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

Arpan Biswas, Anna N. Morozovska+3 more|arXiv (Cornell University)|Aug 29, 2021

Ferroelectric and Negative Capacitance Devices107 references38 citations

TL;DR

This paper presents a physics-informed multi-objective Bayesian optimization (MOBO) framework to simultaneously optimize energy storage and loss in interfacially controlled ferroelectric/antiferroelectric materials. By coupling a 1D Ginzburg-Landau-Devonshire model with Gaussian process surrogate models and acquisition function maximization, the method efficiently identifies Pareto-optimal parameter regions in high-dimensional space, reducing costly simulations while capturing trade-offs between performance metrics via validated ground-truth comparisons.

ABSTRACT

Optimization of materials performance for specific applications often requires balancing multiple aspects of materials functionality. Even for the cases where generative physical model of material behavior is known and reliable, this often requires search over multidimensional parameter space to identify low-dimensional manifold corresponding to required Pareto front. Here we introduce the multi-objective Bayesian Optimization (MOBO) workflow for the ferroelectric/anti-ferroelectric 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 towards the active experiment setting. The associated notebooks provide both the tutorial on MOBO and allow to reproduce the reported analyses and apply them to other systems (https://github.com/arpanbiswas52/MOBO_AFI_Supplements).

Motivation & Objective

• To address the challenge of balancing multiple performance metrics—energy storage and loss—in ferroelectric and antiferroelectric materials for memory and energy storage applications.
• To overcome the computational burden of exploring high-dimensional parameter spaces in materials design for complex interfacial systems.
• To develop a low-cost, efficient optimization workflow that integrates physics-based models with Bayesian inference for materials discovery.
• To enable rapid identification of optimal materials and device parameters by replacing expensive simulations with surrogate modeling.

Proposed method

• The method employs a 1D numerical solution of the Ginzburg-Landau-Devonshire (GLD) equation to model polarization and structural order parameters in ferroelectric/antiferroelectric systems under electrochemical or semiconducting boundary conditions.
• A physics-driven decision tree is constructed from loop structures (P-E hysteresis) to define target functions for energy storage and loss.
• Multi-objective Bayesian Optimization (MOBO) is applied using Gaussian process (GP) surrogate models updated iteratively from prior evaluations.
• The acquisition function is maximized at each step to select the next most informative parameter set for evaluation, balancing exploration and exploitation.
• The framework is validated against a low-sampling (7×7) grid-based exhaustive search to compare Pareto frontiers with ground truth.
• All analyses and workflows are implemented in interactive Colab notebooks for reproducibility and extension to other systems (https://github.com/arpanbiswas52/MOBO_AFI_Supplements).

Experimental results

Research questions

• RQ1 How can multi-objective optimization be efficiently applied to identify the best trade-offs between energy storage and loss in interfacially controlled ferroelectrics?
• RQ2 What role do interfacial parameters—such as partial O2 pressure, temperature, film thickness, and surface ion energy—play in determining the Pareto frontier of performance metrics?
• RQ3 Can a physics-informed surrogate model based on the GLD formalism accurately predict the behavior of complex ferroelectric systems with minimal computational cost?
• RQ4 How does the presence of phase transitions (e.g., between FE and AFE) affect the stability and accuracy of the MOBO surrogate model?
• RQ5 To what extent can the MOBO framework reduce the number of expensive simulations required to identify optimal materials parameters?

Key findings

• The MOBO framework successfully identifies a Pareto frontier that connects regions of high energy storage and high loss, demonstrating a clear trade-off between the two objectives.
• The method achieves accurate Pareto frontier approximation with significantly fewer evaluations than exhaustive grid search, as validated by 7×7 ground-truth comparisons.
• Higher energy storage is correlated with lower partial O2 pressure and lower temperature, while higher loss correlates with higher partial O2 pressure and lower temperature.
• Sudden jumps in storage and loss values on the Pareto frontier are linked to phase transitions between ferroelectric and antiferroelectric phases, indicating challenges for surrogate modeling at phase boundaries.
• The framework enables rapid exploration of high-dimensional parameter spaces and can be extended to 3D finite element models and active experimental settings.
• The entire workflow, including MOBO iterations and model validation, is documented and reproducible via public Colab notebooks.