The representation of material structure geometry is essential to the reconstruction, physical simulation, and the multiscale structure design with Random Heterogeneous Material (RHM). Traditional approaches to material structure representation often need to balance the trade-off between efficacy and accuracy. Recently, deep learning-based techniques have been adopted to reduce the computational time of RHM reconstruction. However, existing approaches generally lack guarantees over key RHM characteristics, including Minkowski functionals and correlation functions.

We propose a novel approach to geometrically enhancing the deep learning-based RHM representation by introducing Minkowski functionals, a set of topological and geometrical characteristics of material structure, into the training of conditional Generative Adversarial Networks (cGAN). This hybrid approach combines the feature learning capability of deep learning with the well-established material structure characteristics, greatly improving the accuracy of the RHM representation while maintaining its efficiency. The effectiveness of the proposed hybrid approach is validated through the reconstruction of a wide range of natural and manmade materials, including Voronoi foam structures, femur, and sandstone. Through computational experiments, we demonstrate that geometrically enhancing the training of cGAN for RHM representation not only significantly decreases the representation error in Minkowski functionals between input sample materials and reconstructed results, but also improves the performance of other material structure characteristics, such as two-point correlation functions.

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