Developing Accurate Exchange-Correlation Functionals through Physics-Informed Machine Learning

We create accurate exchange-correlation (XC) functionals for density functional theory using neural network models and grid-based density descriptors. We investigate the impact of imposing exact constraints based on established physical laws to improve results, using a physics-informed approach. Additionally, we explore how neural networks can be trained to emulate existing XC functionals, such as PBE, by utilizing both the functionals and their derivatives. To facilitate this work, we have developed a new machine learning framework called xcquinox. This framework employs neural network architectures implemented in JAX, a library for automatically differentiable mathematical operations, allowing us to leverage PySCF-AD, an extension of the PySCF package that incorporates automatic differentiation capabilities. We emphasize the importance of incorporating either exact potentials or exact densities in the training process, as training an energy functional without information about functional derivatives—essential for determining the XC potential—can lead to models that predict correct energies but yield incorrect densities.