Lecture notes on Physics Informed Neural Networks, Neural Operators, and their applications
Year: 2026
Type: preprint
Abstract: This is the set of lecture notes for the PhD course \href{https://www.unibz.it/en/faculties/engineering/phd-computer-science/study-course-offering/2025/36967}{\textit{Physics Informed Neural Network}, held at the University of Bozen/Bolzano} in the academic year 2025/2026. The goal of the course was to introduce the concept of Physics Informed Deep Neural Networks (PINN) and Neural Operators (NOs), discuss their implementation from scratch in PyTorch and using advanced ad-hoc developed open-source libraries such as NVIDia PhysicsNeMo to address real-world problems in various fields (engineering, physics, petroleum reservoir). We discuss recent topics such as Mixture-of-Models, Fourier Neural Operators, Physics-Informed Kolmogorov-Arnold Networks (PIKANs) and Fourier Neural Operators.
Source: arXiv (Cornell University)
Author: Bombini, Alessandro
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7213502016
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