Session: 03-03-01: Integrated Computational Materials Engineering (ICME)

Paper Number: 99763

99763 - Synthetic Microstructure Generation via Approximation of the Stochastic Microstructure Function Using Gaussian Random Fields 

The ability to generate microstructures corresponding to desired microstructure statistics (e.g., 2-point statistics) is necessary for rigorously studying random heterogeneous materials within the Integrated Computational Materials Engineering and Materials Informatics frameworks. Within the context of statistical materials theories, the problem of generation is most naturally conceptualized through its relationship to abstract stochastic microstructure functions (i.e., microstructure distributions). These objects are statistical families composed of the individual instances of material microstructures that we observe day to day in experiments and computational modeling. In these theories, stochastic microstructure functions are identified by enumerating a sufficient set of characteristic statistics. As a result, the synthetic generation of microstructures with specific, desired statistics is naturally addressed by approximating these stochastic microstructure functions using computationally tractable probabilistic models. Recently, we developed an efficient generative framework for producing microstructures with specified 2-point statistics by employing N-output Gaussian Random Fields (GRFs) as a second order approximation of periodic stochastic microstructure functions. In this presentation, after briefly discussing the model theory and implementation, we will primarily explore the model’s robustness and the implications of using it as an approximation. To develop the model, we first illustrate how 1- and 2-point statistics can be used to parameterize statistically anisotropic Gaussian Random Fields. Subsequently, we derive analytic relationships between the 2-point statistics and the spatially resolved sampled microstructures. Importantly, the proposed model can successfully approximate stochastic microstructure functions with completely anisotropic 2-point statistics and arbitrary numbers of phases. Finally, we propose the algorithms necessary to efficiently sample these fields in O(SlnS) computational complexity and while incurring O(S) memory cost. To explore the robustness of the proposed model as well as the implications of this approximation, we present two discussions. In our first case study, we will demonstrate that this model successfully synthesizes microstructures for a wide variety of desired 1- and 2-point statistics. Importantly, this success is maintained even as the number of phases present are increased. In our second case study, we will explore the implications of the GRF approximation by using the model to statistically complex structures (e.g., to generate fiber-matrix composites). Here, we observe how the higher-order statistical structure of a Gaussian Random Field implicitly biases the spatial arrangement of synthesized microstructures towards pseudo-amorphous grains. Using this toy example, we will discuss methods for overcoming this bias and advancing GRF-based models in the future. Finally, we will discuss the wider value of parametric generative models to core problems in Materials Informatics.

Presenting Author: Andreas Robertson Georgia Institute of Technology

Presenting Author Biography: Andreas is an early career researcher whose interests lie at the intersection of Materials Informatics and Materials Design, Machine Learning, Probabilistic Signal Processing, and Applied Mechanics. He is currently a doctoral student in Dr. Surya Kalidindi’s MiNED research lab at Georgia Tech. Here, Andreas develops computationally tractable probabilistic models for generating previously unseen synthetic material microstructures. In addition, his research aims to leverage these methods towards problems in active learning, data generation, and materials design. Andreas is particularly excited about the future of machine-learning techniques in this field because of the data-scarcity prevalent in complex engineering problems. One exciting result of this constraint is that it fosters innovative physics-based hybrid learning schemes and leads to richer analysis of the modeling process.

Authors:

Andreas Robertson Georgia Institute of Technology
Surya Kalidindi Georgia Institute of Technology