[Submitted on 15 Sep 2026]
Title:Lecture notes on Physics Informed Neural Networks, Neural Operators, and their applications
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Abstract:This is the set of lecture notes for the PhD course \href{this https URL}{\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.
Comments: 264 pages; Lecture notes for the PhD course Physics Informed Neural Network held at the University of Bozen/Bolzano
Subjects:
Machine Learning (cs.LG); Artificial Intelligence (cs.AI); Computational Engineering, Finance, and Science (cs.CE); Computational Physics (physics.comp-ph)
Cite as: arXiv:2609.17638 [cs.LG]
(or arXiv:2609.17638v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2609.17638
arXiv-issued DOI via DataCite (pending registration)
Submission history
From: Alessandro Bombini [view email] [v1] Tue, 15 Sep 2026 12:57:03 UTC (37,047 KB)
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