Neural Network Estimation of Accessible Free Volume in Archetypical Sphere Assemblies

The accurate quantification of accessible free volume within atomistic structures is fundamental for characterizing transport properties, porosity, and diffusion in dense fluids and porous materials. This diploma thesis proposes the development of neural network architectures designed to calculate this accessible free volume in well-defined archetypical atomic structures, specifically ensembles of non-overlapping spheres, fused sphere systems, and crystalline sphere packings. While traditional geometric algorithms provide exact solutions, they can become computationally prohibitive for large-scale or high-dimensional configurations requiring rapid sampling. By training regression models on systematically generated structural data, this research aims to establish a fast, data-driven alternative that approximates the geometric volume with high fidelity. The performance of the trained neural networks will be rigorously benchmarked against previously developed analytical solutions, which serve as the ground truth for validation. The project will ultimately assess the trade-off between computational efficiency and accuracy, determining whether machine learning offers a viable surrogate for complex geometric calculations or if the approach may lack viability in certain configurations compared to analytical solutions.