Efficient solution of nonlinear, underdetermined inverse problems with a generalized PDE model

Michael Cardiff; Peter K.Kitanidis

Abstract

Several parameter estimation problems (or “inverse” problems) such as those that occur in hydrology and geophysics are solved using partial differential equation (PDE)-based models of the physical system in question. Likewise, these problems are usually underdetermined due to the lack of enough data to constrain a unique solution. In this paper, we present a framework for the solution of underdetermined inverse problems using COMSOL Multiphysics (formerly FEMLAB) that is applicable to a broad range of physical systems governed by PDEs. We present a general adjoint state formulation which may be used in this framework and allows for faster calculation of sensitivity matrices in a variety of commonly encountered underdetermined problems. The aim of this approach is to provide a platform for the solution of inverse problems that is efficient, flexible, and not restricted to one particular scientific application.

We present an example application of this framework on a synthetic underdetermined inverse problem in aquifer characterization, and present numerical results on the accuracy and efficiency of this method. Our results indicate that our COMSOL-based routines provide an accurate, flexible, and scalable method for the solution of PDE-based inverse problems.

Keywords

Hydrogeology; Parameter estimation; Inverse problem; Adjoint state; COMSOL; Numerical model

相关文件下载地址
*该资源需回复评论后下载,马上去发表评论?
©下载资源版权归作者所有;本站所有资源均来源于网络,仅供学习使用,请支持正版!
默认图片
bossliu
清醒 专注 努力
文章: 499

留下评论

Captcha Code

Efficient solution of nonlinear, underdetermined inverse problems with a generalized PDE model