Multi-objective Bayesian optimization of ferroelectric materials with interfacial control for memory and energy storage applications

Abstract

Optimization of materials’ performance for specific applications often requires balancing multiple aspects of materials’ functionality. Even for the cases where a generative physical model of material behavior is known and reliable, this often requires search over multidimensional function space to identify low-dimensional manifold corresponding to the required Pareto front. Here, we introduce the multi-objective Bayesian optimization (MOBO) workflow for the ferroelectric/antiferroelectric performance optimization for memory and energy storage applications based on the numerical solution of the Ginzburg–Landau equation with electrochemical or semiconducting boundary conditions. MOBO is a low computational cost optimization tool for expensive multi-objective functions, where we update posterior surrogate Gaussian process models from prior evaluations and then select future evaluations from maximizing an acquisition function. Using the parameters for a prototype bulk antiferroelectric (PbZrO3), we first develop a physics-driven decision tree of target functions from the loop structures. We further develop a physics-driven MOBO architecture to explore multidimensional parameter space and build Pareto-frontiers by maximizing two target functions jointly—energy storage and loss. This approach allows for rapid initial materials and device parameter selection for a given application and can be further expanded toward the active experiment setting. The associated notebooks provide both the tutorial on MOBO and allow us to reproduce the reported analyses and apply them to other systems (https://github.com/arpanbiswas52/MOBO_AFI_Supplements).

Computational Design of Antimicrobial Active Surfaces via Automated Bayesian Optimization

“…Here, we use the Gaussian kernel, hence the prior covariance is .25ex2ex Σ 0 false( boldx i , boldx j false) = σ 2 R false( boldx i , boldx j false) , R false( boldx i , boldx j false) = exp true( 1 2 ∑ m = 1 d ( x i , m − x j , m ) 2 θ m 2 true) θ m = false( θ 1 , θ 2 , ... , θ d false) where σ 2 is the overall variance parameter and θ m is the correlation length scale parameter in dimension m of the d th dimension of x , which are all hyperparameters of GPR, and R ( x i , x j ) is the spatial correlation function. Our goal is to estimate the parameter...…”

“…Here, we use the Gaussian kernel, hence the prior covariance is where σ 2 is the overall variance parameter and θ m is the correlation length scale parameter in dimension m of the d th dimension of x , which are all hyperparameters of GPR, and R ( x i , x j ) is the spatial correlation function. Our goal is to estimate the parameters σ and θ m that create the surrogate model given the training data at iteration k .…”

Bayesian optimization with active learning of design constraints using an entropy-based approach

“…Varð f ðxÞÞ ¼ 1 e T ΣðxÞ À1 e (7) where e = [1, …, 1] T , μðxÞ ¼ ½μ 1 ðxÞ; ; μ S ðxÞ T given S models, and ΣðxÞ À1 is the inverse of the covariance matrix between the information sources. A more detailed discussion and examples can be found in Refs.…”

“…MOBO schemes have been successfully deployed in various contexts within the domain of materials science. For example, Arpan et al 7 leveraged MOBO to design interfacially controlled ferroelectric materials for superior energy storage and minimal energy loss. The authors performed 4-objective optimization of the following parameters: temperature, partial O 2 pressure, film thickness, and surface ion energy.…”

New Paradigms for Exploiting Parallel Experiments in Bayesian Optimization

“…Recently, the machine learning (ML) community has been using variants of this paradigm to conduct closed-loop experimental design [7]. One of the most effective variations of this paradigm is the Bayesian optimization (BO) algorithm [1]; BO has been shown to be sample-efficient and scalable (requires minimal experiments and can explore large design spaces) [24]. BO is widely used in applications such as experimental design, hyper-parameter tuning, and reinforcement learning.…”