Solving Schrodinger Equation With Soft Constrained Physical Information Neural Network

The study of structural information and dynamics information inside the nucleus is an important research task of nuclear physics,and the complex many-body wave function is an effective means to represent various important information of nuclear physics.Meanwhile deep neural networks(DNNs)and auto differentiation have been widely used in computational physics to solve variational problems.If a loss function similar to the energy form is constructed based on the Schr?dinger equation,then the problem of finding the wave function can also be solved by optimizing the network parameters.It is worth noting that when using DNNs to represent wave functions to solve quantum manybody problems using variational optimization,various physical constraints are often injected into the neural network by construction to increase data and learning efficiency.This paper innovatively proposes to use a monotonic neural network to represent the Cumulative Distribution Function(CDF),design a soft-constrained loss function and use self-differentiation and Stochastic Gradient Descent(SGD)to solve the Schr?dinger equation,and minimize the ground state energy of the trail wave function to update network parameters.This architecture greatly reduces the computational load of the network through the design of the calculation path,special network constraints,and regularization of the fitting target.For several classical problems in quantum mechanics,this network architecture obtains their ground state wave functions and energies with less computation and extremely low errors.The method developed in the present paper may pave a new way in solving nuclear many body problems in the future.Moreover,the optimization of the algorithm makes this method more promising compared to traditional differential optimization algorithms.