Lecture Notes on Physics Informed Neural Networks, Neural Operators, and Their Applications

These lecture notes are from a PhD course on Physics Informed Neural Networks held at the University of Bozen/Bolzano for the 2025/2026 academic year. The course introduces the concepts of Physics Informed Deep Neural Networks and Neural Operators, discussing their theoretical foundations and practical implementation. Materials include hands-on tutorials implemented from scratch in PyTorch, as well as advanced open-source tools for scientific machine learning with partial differential equations.