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Abstract Recent work has demonstrated the potential of convolutional neural networks (CNNs) in producing low-computational cost surrogate models for the localization of mechanical fields in two-phase microstructures. The extension of the same CNNs to polycrystalline microstructures is hindered by the lack of an efficient formalism for the representation of the crystal lattice orientation in the input channels of the CNNs. In this paper, we demonstrate the benefits of using generalized spherical harmonics (GSH) for addressing this challenge. A CNN model was successfully trained to predict the local plastic velocity gradient fields in polycrystalline microstructures subjected to a macroscopically imposed loading condition. Specifically, it is demonstrated that the proposed approach improves significantly the accuracy of the CNN models when compared with the direct use of Bunge–Euler angles to represent the crystal orientations in the input channels. Since the proposed approach implicitly satisfies the expected crystal symmetries in the specification of the input microstructure to the CNN, it opens new research directions for the adoption of CNNs in addressing a broad range of polycrystalline microstructure design and optimization problems.
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This content will become publicly available on April 1, 2025
Statistically conditioned polycrystal generation using denoising diffusion models
Synthetic microstructure generation algorithms have emerged as a key tool for enabling large ICME and Materials Informatics efforts. In particular, statistically conditioned generative models allow researchers to systematically explore complex design spaces encountered in microstructure design. In spite of the engineering importance of polycrystalline materials, generative frameworks for these systems remain extremely limited. This stunted development – in comparison to the N-phase microstructure generation problem – occurs because of the complexities inherent to the representation of the polycrystalline orientation fields. For example, these fields exhibit multiple crystal- and sample-level symmetries. In prior work, these difficulties have resulted in instabilities in deep generative models for polycrystalline microstructures. In this work, we propose the use of a Reduced-Order Generalized Spherical Harmonic (ROGSH) basis to address the challenge described above. The proposed approach accounts for the complex sample- and crystal-level symmetries, and produces well behaved and low dimensional representations whose space has a meaningful Euclidean measure. We then demonstrate the ROGSH basis’s remarkable ability to produce stable denoising diffusion models by using our recently established Local–Global generative framework to create visually realistic synthetic polycrystalline microstructures. Furthermore, we demonstrate that the generation process can be conditioned on both first- and second-order spatial statistics of the polycrystalline orientation fields.
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- Award ID(s):
- 2027105
- PAR ID:
- 10511231
- Publisher / Repository:
- Elsevier
- Date Published:
- Journal Name:
- Acta Materialia
- Volume:
- 267
- Issue:
- C
- ISSN:
- 1359-6454
- Page Range / eLocation ID:
- 119746
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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