Lecture
This lecture explores the prediction of non-scalar properties in scientific machine learning, focusing on dipole moments, polarizability, and hyperpolarizability. The instructor emphasizes the importance of considering properties beyond energies in molecules and condensed matter systems. Various modeling techniques, such as the SOAP kernel and equivariant kernels, are discussed for predicting tensorial properties. The lecture also covers the generation of training data for molecular systems and the application of these predictive models to water monomers and dimers. Additionally, the dielectric response tensor and its prediction methods are explained, highlighting the significance of accurate predictions for complex molecules.