PhD 2023 Summer School on Physics-Informed Neural Networks and Applications

Course description

Physics-Informed Neural Networks is a novel approach to deep learning that allows incorporating existing knowledge about physical systems into the neural network learning process.

Course participants will be able to discover how PINNs can be applied to their discipline and will have an opportunity to work on the project with guidance from the course teachers.
After two weeks program participants will have a working knowledge of PINNs and a starting functional PINN code adapted to their research needs.

You will receive guidance from the course teachers and organisers during the project work. 

Lecture overview

The course syllabus will cover a variety of topics:

• Introduction to Deep Learning Networks
• Neural Network 
• TensorFlow, PyTorch, JAX
• Discovery of differential equations
• Physics-Informed Neural Networks (advanced)
• DeepONet
• {DeepXDE} or {MODULUS}
• Uncertainty quantification
• Multi-GPU machine learning

Project scope overview

We encourage course participants to formulate projects related to their area of research.
Additional project topics will be provided for selection.

Examples of project areas:

• Biomedicine: Modelling blood coagulation
• Control: System identification and decision making
• Dynamical Systems: Charged particles in the electromagnetic field
• Engines: Learning engine parameters
• Fluid Mechanics: Bubble growth dynamics
• Geophysics: Diffusion-reaction in porous media
• Heat Transfer: Non-linear Inverse heat conduction problem
• Materials: Modulus identification of hyperelastic material

Prerequisites

No prior knowledge of PINN or machine learning is required, but participants are encouraged to have some knowledge of Python, NumPy, Jupyter Notebooks, and SciPy. For those without such knowledge, a prior lecture will be taught on the 18th of June.

About the participation

The course can be followed as:

• a full version, intended for PhD students
• a short option (only includes lectures), intended for researchers from academia and industry.

The course syllabus is adapted for participants from engineering disciplines and is focused on providing practical guidance towards the application of PINNs and Deep Learning to problems in engineering research disciplines.

The course's target group is PhD students and researchers in engineering disciplines. We encourage PhD students who will be taking a full version of the course to propose projects that are related to their research.

Guest lecturers

• George Em Karniadakis - The Charles Pitts Robinson and John Palmer Barstow Professor of Applied Mathematics and Engineering, Brown University and MIT & PNNL 
• Khemraj Shukla - Assistant Professor of Applied Mathematics, Brown University

Local Organising committee

Kateryna Morozovska, Amritam Das, Marco Laudato, Federica Bragone, Karl Henrik Johansson

For questions contact: info@pinns.se

More information at the PhD 2023 Summer School website

Registration PhD 2023 Summer School