物理信息神经网络、神经算子及其应用的讲义
Lecture notes on Physics Informed Neural Networks, Neural Operators, and their applications
- Free University of Bozen-Bolzano（博尔扎诺自由大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本讲义介绍物理信息神经网络与神经算子的概念、PyTorch实现及PhysicsNeMo应用，涵盖混合模型、傅里叶神经算子等前沿主题，面向多领域实际问题。
AI中文摘要：
这是2025/2026学年在博尔扎诺大学开设的博士课程《物理信息神经网络》的讲义，课程链接见本URL。课程目标是介绍物理信息深度神经网络（PINN）和神经算子（NOs）的概念，讨论如何从零开始在PyTorch中实现它们，以及使用先进的专门开发的开源库（如NVIDIA PhysicsNeMo）来解决工程、物理、石油储层等各个领域的实际问题。我们讨论了近期主题，如混合模型、傅里叶神经算子、物理信息Kolmogorov-Arnold网络（PIKANs）和傅里叶神经算子。
英文摘要：
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.
