Propagator Mixed with Machine Learning for the Time-Dependent Kohn-Sham Equations

Time-dependent density functional theory (TDDFT), used for solving the time-dependent Schrodinger equation (TDSE), has allowed researchers in-depth access to the electronic structure properties of relatively small systems. Even though novel approaches have been introduced to improve TDDFT's accuracy and efficiency, the computational cost of handling more time-consuming and larger molecule simulations is still expensive. This is due to the intractable analytical solution to the Schrodinger equation for the many-body problem that scales with the system size, which in turn creates cumbersome density matrices calculated in the time propagation. One solution to this challenge is to tap into state-of-the-art data analysis tools, such as machine learning (ML), adept at learning from and predicting TDSE solutions. Encouraged by such an approach, we dive deeper into machine learning capabilities and their application to predicting time-dependent properties and electronic density. This project aims to integrate ML-generated density matrices into TDDFT to enable inexpensive simulations. By carefully re-formulating a conventional fourth-order Runge-Kutta (RK4) propagator to combine TDDFT and ML density matrices, a hybrid ordinary differential equation solver capable of handling large molecules and employing longer-time steps is created. This project consists of two modules, including (1) building and testing feedforward neural network (FNN) algorithms that predict physical properties for large molecules, and (2) training and deploying FNN models that instantaneously generate the time-dependent density matrices during the RK4 propagation. Initial results based on the first model have excellent agreement with well-established computational approaches.