The task of simultaneously reconstructing multiple physical coefficients in partial differential equations 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 model inverse problems. Numerical evidences are provided to demonstrate the feasibility of using data-driven models to improve joint inversion of physical models.
翻译:同时从观察到的数据中重建部分差异方程式中的多种物理系数的任务在应用中是普遍存在的。在这项工作中,我们提议为这类联合倒置问题建立一个综合的数据驱动和基于模型的迭代重建框架,为更好的重建补充关于未知系数的额外数据。我们的方法是将补充数据与PDE模型结合起来,使数据驱动模型进程与基于模型的重建程序相一致。我们说明学习的不确定性对两个典型模型的反向结果的影响。提供了数字证据,以证明使用数据驱动模型改进物理模型的联合反向的可行性。