Incorporating Scientific Knowledge into Neural Network Density Functionals

Density functional theory (DFT) is the workhorse of modern reactions and materials modeling. While the exact functional remains unknown, many approximations to it have been constructed either by hand-crafting functional forms to satisfy exact constraints or by machine learning. In this work, we show how both of these approaches can be fused to build both accurate and robust density functionals: we train a neural network to perform exact-constraints-aware local density-guided fine-tuning of parameters in the physically sound form of Perdew-Burke-Ernzerhof (PBE) functional. The resulting functional reduces the error of its parent PBE in thermochemical tasks by nearly 30%, reaching the accuracy of modern meta-generalized gradient approximations (mGGAs), and shows good accuracy on electron densities. We demonstrate that removing either the PBE form or the adherence to exact constraints significantly degrades functional performance and deteriorates electron densities. Our work shows how uniting the power of machine learning with foundational physical principles creates more accurate and reliable DFT functionals built on both data and knowledge.