A deep learning approach to solve the Schrodinger equation

Abstract

To understand the properties of matter and predict them, it’s crucial to solve the Schrodinger equation, where the solution is a wave vector. Many theoretical methods have been explored in this area.The most common ones are those that reduce the cost and time of calculations, especially for complex particle systems. The rapid advancement in computer science and the emergence of new technologies like machine learning have paved a new path towards solving equations like this. In this work, we propose calculating the fundamental energy of a physical system using the Schrodinger equation with the use of deep learning and proving its efficiency in solving by making a comparison with traditional machine learning techniques. To apply the theoretical study, we conducted an experimental study on solving the Schrodinger equation using CNN, CNN-LSTM, SVR, RF, and XGBoost structures with relevant datasets for calculating the system’s fundamental energy. The results showed that deep learning can be effective in solving the Schrodinger equation, achieving an error of 0.0063(ev/atom) and an accuracy of 0.9807 . These findings open up new possibilities for enhancing and developing models.