一维热传导方程热源反问题基于最小二乘法的正则化方法

计算物理 ›› 2016, Vol. 33 ›› Issue (1): 49-56.

一维热传导方程热源反问题基于最小二乘法的正则化方法

吴自库¹, 李福乐¹, DO Young Kwak²

1. 青岛农业大学理学与信息科学学院, 青岛;
2. 韩国科技学院数学系, 韩国大田

收稿日期:2014-12-29 修回日期:2015-04-21 出版日期:2016-01-25 发布日期:2016-01-25
作者简介:吴自库(1968-),男,博士,教授,从事应用数学研究,E-mail:zkwu1968@126.com
基金资助:
山东省高等学校优秀中青年骨干教师国际合作培养计划，国家自然科学基金（61403233），山东省自然科学基金（ZR2009AL012）资助项目

Least Squares Regularized Method for One-Dimensional Source Inverse Heat Conduction Problem

WU Ziku¹, LI Fule¹, DO Young Kwak²

1. Science and Information College, Qingdao Agricultural University, Qingdao, China;
2. Department of Mathematical Sciences, Korea Advanced Institute of Science and Technology, Daejeon, Korea

Received:2014-12-29 Revised:2015-04-21 Online:2016-01-25 Published:2016-01-25

摘要/Abstract

摘要： 研究一维热传导方程热源反问题.给出基于最小二乘支持向量机（LS-SVM）求解的半解析表达式，此外还给出一种参数调节方法以及算法稳定性的证明.数值实验表明该方法具有较高的数值精度和稳定性.

关键词: 最小二乘支持向量机, 一维热传导方程, 源项反问题, 二次规划

Abstract: We deal with one-dimensional source inverse heat conduction equation. An approach based on least squares support vector machines (LS-SVM) is proposed for semi-analytic approximate solutions. Furthermore, a parameters tuning formulism is shown and stability of the method is presented. The method yields high accuracy and stability solutions in practical examples.

Key words: least squares support vector machines, one-dimensional heat conduction equation, source inverse problem, quadratic programming

中图分类号:

吴自库, 李福乐, DO Young Kwak. 一维热传导方程热源反问题基于最小二乘法的正则化方法[J]. 计算物理, 2016, 33(1): 49-56.

WU Ziku, LI Fule, DO Young Kwak. Least Squares Regularized Method for One-Dimensional Source Inverse Heat Conduction Problem[J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 2016, 33(1): 49-56.

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