Lecture notes on Physics Informed Neural Networks, Neural Operators, and their applications

arXiv:2609.17638v1 Announce Type: cross 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}{extit{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.

SCNO: Spiking Compositional Neural Operator -- Towards a Neuromorphic Foundation Model for Nuclear PDE Solving
Neural Field Thermal Tomography: A Differentiable Physics Framework for Non-Destructive Evaluation
Learning the Kohn-Sham map with neural operators for quasi-linear scaling density functional theory
Multimodal Neural Operators for Real-Time Biomechanical Modelling of Traumatic Brain Injury

Source: arXiv cs.AI | 2026-09-17

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