Solving Schrodinger equations using physically constrained neural network

Abstract Deep neural networks (DNNs) and auto differentiation have been widely used in computational physics to solve variational problems. When a DNN is represent the wave function quantum many-body problems using optimization, various physical constraints be injected into network by construction increase data learning efficiency. We build unitary constraint monotonic cumulative distribution (CDF) . Using this constrained function, we Schrodinger equations auto-differentiation stochastic gradient descent (SGD) minimizing violation of trial $ \psi(x) $?> equation. For several classical mechanics, obtain their ground state energy with very low errors. The method developed present paper may pave new way for solving nuclear future.