Predicting energy of the quantum system from one-and two-electron integrals using Deep Learning

Kimika Teorikoa Seminar

The study of chemical systems at the quantum level is crucial for various scientific disciplines, enabling the design of new materials, drugs, and catalysts. While the wave function and Schrödinger equation are central to theoretical chemistry, exact solutions for complex systems are often challenging. Machine learning (ML) and neural networks (NN) have emerged as powerful alternatives for predicting molecular energies, offering efficiency and the ability to capture complex relationships. However, these methods face challenges such as poor generalizability and the need for enormous amounts of relevant, high-quality, training data. This study presents a novel approach to predicting energies of electronic systems using NN. We demonstrate the effectiveness of our method by training networks on systems of four and six hydrogen atoms, achieving mean absolute errors of 10^-3 a.u.. Furthermore, we introduce a fine-tuning technique to predict energies of larger systems. By exploiting the size consistency of Full Configuration Interaction energies, we construct artificial training data for a 10-electron system using combinations of smaller hydrogen clusters. This approach allows us to train a neural network using only training data small systems and a very small amount of data for larger systems. Our results show that this fine-tuning method outperforms other approaches in terms of Mean Absolute Error, demonstrating its potential for accurate energy predictions of larger molecular systems. This work highlights the powerof combining artificial data construction, transfer learning, and fine-tuning in electronic structure theory, opening new avenues for efficient and accurate energy predictions of complex systems.