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PolyCrysDiff: Controllable Generation of Three-Dimensional Computable Polycrystalline Material Structures

Chi Chen, Tianle Jiang, Xiaodong Wei, Yanming Wang

Abstract

The three-dimensional (3D) microstructures of polycrystalline materials exert a critical influence on their mechanical and physical properties. Realistic, controllable construction of these microstructures is a key step toward elucidating structure-property relationships, yet remains a formidable challenge. Herein, we propose PolyCrysDiff, a framework based on conditional latent diffusion that enables the end-to-end generation of computable 3D polycrystalline microstructures. Comprehensive qualitative and quantitative evaluations demonstrate that PolyCrysDiff faithfully reproduces target grain morphologies, orientation distributions, and 3D spatial correlations, while achieving an $R^2$ over 0.972 on grain attributes (e.g., size and sphericity) control, thereby outperforming mainstream approaches such as Markov random field (MRF)- and convolutional neural network (CNN)-based methods. The computability and physical validity of the generated microstructures are verified through a series of crystal plasticity finite element method (CPFEM) simulations. Leveraging PolyCrysDiff's controllable generative capability, we systematically elucidate how grain-level microstructural characteristics affect the mechanical properties of polycrystalline materials. This development is expected to pave a key step toward accelerated, data-driven optimization and design of polycrystalline materials.

PolyCrysDiff: Controllable Generation of Three-Dimensional Computable Polycrystalline Material Structures

Abstract

The three-dimensional (3D) microstructures of polycrystalline materials exert a critical influence on their mechanical and physical properties. Realistic, controllable construction of these microstructures is a key step toward elucidating structure-property relationships, yet remains a formidable challenge. Herein, we propose PolyCrysDiff, a framework based on conditional latent diffusion that enables the end-to-end generation of computable 3D polycrystalline microstructures. Comprehensive qualitative and quantitative evaluations demonstrate that PolyCrysDiff faithfully reproduces target grain morphologies, orientation distributions, and 3D spatial correlations, while achieving an over 0.972 on grain attributes (e.g., size and sphericity) control, thereby outperforming mainstream approaches such as Markov random field (MRF)- and convolutional neural network (CNN)-based methods. The computability and physical validity of the generated microstructures are verified through a series of crystal plasticity finite element method (CPFEM) simulations. Leveraging PolyCrysDiff's controllable generative capability, we systematically elucidate how grain-level microstructural characteristics affect the mechanical properties of polycrystalline materials. This development is expected to pave a key step toward accelerated, data-driven optimization and design of polycrystalline materials.
Paper Structure (19 sections, 5 equations, 6 figures, 1 table)

This paper contains 19 sections, 5 equations, 6 figures, 1 table.

Table of Contents

  1. INTRODUCTION
  2. RESULTS
  3. Model architecture
  4. Unconditional generation
  5. Generation with controlled parameters
  6. Comparison with existing models
  7. End to end generation and CPFEM results
  8. Discussion
  9. METHODS
  10. Training details
  11. Structure analysis
  12. Distribution similarity metrics
  13. CPFEM simulation
  14. Framework test case
  15. Data availability
  16. ...and 4 more sections

Figures (6)

  • Figure 1: Model architecture of the proposed PolyCrysDiff framework. The blue blocks represent the encoder–decoder components of the 3D variational autoencoder (VAE). The green blocks denote the conditional generation module.
  • Figure 2: Qualitative and quantitative evaluation of the proposed PolyCrysDiff model for unconditioned polycrystalline microstructure generation (a) 3D view and orthogonal slices of a reference polycrystalline microstructure from the training dataset. (b) 3D view and slices of an unconditionally generated microstructure with a comparable grain count to (a). (c)-(e) Distributions of grain size, aspect ratio, and sphericity for generated and reference structures. (f) Distribution of VGG perceptual similarity scores for 2D slices sampled from generated and reference 3D microstructures.(g) Range and mean of the two-point correlation function ($S_2$) for both datasets. (h) Cumulative distribution functions of RGB channels representing crystallographic orientation.
  • Figure 3: Qualitative and quantitative evaluation of the proposed PolyCrysDiff model for conditioned polycrystalline microstructure generation. (a) Microstructures generated under mean grain size conditions of 437, 262, 187, and 146 µ m$^3$, v stands for mean grain size(µ m$^3$) and n stands for total grain number. (b) Correlation between target and generated grain numbers. (c) Distribution of generated grain numbers for six samples per condition, demonstrating stability and repeatability. (d) Microstructures generated under mean sphericity conditions of 0.725, 0.75, 0.775, and 0.800, s stands for grain sphericity. (e) Correlation between target and generated sphericity values for grain mean sphericity. (f) Variability of generated sphericity across repeated samples for each condition.
  • Figure 4: (a) Microstructure generated by the proposed PolyCrysDiff model, showing clear grain morphology, sharp grain boundaries, and consistent orientation distribution. (b) Microstructure generated by the MRF model, having indistinguishable grains and unrealistic structures. (c) Microstructure generated by the SolidTexture model, which fails to reconstruct coherent 3D grain structures and exhibits missing orientations.
  • Figure 5: (a) Workflow of the proposed end-to-end framework based on PolyCrysDiff. User-defined condition inputs are given to PolyCrysDiff and structures satisfying these inputs are generated. Structures can be easily meshed and then CPFEM simulation is applied. (b) Stress–strain curves from CPFEM simulations of 50 PolyCrysDiff-generated structures conditioned on a grain count of 125. (c) Stress–strain curves from CPFEM simulations of 50 PolyCrysDiff-generated structures conditioned on a grain count of 250. (d) Histogram of the tensile strength distribution for results in (b) and (c). Grain count are represented in mean grain size. (e) PDFs of the CPFEM-predicted tensile strength.
  • ...and 1 more figures