# Leibniz MMS Days 2024 - Key Note Lecture

**Redenbach, Claudia (University of Kaiserslautern-Landau - RPTU)**

*Stochastic modelling of microstructures*

The investigation of random microstructures is of interest in many fields of research including materials science, biomedicine or geology. For instance, the properties of engineering materials such as foams, fibre composites or concrete are heavily influenced by the microstructure geometry. Similarly, abnormal changes in the blood vessel morphology due to a disease will influence the performance of organs such as the lung or the liver. Quantitative analysis of 3D images provided, e.g., by micro computed tomography allows for a characterization and comparison of microstructures. Based on characteristics derived from the image data, models from stochastic geometry can be fitted to the observed samples.

In materials science, such models can be used for virtual material design. Models allow for the simulation of large numbers of virtual materials samples of basically arbitrary size. Additionally, by changing the model parameters, samples with modified microstructure geometry can be generated. By finite element simulations of macroscopic materials properties, the influence of certain geometric characteristics on the material behaviour can be investigated. Repeating such microstructure generation-simulation cycles may then result in optimized materials' properties.

Additionally, the use of microstructure models can also support the image processing and analysis. In particular, microstructure characterization typically requires segmentation of the components of interest. Neural networks have become common tools for this task. Training data are often produced by manual annotation of images which is time-consuming and error-prone, in particular in 3D. We propose to use synthetic training data that are obtained by combining a stochastic geometry model for the imaged structure with a model for the imaging process.

In this talk, we will summarize results of recent projects in our group giving several examples of stochastic microstructure modelling in the fields mentioned above.