3D Periodic Polycrystals with Finite-Element Stress-Localization Labels and Trained U-Net Surrogate Models

This record holds the data and the trained models of the PINN-UNet-Polycrystals study: periodic three-dimensional polycrystals on a 32³ voxel grid with finite-element stress-localization labels, and the trained U-Net surrogate models that predict the local stress fields of a polycrystal from the elastic stiffness of its voxels. Code: github.com/MME-NTU-KhPI/PINN-UNet-Polycrystals (reading the files, training, inference, scoring)Microstructure software of the group: github.com/MME-NTU-KhPI/MatViz3D Files file content data.zip the volumes with their labels, data/copper/sve_<seed>.hdf5 and data/zener-8/sve_<seed>.hdf5 trained-models.zip 34 PyTorch checkpoints: the trained models and the initial weights of the training runs preview.png one training volume: grains, and the label A11 for both materials Unpack data.zip into the data/ folder of the repository and trained-models.zip into checkpoints/. Volumes Each volume is a periodic Voronoi polycrystal of 1,638 grains on a 32 × 32 × 32 voxel grid, about 20 voxels per grain, with grain orientations drawn uniformly from the rotation group (no texture). The two materials share the geometry and the orientations of each volume: files with the same seed hold the same grains. material C11, GPa C12, GPa C44, GPa Zener ratio copper 168.4 121.4 75.4 3.21 zener-8 (synthetic) 168.4 121.4 188.0 8.0 The split is fixed by the seed: training 1000–1139, validation 1140–1159, test 1160–1199. The test volumes were also read during the development of the method, so they form a development test set. Labels The labels solve the periodic problem of the eight-node SOLID185 element of ANSYS in its B-bar form, one element per voxel, under the six Mandel unit strains. A matrix-free conjugate-gradient solver in double precision with a Fourier preconditioner runs to a relative residual of 10−10. The label of a voxel is the mean stress over the eight Gauss points of its element. On ten volumes of each material the pooled relative difference from ANSYS Mechanical APDL 2025 R2 was at most 9.78 · 10−9. File format One HDF5 file per volume, sve_<seed>.hdf5: dataset shape type content voxels (32, 32, 32) int32 zero-based grain index of each voxel, axes x, y, z quat (1638, 4) float64 orientation of each grain, unit quaternion (w, x, y, z) C_grain (1638, 6, 6) float64 stiffness of each grain in Mandel notation, Pa A (32, 32, 32, 6, 6) float64 stress-localization tensor; A[x, y, z, i, l] is the stress component i in Pa under a unit Mandel strain l sigma_avg (6, 6) float64 mean stress of the volume under each load case iters (6,) int64 solver iterations per load case The Mandel order is xx, yy, zz, xy, yz, xz, with the factor √2 on the shear components. The stress under any macroscopic strain E is σ(x) = A(x) : E. The root attributes of each file record the seed, the material constants and the solver settings. Trained models The checkpoints are named <material>-<configuration>-s<seed>.pt. The U-Net has 39 input channels and 1,445,106 weights. The configurations differ in the loss: labels-only: the label loss; energy-only: the discrete potential energy of the element problem, no labels; labels-energy-fixed: labels and energy at a fixed weight; labels-energy-adaptive: labels and energy, gradient-norm balancing; labels-energy-uncertainty: labels and energy, uncertainty weighting; labels-energy-lagrangian: energy subject to a bound on the label loss, augmented Lagrangian. The files initial-<material>-s<seed>.pt are the initial weights of the training runs; a run started from them repeats the published run. The commands are in the repository. Notes The volume generator and the labels solver are not part of this release. The element model of the labels follows the conventions of the ANSYS input of MatViz3D.