This repository contains the slides and practical Jupyter notebooks from the tutorial A statistical tour of physics-informed machine learning, presented at the summer school Mathematical foundations of data science at the University of Montreal, Canada. For a more user-friendly interface, please visit the tutorial’s dedicated webpage: https://claireboyer.github.io/tutorial-piml/.
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Lab_student/: Jupyter notebooks for the hands-on practical sessions.
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Lab_correction/: Corrected versions of the practical notebooks.
1- Physics-Informed Neural Networks (PINNs). This session introduces the architecture of PINNs and demonstrates their use in solving partial differential equations (PDEs) and in hybrid modeling.
2- Kernel Methods. This session covers the mathematical foundations of kernel methods, including key concepts like the kernel trick. It also explores applications to electricity load forecasting using polynomial and Sobolev kernels.
3- Physics-Informed Kernel Learners (PIKL). This session presents kernel methods informed by PDEs. It includes an introduction to the pikernel Python package (see https://pypi.org/project/pikernel/), which offers efficient CPU and GPU implementations of PIKL.