Bayesian Modelling of Phase-Field Crystal Models for Targeted Crystalline Patterns

Partial differential equations (PDE) have been widely used to reproduce patterns in nature and to give insight into the mechanism underlying pattern formation. Although many PDE models have been proposed, they rely on the pre-request knowledge of physical laws and symmetries, and developing a model to reproduce a given desired pattern remains difficult. We propose a novel method to estimate the best dynamical PDE for one snapshot of a target pattern under the stationary state without ground truth. We apply our method to nontrivial patterns, such as quasi-crystals (QCs), a double gyroid and Frank Kasper structures. Our method works for noisy patterns and the pattern synthesised without the ground truth parameters, which are required for the application toward experimental data.