The innovations needed for a change in mobility, for a climate-neutral industry and for an improvement in medical care cannot be achieved without solid theoretical models and associated numerical simulations. The mathematical equations resulting from the theoretical models can only be solved numerically for real engineering applications. The IKM focuses on both areas. We characterize materials on several length scales in order to create optimized materials by specific manipulations in the micro range. In addition, we develop algorithms for complex dynamic processes, such as additive manufacturing. In addition to high-resolution models, algorithms of artificial intelligence are increasingly used to reproduce the manufacturing processes in real time.