Deep greedy kernel methods for submodel coupling in fluid- and biomechanics

The goal of this project is the analysis, the efficient implementation, and the application of multilayer kernel methods to surrogate modeling in complex simulation settings. Kernel techniques for surrogate modeling provide already promising results using shallow models, which are expected to be significantly improved to produce models which are suited to the particular simulation. New methodological advancements will be achieved by a novel combination of kernel models in a multilayer structure, which will provide new and improved algorithms able to learn not only an input-output relation, but also a representation of the data. This feature is especially crucial when dealing with the high-dimensional data typically provided by numerical simulations. Particular attention will be devoted to the combination of these new techniques with strategies that allow the incorporation of physical-based, a-priori knowledge in the learned models, so that the resulting surrogates will have some physical guarantees, while being entirely data-based. These methodological results will be developed particularly around two challenging application scenarios. Through the cooperation with A. Beck (PN1), these kernel methods will be applied in the construction of closure relations in the simulation of turbulent flows. Here, the speedup provided by the surrogates will be made reliable via the physical guarantees provided by the new methodologies. In collaboration with Syn Schmitt (PN2), we will instead include data-based surrogates in the biomechanical simulations of the human spine, where these machine learning model will be able to resolve micro-scale simulations within the necessary accuracy, to be combined with the overall, physical-based simulation.