aiqbench analysis
These lecture notes provide a rigorous technical foundation for Physics-Informed Neural Networks (PINNs) and Neural Operators, bridging the gap between deep learning architectures and physical laws. By covering implementations in PyTorch alongside specialized libraries like NVIDIA's PhysicsNeMo, the material addresses critical challenges in computational physics and engineering simulations. This resource is essential for researchers aiming to deploy AI models that respect conservation laws and differential equations in complex domains like petroleum reservoir modeling.
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}{\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.
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.
Machine Learning (cs.LG); Artificial Intelligence (cs.AI); Computational Engineering, Finance, and Science (cs.CE); Computational Physics (physics.comp-ph)
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)
Full text under the publisher's open licence · 126 words
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