Leveraging Unitary Invariance of the Wavefunction for Energy Prediction in Strongly Correlated Systems

Study of chemical systems at the quantum level is crucial for many scientific disciplines, enabling design of new materials, drugs, and catalysts. While Schrödinger equation is 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.

This study presents a new approach to predicting energies of electronic systems using NN. We demonstrate the effectiveness of our method by training networks on systems of 4 and 6 hydrogen atoms, achieving mean absolute errors (MAE) of 10^-3 a.u.

Furthermore, we introduce a fine-tuning technique to predict energies of larger systems. By exploiting size consistency of Full Configuration Interaction energies, we construct artificial training data for 10-electron system using combinations of smaller systems. This approach allows us to train NN using only training data of small systems and very small amount of data for larger systems.

Our results outperform other approaches in terms of MAE demonstrating its potential for accurate energy predictions of larger molecular systems. This work highlights power of 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.