Multi-Fidelity Bayesian Optimization for Efficient Materials Design

Abstract

Materials design is a process of identifying compositions and structures to achieve desirable properties. Usually, costly experiments or simulations are required to evaluate the objective function for a design solution. Therefore, one of the major challenges is how to reduce the cost associated with sampling and evaluating the objective. Bayesian optimization is a new global optimization method which can increase the sampling efficiency with the guidance of the surrogate of the objective. In this work, a new acquisition function, called consequential improvement, is proposed for simultaneous selection of the solution and fidelity level of sampling. With the new acquisition function, the subsequent iteration is considered for potential selections at low-fidelity levels, because evaluations at the highest fidelity level are usually required to provide reliable objective values. To reduce the number of samples required to train the surrogate for molecular design, a new recursive hierarchical similarity metric is proposed. The new similarity metric quantifies the differences between molecules at multiple levels of hierarchy simultaneously based on the connections between multiscale descriptions of the structures. The new methodologies are demonstrated with simulation-based design of materials and structures based on fully atomistic and coarse-grained molecular dynamics simulations, and finite-element analysis. The new similarity metric is demonstrated in the design of tactile sensors and biodegradable oligomers. The multi-fidelity Bayesian optimization method is also illustrated with the multiscale design of a piezoelectric transducer by concurrently optimizing the atomic composition of the aluminum titanium nitride ceramic and the device’s porous microstructure at the micrometer scale.