Bgolearn: a Unified Bayesian Optimization Framework for Accelerating Materials Discovery

TL;DR

The paper tackles data-efficient materials discovery in high-dimensional design spaces by introducing Bgolearn, a unified Bayesian optimization framework tailored for materials science. It combines MOBO capabilities (EHVI, qNEHVI, MO-PI, MO-UCB), flexible surrogates (GPs, RF, GB, SVR, MLP), bootstrap-based uncertainty, and a GUI (BgoFace) with an intuitive API to lower barriers to adoption. Benchmark and case-study results show Bgolearn reduces experimental requirements by about 40–60% while maintaining or improving solution quality across metallic and functional materials and industrial applications, including TPMS structures, high-entropy alloys, and medium-Mn steels. The open-source, modular design supports seamless integration into existing workflows and autonomous laboratories, enabling scalable, reproducible, and practical materials discovery.

Abstract

Efficient exploration of vast compositional and processing spaces is essential for accelerated materials discovery. Bayesian optimization (BO) provides a principled strategy for identifying optimal materials with minimal experiments, yet its adoption in materials science is hindered by implementation complexity and limited domain-specific tools. Here, we present Bgolearn, a comprehensive Python framework that makes BO accessible and practical for materials research through an intuitive interface, robust algorithms, and materials-oriented workflows. Bgolearn supports both single-objective and multi-objective Bayesian optimization with multiple acquisition functions (e.g., expected improvement, upper confidence bound, probability of improvement, and expected hypervolume improvement etc.), diverse surrogate models (including Gaussian processes, random forests, and gradient boosting etc.), and bootstrap-based uncertainty quantification. Benchmark studies show that Bgolearn reduces the number of required experiments by 40-60% compared with random search, grid search, and genetic algorithms, while maintaining comparable or superior solution quality. Its effectiveness is demonstrated not only through the studies presented in this paper, such as the identification of maximum-elastic-modulus triply periodic minimal surface structures, ultra-high-hardness high-entropy alloys, and high-strength, high-ductility medium-Mn steels, but also by numerous publications that have proven its impact in material discovery. With a modular architecture that integrates seamlessly into existing materials workflows and a graphical user interface (BgoFace) that removes programming barriers, Bgolearn establishes a practical and reliable platform for Bayesian optimization in materials science, and is openly available at https://github.com/Bin-Cao/Bgolearn.

Figures (5)

• Figure 1: The components and workflow of Bgolearn for materials discovery.
• Figure 2: Overview of the Bgolearn software architecture, data flow, and the integrated BgoFace ecosystem interface.
• Figure 3: a, Optimization efficiency comparison across methods, including Bgolearn, random search, Latin hypercube sampling, and NSGA-II (only applicable to multi-target optimization), evaluated on four benchmark functions. b, Optimization traces of each method, where the simple regret represents the difference between the best observed objective value and the global optimum.
• Figure 4: a, Evolution of the elastic modulus across optimization iterations for TPMS structures. The red dotted line indicates the best configuration with the highest elastic modulus identified in the initial training set. b, Experimentally measured yield strength (MPa) and total elongation (%) of medium-Mn steels. The black line denotes the experimental Pareto front, while the red star markers indicate the steels recommended by Bgolearn.
• Figure 5: Depth–load curves measured from three independent nanoindentation experiments on the sample.