A novel model reduction method to solve inverse problems of parabolic type

TL;DR

This paper introduces a new POD-based model reduction technique for parabolic inverse problems, effectively addressing inverse crime issues and improving solution accuracy through convergence analysis and extensive testing.

Contribution

The paper presents a novel POD-based reduction method that mitigates inverse crime and enhances the reliability of solving parabolic inverse problems.

Findings

Effective reduction of forward model complexity

Successful mitigation of inverse crime

Improved accuracy in inverse problem solutions

Abstract

In this paper, we propose novel proper orthogonal decomposition (POD)--based model reduction methods that effectively address the issue of inverse crime in solving parabolic inverse problems. Both the inverse initial value problems and inverse source problems are studied. By leveraging the inherent low-dimensional structures present in the data, our approach enables a reduction in the forward model complexity without compromising the accuracy of the inverse problem solution. Besides, we prove the convergence analysis of the proposed methods for solving parabolic inverse problems. Through extensive experimentation and comparative analysis, we demonstrate the effectiveness of our method in overcoming inverse crime and achieving improved inverse problem solutions. The proposed POD model reduction method offers a promising direction for improving the reliability and applicability of inverse problem-solving techniques in various domains.