal of Numerical Analysis Pub Date : 2025-04-26 DOI: 10.1093/imanum/draf024

Klas Modin, Michael Roop

引用次数: 0

On the approximation of singular functions by series of noninteger powers 关于用非整数幂级数逼近奇异函数

IF 2.1 2区数学

IMA Journal of Numerical Analysis Pub Date : 2025-04-26 DOI: 10.1093/imanum/draf006

Mohan Zhao, Kirill Serkh

{"title":"On the approximation of singular functions by series of noninteger powers","authors":"Mohan Zhao, Kirill Serkh","doi":"10.1093/imanum/draf006","DOIUrl":"https://doi.org/10.1093/imanum/draf006","url":null,"abstract":"In this paper, we describe an algorithm for approximating functions of the form $f(x)=int _{a}^{b} x^{mu } sigma (mu ) , {text{d}} mu $ over $[0,1]$, where $sigma (mu )$ is some signed Radon measure, or, more generally, of the form $f(x) = {{langle sigma (mu ), x^mu rangle }}$, where $sigma (mu )$ is some distribution supported on $[a,b]$, with $0 &lt;a &lt; b&lt; infty $. One example from this class of functions is $x^{c} (log{x})^{m}=(-1)^{m} {{langle delta ^{(m)}(mu -c), x^mu rangle }}$, where $aleq c leq b$ and $m geq 0$ is an integer. Given the desired accuracy $varepsilon $ and the values of $a$ and $b$, our method determines a priori a collection of noninteger powers $t_{1}$, $t_{2}$, …, $t_{N}$, so that the functions are approximated by series of the form $f(x)approx sum _{j=1}^{N} c_{j} x^{t_{j}}$, and a set of collocation points $x_{1}$, $x_{2}$, …, $x_{N}$, such that the expansion coefficients can be found by collocating the function at these points. We prove that our method has a small uniform approximation error, which is proportional to $varepsilon $ multiplied by some small constants, and that the number of singular powers and collocation points grows as $N=O(log{frac{1}{varepsilon }})$. We demonstrate the performance of our algorithm with several numerical experiments.","PeriodicalId":56295,"journal":{"name":"IMA Journal of Numerical Analysis","volume":"32 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2025-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143878121","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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

Optimal convergence rates of an adaptive hybrid FEM-BEM method for full-space linear transmission problems 全空间线性传输问题的自适应混合有限元-边界元法的最优收敛速率

IF 2.1 2区数学

IMA Journal of Numerical Analysis Pub Date : 2025-04-25 DOI: 10.1093/imanum/draf023

Gregor Gantner, Michele Ruggeri

引用次数: 0

Space-time hybridizable discontinuous Galerkin method for advection-diffusion: the advection-dominated regime 平流-扩散的时空可杂化不连续Galerkin方法：平流主导型

IF 2.1 2区数学

IMA Journal of Numerical Analysis Pub Date : 2025-04-23 DOI: 10.1093/imanum/draf013

Yuan Wang, Sander Rhebergen

引用次数: 0

A hybridizable discontinuous Galerkin method for Stokes/Darcy coupling on dissimilar meshes 不同网格上Stokes/Darcy耦合的可杂交不连续Galerkin方法

IF 2.1 2区数学

IMA Journal of Numerical Analysis Pub Date : 2025-04-19 DOI: 10.1093/imanum/drae109

Isaac Bermúdez, Jaime Manríquez, Manuel Solano

引用次数: 0

A priori error estimates for optimal control problems governed by the transient Stokes equations and subject to state constraints pointwise in time 由瞬态Stokes方程控制并受状态约束的最优控制问题的先验误差估计

IF 2.1 2区数学

IMA Journal of Numerical Analysis Pub Date : 2025-04-13 DOI: 10.1093/imanum/draf018

Dmitriy Leykekhman, Boris Vexler, Jakob Wagner

引用次数: 0

Numerical methods and regularity properties for viscosity solutions of nonlocal in space and time diffusion equations 非局部时空扩散方程的粘性解的数值方法和正则特性

IF 2.1 2区数学

IMA Journal of Numerical Analysis Pub Date : 2025-04-09 DOI: 10.1093/imanum/draf011

Félix del Teso, Łukasz Płociniczak

引用次数: 0