A Model-Consistent Data-Driven Computational Strategy for PDE Joint Inversion Problems

TL;DR

This paper introduces a combined data-driven and model-based iterative framework for joint PDE coefficient inversion, improving reconstruction accuracy by integrating supplementary data and analyzing learning uncertainty effects.

Contribution

It presents a novel integrated approach that couples data-driven models with PDE-based reconstruction for joint inversion, ensuring model consistency and robustness.

Findings

Data-driven models enhance joint inversion accuracy.

The framework effectively incorporates supplementary data.

Numerical results demonstrate improved reconstructions.

Abstract

The task of simultaneously reconstructing multiple physical coefficients in partial differential equations (PDEs) from observed data is ubiquitous in applications. In this work, we propose an integrated data-driven and model-based iterative reconstruction framework for such joint inversion problems where additional data on the unknown coefficients are supplemented for better reconstructions. Our method couples the supplementary data with the PDE model to make the data-driven modeling process consistent with the model-based reconstruction procedure. We characterize the impact of learning uncertainty on the joint inversion results for two typical inverse problems. Numerical evidence is provided to demonstrate the feasibility of using data-driven models to improve the joint inversion of multiple coefficients in PDEs.