Innovative Neural Network Approach for Solving TDKS Equations with Jensen’sInequality

Abstract. We propose a novel neural network-based approach for solv-ing the Time Dependent Kohn-Sham (TDKS) equations, central to Time-Dependent Density Functional Theory (TDDFT). Focusing on the one-electron case, where the TDKS reduces to the time-dependent Schrodinger ¨ equation, we employ modified Physics Informed Neural Networks (PINNs) incorporating Jensen’s inequality in place of the traditional Mean Squared Error (MSE) loss. This convex formulation improves training stability and solution accuracy. Compared to the classical Runge-Kutta (RK4) method, our approach achieves comparable accuracy while demonstrating supe-rior scalability and smoother convergence, especially for stiff or nonlinear dynamics. This work establishes a foundation for extending neural PDE solvers to more complex quantum systems that the classroom teaching ex-periment began.