Exploring LC parameter space with experimentally-informed Bayesian optimization

Characterization and design of liquid crystalline systems can be successfully aided by modeling and simulation at the continuum scale. The insight provided by simulations often helps distinguish the effects of confinement, geometry, and external fields. However, the relationship between an experimental observation and LC parameter space is not necessarily injective. This poses an obstacle when searching for model parameters that yield a quantitative and qualitative match. Our model uses a tensorial representation of the LC order field, and equilibrium configurations are found through a Ginzburg-Landau relaxation. The numerical relaxation is done using a finite element discretization, which allows for a fine representation of intricate geometries. While a grid search of the appropriate parameters is commonplace, it can result in an inefficient use of resources. We propose the use of Bayesian optimization to circumvent the computational cost, while providing a proficient approach that is directly informed by the qualitative match between experiments and simulations. Two scenarios serve as proof of concept. First, finding the anchoring strength that successfully reproduces the cross polarized image of a radial droplet. Second, the optimization yields the anchoring tilt angle and strength of a nematic colloid that generates hexadecapolar defects. Through this methodology, we offer a computationally efficient way of exploring parameter space that is directly informed by experimental observations, and in doing so, paving the way towards inverse design and characterization of LC systems.