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Understand relevant modeling techniques in "Scientific Machine Learning" and apply them in a capstone project.
Learning Goals:
- Formulate and numerically solve differential equations using finite difference and finite element methods.
- Explain the principles of Physics-Informed Neural Networks (PINNs) and implement a basic PINN for a given problem.
- Describe operator learning and uncertainty quantification methods. and apply them to illustrative case studies.
- Apply hybrid workflows for neural differential equations and demonstrate their application in life sciences.
What you get:
The course emphasizes using AI to understand complex systems modeled by Differential Equations and modern approaches to simulate such systems.
It delves into key scientific machine learning concepts, providing a framework for both theoretical knowledge and practical application. The primary learning objectives include:
-Becoming aware of advanced AI applications in science and engineering.
-Gaining familiarity with the design, implementation, and theoretical principles of these algorithms.
-Understanding the advantages and limitations of using AI and deep learning for scientific research.
-Grasping key concepts and themes within scientific machine learning.
This course begins with deep learning and PDEs, it covers Physics-Informed Neural Networks (PINNs) - including fundamentals, limitations, and theoretical foundations. We then continue with various Operator Learning approaches, plus time-dependent models, attention mechanisms towards hybrid methods. Finally we discuss Neural Differential Equations, Diffusion Models, and AI in Life Science.
Hands-on tutorials provide practical experience with Python-PyTorch-Tensorflow.
What you should bring
This course is a blend of theoretical concepts and practical applications. Your willingness to engage with challenging material and a desire to explore the exciting intersection of AI and science will be your greatest assets.
Technical Skills
A brain that's not afraid of numbers. You don't need to be a math genius, but a basic understanding of things like calculus, linear algebra, and differential equations will save you a lot of headaches. Just think of it as the secret code you need to speak.
Python Skills
You've got to know your way around Python and maybe a little PyTorch so you can boss the computer around. We highly recommend having comparable knowledge from the "Machine learning with Tensorflow"-course at hand.
A Sense of Humor:
When things get weird (and they will), a good laugh helps.
You should plan to spend around 10 hours per week working through the learning content and completing the assignments.
Additional time will be needed to prepare the final project presentation.
Allocating sufficient time is therefore critical.
To receive a certificate of achievement (Leistungszertifikat/ECTS) for this course, active participation is expected, no more than two classes may be missed, and you have to conduct an applied capstone project in a team. At the end of the course, the project has to be presented and a well-documented project source code (GitHub) has to be submitted