Lecture
This lecture explores the concept of spinless on-top pair density, which represents the probability of two electrons being in the same position in a system of n molecules. The instructor discusses the challenges of modeling systems with strong multi-configuration character and the importance of understanding electron correlation. The use of machine learning, specifically Gaussian process regression, to predict the spinless on-top pair density is detailed, along with the creation of a specialized basis set to improve accuracy. The lecture showcases how this approach can accurately model electronic structures with high correlation, providing benchmark quality results. The application of this method to larger systems and the significance of learning locally for scalability are also highlighted.