Working Group 4 focuses on probabilistic and stochastic approaches to multiscale structures, with a strong emphasis on applications in materials science, particularly those relevant to the green transition and energy storage technologies. Its overarching aim is to develop mathematically grounded models that link random microstructures to macroscopic physical properties.

The group studies a broad class of stochastic geometric models, including Poissonian systems, random point processes, germ-grain models, and simplicial complexes, as idealized representations of spatial randomness. Building on these, WG4 extends its investigations to more realistic hyperuniform and Gibbsian structures that capture suppressed fluctuations, spatial correlations, and singularities observed in functional materials.

A distinctive feature of WG4 is its comparative perspective on stochastic geometry and machine-learning-based generative models. By systematically analyzing their statistical fidelity and interpretability, the group aims to improve both classical stochastic models and modern neural-network approaches used in materials imaging and reconstruction. WG4 also investigates physical properties governed by fractional and non-local partial differential equations, such as those arising in viscoelasticity, fracture, and plasticity, and develops efficient numerical and homogenization techniques to connect structure and performance. The expected outcomes include new tools for virtual material design and a deeper mathematical understanding of morphology–property relationships.