Microstructure Property Forecasting using Machine Learning

Interactive workflow for microstructure-based thermal homogenization: select or create a structure, adjust conductivity and direction, then analyze heat flux and temperature distributions in real time.

Link to DemonstratorLink to IUC18

The forecasting of effective material properties is essential for the consideration of natural and man-made materials. Oftentimes, the relation between microstructure and effective properties, e.g., effective stiffness or thermal conductivity, are nontrivial. We present an interactive tool showcasing the possibilities offered by machine learning with consideration of the underlying physics. Arbitrary binary images can be uploaded or generated and the related properties can be predicted in real time [1, 2, 3]. A fast solver [4, 5, 6] also simulates the response in order to show how close the ML prediction and the actual simulation are.

Publications:

[1] J. Lißner and F. Fritzen, “Data-driven microstructure property relations,” Mathematical and Computational Applications, vol. 24, no. 2, pp. 1–27, 2019, doi: 10.3390/mca24020057.

[2] J. Lißner and F. Fritzen, “Microstructure homogenization: human vs machine,” Advanced Modeling and Simulation in Engineering Sciences, vol. 11, no. 1, Nov. 2024, doi: 10.1186/s40323-024-00275-1.

[3] S. Keshav, J. Herb, and F. Fritzen, “Spectral Normalization and Voigt–Reuss net: A universal approach to microstructure‐property forecasting with physical guarantees,” GAMM-Mitteilungen, vol. 48, no. 3, Aug. 2025, doi: 10.1002/gamm.70005.

[4] M. Leuschner and F. Fritzen, “Fourier-Accelerated Nodal Solvers (FANS) for homogenization problems,” Computational Mechanics, vol. 62, no. 3, pp. 359–392, 2018, doi: 10.1007/s00466-017-1501-5.

[5] S. Keshav, F. Fritzen, and M. Kabel, “FFT-based Homogenization at Finite Strains using Composite Boxels (ComBo),” Computational Mechanics, vol. 71, pp. 191–212, 2023, doi: 10.1007/s00466-022-02232-4.

[6] J. Herb and F. Fritzen, “Accelerating Conjugate Gradient Solvers for Homogenization Problems with Unitary Neural Operators.” arXiv preprint, 2025. doi: 10.48550/arxiv.2508.02681.