Local-Global Decompositions for Conditional Microstructure Generation

Conditional microstructure generation tools offer an important, inexpensive pathway to constructing statisti-cally diverse datasets for Integrated Computational Materials Engineering and Materials Informatics efforts. To provide this utility in practice, an ideal generative framework must be able to efficiently, systematically, and robustly generate microstructures corresponding to selected spatial statistics (e.g., 1-and 2-point statistics) while also producing realistic local features (e.g., shapes and sizes of individual phase constituents). Because of the austerity of these requirements, generative frameworks often target either statistical conditioning or visual realism, but not both. In this paper, we propose to bridge these two approaches by approximating a microstructure's generating process (i.e., its stochastic microstructure function) using a two layer semi-directed probabilistic graphical model. The first layer - a Gaussian Random Field (GRF) - provides direct control of the 1-and 2-point statistics. The second layer - a Score Based Generative Deep Learning model - postprocesses GRF predictions to refine local features while preserving global patterning. To understand and evaluate our proposed framework, we apply it to generate statistically equivalent N-phase microstructures from experimental references, including a 2-Phase Nickel-based Super Alloy and a 3-phase ������ - ������ Titanium alloy. Through these two case studies, we demonstrate that our framework successfully matches both lower-order (1-and 2-point statistics) and several salient higher-order statistics. Additionally, we briefly explore the capacity of these models to extrapolate outside of their training data by varying the input 2-point statistics. We discuss the value of this ability towards systematically generating diverse microstructure datasets.

Automated summary

Conditional microstructure generation tools provide an important and affordable method for creating statistically diverse datasets for Integrated Computational Materials Engineering and Materials Informatics. In this paper, a generative framework is proposed that combines statistical conditioning and visual realism by approximating a microstructure's generating process using a two-layer probabilistic graphical model. Through case studies, the framework is shown to successfully match both lower-order and higher-order statistics. The ability of these models to extrapolate outside of the training data is briefly explored, highlighting the value of systematically generating diverse microstructure datasets.