In this tutorial, methods of machine learning are to be used to solve typical problems in solid mechanics. In particular, artificial neural networks are used here, which are to be formulated and trained in such a way that important physical and mathematical properties of the problems are taken into account. This shall ensure that neural networks yield reliable, robust, and physically meaningful predictions.
The tasks and the documentation of results will be done in teams of 2 students. Each of the problems will be first introduced and discussed in a common session, then the teams will have 2-3 weeks to solve the current problem and document their results.
Participants should have basic knowledge in machine learning methods and solid mechanics.
Contents
Theoretical part:
- Structure and functioning of “Feed-Forward Neural Networks” (FFNNs)
- Construction principles for “Physics-Augmented Neural Networks” (PANNs) that fulfill essential physical and mathematical problem requirements and properties, e.g. by network structure or training algorithms
- Basics of solid mechanics and numerical mechanics
Practical tasks:
- Implementation, training, and evaluation of FFNNs / PANNs in TensorFlow / Python
- Construction of PANNs with the help of convex neural networks, data augmentation, and analytical formulations
- Application on problems such as material modeling
Winter term 2024-2025
Please register for the tutorial as a group of 2 students by sending an email to Dominik Klein (klein@cps.tu-darmstadt.de) until October 14, 2024. In the email, include your names, matriculation numbers, and a short summary of your knowledge and courses on the subjects of solid mechanics and machine learning. For further information see: https://www.maschinenbau.tu-darmstadt.de/cps/cps_teachi…sm/index.en.jsp. If you don’t have a group yet, we will try to find you a group partner in the first lecture of the tutorial.
