Greedy deep kernel methods for data-based-modelling in biomechanics

Shallow and deep kernel models have demonstrated to be successful techniques for submodel coupling in the previous project phase. Especially we provided efficient models for intervertebral discs of the human spine. In the current continuation proposal we want to extend those techniques from three different angles: Firstly, we extend kernel models methodologically by combining greedy and deep kernel models in order to obtain both expressivity as well as efficiency. Secondly, we investigate how kernel models can be improved by including additional contextual prior knowledge. By this we mean (i) prior knowledge of physical properties like conservation laws or conservative force fields and (ii) prior knowledge in the form of coarse models that are refined by our data-based techniques and allows to build more comprehensive models. Lastly, we aim for quantitative error statements such as convergence rate statements for the multilayer architectures and certification by residual-based a-posteriori error control for some of the models. In terms of the application, we focus on a biomechanical model of the human spine involving both coupled intervertebral disks as well as vertebral bodies.