Electrolyte recommender system for batteries using ensemble Bayesian optimization

Abstract

Bayesian optimization (BO) is a useful technique for optimizing unknown target functions that require computationally demanding evaluations and have noisy outputs. In addition, BO can be easily extended to parallel experiments. Ensemble BO, involving multiple BO algorithms, is suitable for such settings and resolves some of the issues associated with classical BO such as mismatches between the unknown target and surrogate functions. In ensemble BO, low-performance results are actively gathered for the purpose of training BO algorithms and for use in analyzing target phenomena of interest. In this study, we apply ensemble BO to a real experimental system: a system to recommend the optimal electrolytes for Li-ion batteries. The purpose of this recommender system is to determine the best solution (solvents and salt) ratios for the electrolyte to maximize ionic conductivity. The system has a large search space in terms of the possible combinations of solution ratios, and must deal with noisy observations. The proposed electrolyte recommender system, based on ensemble BO, was experimentally demonstrated to be effective for a battery electrolyte with four solutions. Furthermore, based on the solution ratios recommended by the system, a useful solution-mixing rule for maximizing ionic conductivity was obtained.

Introduction

Bayesian optimization (BO) is a powerful optimization technique that can be used for unknown target functions and is robust against noisy observations (Frazier and Wang, 2016, Močkus, 1974, Shahriari et al., 2016). Hence, BO has been applied to a wide variety of applications, including optimizing the hyper-parameter settings of deep neural networks (Falkner et al., 2018, Swersky et al., 2014), robot control systems (Antonova et al., 2017, Cornejo Bueno et al., 2018, Marco et al., 2017), material designs (Ju et al., 2017, Todorović et al., 2017), and drug discovery (Negoescu et al., 2011). Recently, BO has been also applied to applications related to not only simulations but also real experimental systems in materials science (Dave et al., 2020, Li et al., 2017, Schweidtmann et al., 2018). Furthermore, although there are commercial products such as automated liquid distribution systems, which can apply to electrolytes in batteries, optimization algorithms (such as BO) are not used in these systems.

In BO, Gaussian process (GP) regression is often used to derive an expressive, non-parametric surrogate function that represents the unknown target function but is more flexible and tractable (Snoek et al., 2012). This approach has been utilized in the exploration–exploitation trade-off of BO (Schulz et al., 2018). However, according to Schulz et al. (2016), a mismatch between the smoothness properties of the kernel function and the unknown target function can reduce the convergence speed of BO. In addition, the convergence speed in BO differs depending on the type of acquisition function (Hennig and Schuler, 2012, Srinivas et al., 2010). Thus, a suitable acquisition function must be selected depending on the unknown target functions. To resolve such issues, Hoffman et al. (2011) proposed a method of portfolio allocation of acquisition functions, named GP-Hedge, and demonstrated its effectiveness compared to the best acquisition function. This method can be used as a BO as a part of an ensemble, but further hyper-parameter tuning of GP-Hedge is needed. For BO, hyper-parameter tuning of the acquisition function is needed, which increases experimental costs.

To address these issues, we previously developed an ensemble BO (EBO) (Ohno, 2018), consisting of several BO algorithms (hereafter referred to as BOs) with different kernel functions, acquisition functions, and associated hyper-parameters. A single common database is used for all kernel functions within an EBO. Hence, an empirical Gram matrix of the GP for each BO in the ensemble is based on the common database. However, in the absence of a priori knowledge about the target functions, suitable kernel and acquisition functions cannot be selected. In such cases, EBO can be conducted using an ensemble of several BOs with different kernel and acquisition functions to match the characteristics of the target functions as closely as possible. In addition, for practical experiments, iterations of experiments are often restricted due to limitations such as tank capacity and the cost of materials. Here, the characteristics of EBO are summarized as follows:

• Easy to use practically due to its simple structure.

• Enlarges the search space in combination with different search strategies, which can improve the training of surrogate functions.

• Reduces the computational costs associated with hyper-parameter tuning due to the use of acquisition functions with distinct parameter values.

In 2, the search strategy is determined by the combination of acquisition functions and kernel functions. Differences in the performance of results, due to different search strategies, can enlarge the search space. In addition, low-performance results are actively gathered for the purpose of training BOs and for use in analyzing target phenomena of interest. This characteristic is not seen in previous work such as Hoffman et al. (2011). Characteristic 3 can be achieved by setting different hyper-parameter values to each acquisition function. This is available for the limited iterations for the experiments. Recently, Wang, Clement et al. (2018) proposed an EBO to tackle high-dimensional and large-scale parameter-search problems by using a Mondrian process to partition the search space and assign a different BO in the ensemble in order to search each partitioned space. However, this approach did not resolve the above-mentioned issues. Furthermore, although the partitioning of the search space may mitigate the mismatch in smoothness locally, it does not sufficiently deal with the mismatch issue.

As a feasibility study of EBO, we develop a recommender system for electrolytes, in which an EBO optimizes the electrolytes used in Li-ion batteries, which is challenging due to the large number of possible combinations of solution ratios for the electrolytes as well as the noise in the observations. The proposed recommender system is designed to identify the solution (solvents and salt) compositions that maximize ionic conductivity, and to reduce costs associated with hyper-parameter tuning and the selection of the acquisition functions and kernel functions. Thus, in practical situations, scientists who may not have expert knowledge of optimization techniques can easily set up and utilize the proposed system. Experimental optimizations were conducted for four different solutions and the results obtained demonstrated the effectiveness of the EBO. Moreover, the experimental results provided additional insight in the form of a useful mixing rule for maximizing the ionic conductivity with the four solutions used here. This rule states that a small amount of a solvent with a low dielectric constant and high viscosity should be included in the mixture of solutions in order to attain high ionic conductivity. Furthermore, the behavior of each BO in the ensemble was investigated after carrying out the optimization process in the system, and it was revealed that the convergence to the maximum ionic conductivity differed depending on the type of kernel and acquisition functions used. This suggests that the proposed EBO system can be generalized to other optimization problems.

The remainder of this paper is organized as follows. Prior related work is described in Section 2. In Section 3, we describe the proposed EBO algorithm in detail. An overview of the electrolyte recommender system is provided in Section 4 along with the experimental results and an analysis of the findings. In Section 5, we discuss the limitations of the present method and obtained results. Finally, a summary and conclusion, as well as future work, are presented in Section 6.