A clever neural network in solving inverse problems of Schr\"{o}dinger equation

This project constructs a physic-preserving neural network combined with a library-search method to solve inverse problems of Schr\"{o}dinger equation. The complete code as well as the corresponding preprint is included in the uploaded files. Here is some necessary information about the code.It mainly contains two parts: forward and inverse part of the solver. In particular, to test the performance of the forward solver, run SSFM_potential_test_cos.py. For the inverse problem, run SSFM_potential_cos.py. It is similar for the other two examples. Specially, for the coupled equation, we also plot the landscape the loss function, which is implemented in the file ssfm_potential_couple_landscape.py. The generated data is under separate subfolders, for example, ./result_cos. Generally, to train the network, we use the proximal gradient descent and one can refer to the file SSFM_potential_cos.py for details. We remark that the current coefficient of regularization term is given in "reg_list" which is tested relatively suitable for the setting.