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This lecture explores the application of physics-inspired machine learning in materials discovery, focusing on atomic-scale materials modeling, finite-temperature thermodynamics, anharmonic free energies, and the role of symmetry in atomistic machine learning models. The instructor discusses the challenges in accurate electronic structure calculations, the use of machine learning to improve accuracy, and the importance of data efficiency and transferability. Various topics such as machine-learning for tensors, understanding the range of interactions, and the effectiveness of different model representations are covered, highlighting the potential of machine learning to enhance first-principles energetics in materials science.