Bayesian optimization in continuous spaces via virtual process embeddings

Mani Valleti, Rama K. Vasudevan, Maxim A. Ziatdinov, Sergei V. Kalinin

Research output: Contribution to journalArticlepeer-review

5 Scopus citations

Abstract

Automated chemical synthesis, materials fabrication, and spectroscopic physical measurements often bring forth the challenge of process trajectory optimization, i.e., discovering the time dependence of temperature, electric field, or pressure that gives rise to optimal properties. Due to the high dimensionality of the corresponding vectors, these problems are not directly amenable to Bayesian Optimization (BO). Here we propose an approach based on the combination of the generative statistical models, specifically variational autoencoders, and Bayesian optimization. Here, the set of potential trajectories is formed based on best practices in the field, domain intuition, or human expertise. The variational autoencoder is used to encode the thus generated trajectories as a latent vector, and also allows for the generation of trajectories via sampling from latent space. In this manner, Bayesian optimization of the process is realized in the latent space of the system, reducing the problem to a low-dimensional one. Here we apply this approach to a ferroelectric lattice model and demonstrate that this approach allows discovering the field trajectories that maximize curl in the system. The analysis of the corresponding polarization and curl distributions allows the relevant physical mechanisms to be decoded.

Original languageEnglish
Pages (from-to)910-925
Number of pages16
JournalDigital Discovery
Volume1
Issue number6
DOIs
StatePublished - Dec 1 2022

Funding

This work was supported by the Energy Frontier Research Centers program: CSSAS – The Center for the Science of Synthesis Across Scales – under Award Number DE-SC0019288, located at the University of Washington (original idea and prototypes – S. V. K.), and the modeling and process optimization by the US Department of Energy Office of Science under the Materials Sciences and Engineering Division of the Basic Energy Sciences program (S. M. V. and R. K. V.). The Bayesian optimization research was supported by the Center for Nanophase Materials Sciences (CNMS) which is a US Department of Energy, Office of Science User Facility at Oak Ridge National Laboratory. We would also like to thank JoséMiguel Hernández-Lobato for pointing us to relevant references that were missing initially. This work was supported by the Energy Frontier Research Centers program: CSSAS – The Center for the Science of Synthesis Across Scales – under Award Number DE-SC0019288, located at the University of Washington (original idea and prototypes – S. V. K.), and the modeling and process optimization by the US Department of Energy Office of Science under the Materials Sciences and Engineering Division of the Basic Energy Sciences program (S. M. V. and R. K. V.). The Bayesian optimization research was supported by the Center for Nanophase Materials Sciences (CNMS) which is a US Department of Energy, Office of Science User Facility at Oak Ridge National Laboratory. We would also like to thank José Miguel Hernández-Lobato for pointing us to relevant references that were missing initially.

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