In dieser Abschussarbeit sollen Konstitutivmodelle zur effizienten Beschreibung von hyperelastischem oder elasto-plastischen Materialverhalten im Rahmen klassischer Balkentheorien entwickelt werden. Hierzu sollen Physik-erweiterte neuronale Netzen verwendet werden, die die Flexibilität bieten um stark nichtlineare funktionale Zusammenhänge darzustellen und dabei aber wichtige physikalische Eigenschaften sicher stellten.
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The University of Colorado at Boulder (USA) offers scholarships for European students who want to do their master's thesis there. For students interested in numerical mechanics and topology optimization, there is the possibility of a thesis supervised jointly by Prof. Kurt Maute (CU Boulder, Aerospace Mechanics Research Center) and Prof. Oliver Weeger (TUDa, Cyber-Physical Simulation).
If you are interested, please contact Prof. Weeger by February 15, 2023 at the latest.
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.
- Structure and functioning of “Feed-Forward Neural Networks” (FFNNs)
- Construction principles for “Physics-Informed Neural Networks” (PINNs) 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
- Implementation, training, and evaluation of FFNNs / PINNs in TensorFlow / Python
- Construction of PINNs with the help of convex neural networks, data augmentation, and analytical formulations
- Application on problems such as material modeling, multiscale simulation, dynamics, or model order reduction
Winter term 2022-2023
This tutorial will be offered for the first time in the winter term 2022-2023.
Please register for the tutorial as a group of 2 students by sending an email to Dominik Klein after September 1, 2022. 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.