Design of physics-aware neural networks: Symmetry constraints

The project aims at the development of Physics-Aware Neural Networks (PANN) accounting for symmetry constraints. These enable the user to include physics into the NN models in a straight-forward fashion. Within this overarching objective, the project has the following goals:

• Collect and develop NN modelling strategies for strain energies with symmetry constraints;
• Develop a list of input features for qualitative and quantitative description of the information available for the problem at hand considering the computational environment. Such a list can include type of symmetry, available training resources, strictness of symmetry constraints and so on;
• Implement and evaluate different NN models;
• Evaluate the influence of input parameters on output features, such as accuracy of symmetry of the surrogate and required number of samples vs. accuracy of the model;
• Develop a modelling language for PANN-Sym;
• Apply the model to single crystals and in multiscale modelling of hyper-elastic solids.

The project also considers more specific intermediate goals targetting independent student research projects on the B.Sc./M.Sc. level.