Bayesian Optimization in Continuous Spaces via Virtual Process Embeddings

TL;DR

This paper introduces a novel method combining variational autoencoders with Bayesian optimization to efficiently optimize high-dimensional process trajectories in physical systems, demonstrated on a ferroelectric lattice model.

Contribution

It presents a new approach that encodes complex trajectories into a low-dimensional latent space for Bayesian optimization, enabling effective exploration of high-dimensional process parameters.

Findings

Successfully optimized field trajectories to maximize curl in a ferroelectric model

Enabled decoding of physical mechanisms through polarization and curl analysis

Reduced high-dimensional optimization to a manageable latent space

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.