论文标题
PDE联合反转问题的模型符合数据驱动的计算策略
A Model-Consistent Data-Driven Computational Strategy for PDE Joint Inversion Problems
论文作者
论文摘要
从观察到的数据中同时重建部分微分方程（PDE）中多个物理系数的任务在应用中无处不在。在这项工作中，我们为此类联合反转问题提出了一个集成的数据驱动和基于模型的迭代重建框架，其中补充了未知系数的其他数据以进行更好的重建。我们的方法将补充数据与PDE模型融合在一起，以使数据驱动的建模过程与基于模型的重建过程一致。我们表征了学习不确定性对两个典型反问题的关节反转结果的影响。提供了数值证据来证明使用数据驱动模型改善PDE中多个系数的关节反转的可行性。
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.
