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.

Theoretical part:

• Structure and functioning of “Feed-Forward Neural Networks” (FFNNs)
• Construction principles for “Physics-Informed Neural Networks” (PINNs) that fulfil 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 / 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 modelling, multiscale simulation, dynamics, or model order reduction