A Model-Consistent Data-Driven Computational Strategy for PDE Joint Inversion Problems
This work addresses joint inversion problems in PDEs for applications like geophysics or medical imaging, but it appears incremental as it builds on existing data-driven and model-based methods without claiming major breakthroughs.
The authors tackled the problem of simultaneously reconstructing multiple physical coefficients in PDEs from observed data by proposing an integrated data-driven and model-based iterative reconstruction framework that couples supplementary data with the PDE model to ensure consistency. Numerical evidence demonstrated the feasibility of using data-driven models to improve joint inversion, though no concrete numbers were provided.
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.