Interpolation of symmetric positive definite tensors using neural networks

Motivation

Manufacturing processes for complex engineering components require numerous, successive interconnected process steps. In a CAE chain these process steps are mapped by separate simulations and scalar (e.g. temperatures) and tensor-valued field variables (e.g. fiber orientations, stresses) are transferred between the individual simulation models. For a consistent interpolation of these tensors, special, non-linear methods are necessary, the calculations of which are, however, very computationally expensive. The aim of the work is to develop a neural network that learns this interpolation and thus efficiently predicts tensor values values. The training can be done either on the basis of reference data or with the help of geometrically motivated equations.

Work content:

• Literature research on interpolation methods and neural networks
• Implementation of a data generator for synthetic tensor fields tensor fields
• Development of a neural network for tensor interpolation
• Evaluation with regard to accuracy, compliance with tensorial properties and efficiency
• Optional: Application to real material data

Prerequisites:

• Fundamentals of continuum mechanics and related tensor algebra
• Interest in machine learning
• Programming experience in Python is a strong advantage
• Structured and goal-oriented way of working

Subject area: mechanical engineering or similar
Type of work: theoretical/numerical
Start: immediately

Application: Please send your CV and transcript of records to the contact email address

Contact: Julius Gulde, M.Sc.
E-mail: julius.gulde∂kit.edu