Neural network scaling and generalization for 3D strain fields in heterogeneous materials

Computational homogenization and coupled multiscale simulations of heterogeneous materials require repeated solution of mechanical fields on Representative Volume Elements, which becomes prohibitively expensive for high-resolution three-dimensional microstructures. Machine-learning surrogates can accelerate these computations, yet most existing approaches predict fields for fixed macroscopic loadings and provide limited guidance on how to scale network architectures for high-resolution 3D tensor-field prediction. This work presents a U-Net surrogate trained to predict the full 36-component strain localization tensor field in voxelized concrete mesostructures at resolutions up to 256³. Training localization tensors are generated with an FFT-based linear elastic solver, and an extensive hyperparameter optimization is performed to derive scaling rules and an accuracy-speed trade-off analysis. The results show that only network width and depth need to be scaled with problem complexity, while several conventional U-Net design choices, such as doubling channels after downsampling, are suboptimal for this problem. The final neural network achieves a Mean Absolute Error of 1.118% on both the validation and the held-out test sets, and an inference speedup of approximately 8.7x over the FFT-based solver on an Nvidia H100 GPU. Generalization experiments reveal transfer across aggregate volume fractions and highlight the importance of training on diverse morphologies. To safeguard reliability, a Maximum Mean Discrepancy metric computed on internal feature maps is proposed for detecting out-of-distribution microstructures without costly reference computations.