Best Practices for Multi-Fidelity Bayesian Optimization in Materials and Molecular Research (2410.00544v3)

Abstract: Multi-fidelity Bayesian Optimization (MFBO) is a promising framework to speed up materials and molecular discovery as sources of information of different accuracies are at hand at increasing cost. Despite its potential use in chemical tasks, there is a lack of systematic evaluation of the many parameters playing a role in MFBO. In this work, we provide guidelines and recommendations to decide when to use MFBO in experimental settings. We investigate MFBO methods applied to molecules and materials problems. First, we test two different families of acquisition functions in two synthetic problems and study the effect of the informativeness and cost of the approximate function. We use our implementation and guidelines to benchmark three real discovery problems and compare them against their single-fidelity counterparts. Our results may help guide future efforts to implement MFBO as a routine tool in the chemical sciences.

• The paper shows that integrating low- and high-fidelity data, with criteria of ρ ≤ 0.2 and R² > 0.75, significantly outperforms single-fidelity approaches.
• The paper employs Gaussian Process models with acquisition functions like MES and EI, validated through synthetic benchmarks (Branin, Park) and real-world chemistry cases.
• The paper outlines a decision-making framework that guides practical MFBO application, achieving cost reductions of up to 67% in experimental designs.

Overview of Multi-Fidelity Bayesian Optimization in Materials and Molecular Research

The paper "Best Practices for Multi-Fidelity Bayesian Optimization in Materials and Molecular Research" explores optimizing the use of Multi-Fidelity Bayesian Optimization (MFBO) for materials and molecular discovery. Bayesian Optimization (BO) has become a cornerstone in the chemical domain for guiding experimental designs. The extension to a multi-fidelity approach aims to exploit varying accuracies and costs of data sources, maximizing efficiency and minimizing budget.

Core Concepts and Implementation

MFBO extends the classical BO framework by introducing a multi-fidelity probabilistic model. This model differentiates between high-fidelity (HF) and low-fidelity (LF) sources, each with its cost implications. A critical aspect of MFBO is balancing cost-effectiveness with informativeness. The authors propose using Gaussian Processes (GP) to manage these complexities, extending the input space to accommodate fidelity levels.

The paper evaluates two families of acquisition functions: Maximum Entropy Search (MES) and Expected Improvement (EI). These guide the selection of the next data points, factoring in the overall cost of solutions. By applying MFBO to synthetic benchmarks and real-world chemistry problems, the paper assesses its practicality and performance enhancement over single-fidelity BO (SFBO).

Key Results

The analysis begins by exploring synthetic functions like Branin and Park, revealing that MFBO's benefits are contingent upon the LF data being both informative (high $R^2$) and cost-effective ($\rho \leq 0.2$). Scenarios with high informativeness and lower costs showed superior performance, highlighting the importance of these factors in MFBO application.

Subsequently, the paper validates its findings through chemistry and materials science benchmarks, including Covalent Organic Frameworks (COFs) and molecule polarizability. These cases demonstrated that MFBO successfully identifies optimal experimental conditions more cost-effectively than SFBO, with maximum discounts up to 0.67 in budgetary terms.

Guidelines and Implications

The authors propose a decision-making framework to determine when MFBO is advantageous. Key metrics include the cost ratio ($\rho$) and informativeness ($R^2$). Their findings suggest that MFBO should be considered when $\rho < 0.2$ and $R^2 > 0.75$.

The implications of this paper are twofold. Practically, it provides a framework for integrating MFBO into experimental designs, potentially reducing time and resource expenditure in chemical discovery. Theoretically, it establishes a baseline for future MFBO applications, inviting further exploration into adaptation across various domains.

Future Directions

The findings encourage extending the MFBO approach to other surrogate models like Bayesian Neural Networks, which could further enhance prediction accuracies and model adaptivity. Additionally, investigating more complex experimental designs with varying fidelity levels and datasets could refine the MFBO's applicability and robustness.

In conclusion, this work methodically outlines MFBO's practices and potential, offering researchers in chemical sciences a structured approach to experimental optimization. As this framework evolves, it promises to become an integral tool for cost-aware, efficient discovery in materials and molecular research.