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.

本项目构建了结合库检索方法的物理守恒神经网络（physic-preserving neural network），用于求解薛定谔方程（Schrödinger equation）的逆问题。上传文件中包含完整代码及对应的预印本。以下为该代码的必要说明：代码主要包含两大模块，即求解器的正问题模块与逆问题模块。具体而言，若需测试正问题求解器的性能，请运行SSFM_potential_test_cos.py；针对逆问题求解任务，可运行SSFM_potential_cos.py。其余两个示例的操作逻辑与此一致。针对耦合方程场景，我们还在ssfm_potential_couple_landscape.py中实现了损失函数景观图的绘制功能。生成的数据集将存储于各自独立的子文件夹中，例如./result_cos。通常情况下，我们采用近端梯度下降法（proximal gradient descent）训练该神经网络，具体训练细节可参考SSFM_potential_cos.py文件。需特别说明的是，当前正则项的系数已在"reg_list"中给出，经测试该系数相对适配当前实验设置。