%0 Journal Article
%T 热传导方程两类参数的统计反演方法<br>Statistical Inversion Methods for Two Types of Parameters in the Heat Conduction Equation
%A 胥文博
%J Advances in Applied Mathematics
%P 203-215
%@ 2324-8009
%D 2025
%I Hans Publishing
%R 10.12677/aam.2025.143106
%X 本文以热传导方程为背景&#65292;分别研究了不同位置上的常数型未知参数与函数型未知参数&#65292;并给出统计反演算法&#65292;完成数值反演试验。两类方法均能高效完成反演任务&#65292;且在面对高噪声观测信息时&#65292;具有很强的鲁棒性。<br>Focusing on the heat conduction equation, this paper investigates constant-type unknown parameters and function-type unknown parameters at different positions, and provides statistical inversion algorithms to complete numerical inversion experiments. Both methods can efficiently accomplish the inversion tasks and exhibit strong robustness in the presence of high-noise observational information.
%K 参数反演问题&#65292
%K 贝叶斯反演&#65292
%K 物理信息神经网络<br>Parameter Inverse Problem
%K Bayesian Inversion Method
%K Physics-Informed Neural Networks
%U http://www.hanspub.org/journal/PaperInformation.aspx?PaperID=109424