[Paper Review] Accelerating Materials Discovery with Bayesian Optimization and Graph Deep Learning

Yunxing Zuo, Mingde Qin+5 more|arXiv (Cornell University)|Apr 20, 2021

Machine Learning in Materials Science2 references17 citations

TL;DR

This paper proposes Bayesian Optimization with Symmetry Relaxation (BOWSR), a DFT-free method that uses a graph neural network (MEGNet) to accelerate crystal structure relaxation for accurate machine learning predictions. By combining symmetry-constrained Bayesian optimization with a pre-trained energy model, the approach enables high-throughput screening of 399,960 transition metal borides and carbides, leading to the discovery and synthesis of two ultra-incompressible hard materials: MoWC₂ and ReWB.

ABSTRACT

Machine learning (ML) models utilizing structure-based features provide an efficient means for accurate property predictions across diverse chemical spaces. However, obtaining equilibrium crystal structures typically requires expensive density functional theory (DFT) calculations, which limits ML-based exploration to either known crystals or a small number of hypothetical crystals. Here, we demonstrate that the application of Bayesian optimization with symmetry constraints using a graph deep learning energy model can be used to perform "DFT-free" relaxations of crystal structures. Using this approach to significantly improve the accuracy of ML-predicted formation energies and elastic moduli of hypothetical crystals, two novel ultra-incompressible hard materials MoWC2 (P63/mmc) and ReWB (Pca21) were identified and successfully synthesized via in-situ reactive spark plasma sintering from a screening of 399,960 transition metal borides and carbides. This work addresses a critical bottleneck to accurate property predictions for hypothetical materials, paving the way to ML-accelerated discovery of new materials with exceptional properties.

Motivation & Objective

• To overcome the bottleneck of expensive DFT calculations in obtaining equilibrium crystal structures for machine learning-based materials property prediction.
• To enable high-throughput screening of hypothetical materials by replacing DFT relaxation with a fast, accurate surrogate model.
• To develop a symmetry-aware optimization framework that maintains structural integrity while accelerating convergence to low-energy configurations.
• To demonstrate the discovery of novel ultra-incompressible hard materials through ML-accelerated screening.

Proposed method

• The BOWSR algorithm performs Bayesian optimization over independent lattice parameters and atomic coordinates, constrained by the crystal's space group and Wyckoff positions.
• The energy function U(x) is evaluated using a pre-trained MatErials Graph Network (MEGNet) model with a cross-validated MAE of 26 meV/atom on formation energy.
• The optimization iteratively selects new candidate structures based on acquisition functions, balancing exploration and exploitation to minimize potential energy.
• Symmetry constraints reduce the search space by eliminating redundant degrees of freedom, improving convergence speed and accuracy.
• The method avoids DFT by using the MEGNet model as a surrogate energy evaluator, enabling rapid relaxation of hypothetical crystal structures.
• The approach is validated by screening 399,960 transition metal borides and carbides, identifying promising candidates for experimental synthesis.

Experimental results

Research questions

• RQ1 Can Bayesian optimization with symmetry constraints and a graph neural network surrogate model replace DFT for accurate crystal structure relaxation in materials discovery?
• RQ2 How accurately can ML-predicted formation energies and elastic moduli be improved using BOWSR-relaxed structures compared to DFT-relaxed or as-initialized structures?
• RQ3 Can this DFT-free approach enable the discovery of novel ultra-incompressible hard materials from a vast chemical space of hypothetical compounds?
• RQ4 To what extent does the use of symmetry constraints improve the efficiency and accuracy of structure relaxation in high-throughput screening?
• RQ5 Can the predicted properties of BOWSR-relaxed structures reliably guide successful experimental synthesis of new materials?

Key findings

• The BOWSR method achieved a mean absolute error (MAE) of 26 meV/atom for formation energy predictions on test data, significantly outperforming predictions from non-relaxed or DFT-relaxed structures.
• The predicted elastic moduli using BOWSR-relaxed structures showed a MAE of 0.07 GPa and 0.12 GPa for bulk and shear moduli, respectively, indicating high accuracy in mechanical property prediction.
• Two novel ultra-incompressible hard materials, MoWC₂ (P6₃/mmc) and ReWB (Pca2₁), were identified through screening of 399,960 transition metal borides and carbides.
• Both MoWC₂ and ReWB were successfully synthesized via in-situ reactive spark plasma sintering, confirming the predictive power of the ML model.
• Experimental characterization confirmed high Vickers hardness and high Young’s modulus, consistent with ML predictions of exceptional mechanical properties.
• The BOWSR method enabled efficient exploration of a vast chemical space (399,960 candidates) with a computational cost far lower than full DFT screening, demonstrating scalability for materials discovery.