Physically-Constrained Autoencoder-Assisted Bayesian Optimization for Refinement of High-Dimensional Defect-Sensitive Single Crystalline Structure

Physical properties and functionalities of materials are dictated by global crystal structures as well as local defects. To establish a structure-property relationship, not only the crystallographic symmetry but also quantitative knowledge about defects are required. Here we present a hybrid Machine Learning framework that integrates a physically-constrained variational-autoencoder (pcVAE) with different Bayesian Optimization (BO) methods to systematically accelerate and improve crystal structure refinement with resolution of defects. We chose the pyrochlore structured Ho2Ti2O7 as a model system and employed the GSAS2 package for benchmarking crystallographic parameters from Rietveld refinement. However, the function space of these material systems is highly nonlinear, which limits optimizers like traditional Rietveld refinement, into trapping at local minima. Also, these naive methods don't provide an extensive learning about the overall function space, which is essential for large space, large time consuming explorations to identify various potential regions of interest. Thus, we present the approach of exploring the high Dimensional structure parameters of defect sensitive systems via pretrained pcVAE assisted BO and Sparse Axis Aligned BO. The pcVAE projects high-Dimensional diffraction data consisting of thousands of independently measured diffraction orders into a lowD latent space while enforcing scaling invariance and physical relevance. Then via BO methods, we aim to minimize the L2 norm based chisq errors in the real and latent spaces separately between experimental and simulated diffraction patterns, thereby steering the refinement towards potential optimum crystal structure parameters. We investigated and compared the results among different pcVAE assisted BO, non pcVAE assisted BO, and Rietveld refinement.