Solving Schrodinger equation with soft constrained monotonic neural network

Abstract: Artificial Neural Network (ANN) has become a powerful tool in the field of scientific research with its powerful information encapsulation ability and convenient variational optimization method. In particular, there have been many recent advances in computational physics to solve variational problems. Deep neural network (DNN) is used to represent the wave function to solve quantum many-body problems using variational optimization. In this work we used a new Physics-Informed Neural Network (PINN) to represent the Cumulative Distribution Function (CDF) of some classical problems in quantum mechanics and to obtain their ground state wave function and ground state energy through the CDF. By benchmarking against the exact solution, the error of the results can be controlled at a very low level. This new network architecture and optimization method can provide a new choice for solving quantum many- body problems.