A data-driven model reduction approach for backward fractional diffusion-wave equations

TL;DR

This paper introduces a data-driven model reduction method for backward fractional diffusion-wave equations, enhancing inverse problem solving efficiency through an observation system that shares the same linear structure as the forward problem.

Contribution

The work develops a novel observation system approach that improves computational efficiency for inverse problems in fractional diffusion-wave equations.

Findings

The observation system solution maps one-to-one with the forward problem.

Model reduction approaches for the observation system are effective for the forward problem.

Numerical examples confirm the efficiency improvements.

Abstract

In this work, we propose an observation system based on the available data which solution is one-be-one mapping to the forward problem(with the unknown initial function) solution. It implies their solutions share the same linear structure in the finite dimensional space. Theoretical results show model reduction approaches constructed for the observation system also work well for the forward problem, which significantly improve the efficiency of solving the inverse problem. Several numerical examples are presented to support our finding.