| Abstract: |
| The principle of developing structure-conforming numerical algorithms widely exists in scientific computing. In this work, following this principle, we propose an operator learning method for solving a class of geometric inverse problems. The architecture here is inspired by Direct Sampling Methods and is also closely related to convolutional network and Transformer. The latter one is state-of-art architecture for many scientific computing tasks. To obtain the optimal hyperparameters in this method, we propose a FEM and OpL joint-training framework and a Leaning-Automated FEM package. Numerical examples demonstrate that the proposed architecture outperforms many existing operator learning methods in the literature. |
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