Machine Learning Chemically Accurate Orbital-Free Density Functional Theory

Orbital-free density functional theory (OF-DFT) is a cost-effective framework for electronic structure calculations. We demonstrate the feasibility of machine learning accurate and generalizable density functionals, particularly comprising the kinetic energy required for OF-DFT. We introduce KineticNet, a deep neural network tailored to predict the kinetic energy density. Trained on varied data generated with a novel scheme based on sampling the external potential, KineticNet achieves chemical accuracy on small molecules and reproduces chemical bonding in orbital-free density optimization. Expanding this success, we transition from grid-based density representations to the more effcient linear combination of atomic basis functions Ansatz. Adapting and improving our external potential sampling strategy, we achieve state-of-the-art results for OF-DFT on the QM9 dataset of organic molecules, in both energy and density prediction. Crucially, we address a key limitation of previous approaches by enabling convergent density optimization with chemical accuracy. Finally, we propose surrogate functionals, enabling optimization of electron densities without directly replicating physical energy functionals. By integrating surrogate loss functions and a novel train-time density optimization scheme, we further boost the accuracy of density predictions while reducing training data requirements. This innovative approach opens new avenues for effcient and scalable energy functional development.