Bayesian Optimization Strategies for Electrochemical Technology Development
Authors: O'Sullivan Eugene J. 
Published: December 2024

Traditional design of experiments (DOE) often proves inefficient in technology development, particularly in emerging or rapidly evolving fields. This inefficiency stems from several challenges: a) high-dimensional spaces, which complicate the experimental design because of the exponential increase in the number of experiments; b) resource intensity, since achieving comprehensive coverage of the experimental space may require a multitude of experiments; and c) sensitivity to noise that can undermine the reliability of conclusions and force much repetition to achieve statistical significance. These limitations underscore the need for more adaptable and efficient experimental approaches in the face of rapid technological innovation.
In contrast, Bayesian Optimization (BO) [1] can dynamically adjust based on initial findings, prioritize the most promising regions of the experimental space, promising faster and more efficient technology development. At the heart of BO is a probabilistic 'surrogate' model, embodying two main concepts:

A Gaussian process (GP) simultaneously models the predicted mean µt(x) and the uncertainty σt(x) at a point x in the input space, given a set of observations (e.g., our prior experimental results)

S1t = {(x1; y1), {(x2; y2), ... (xt, yt)}
where xt is the process input, and yt is the corresponding output at time t.

An acquisition function expresses the most promising setting for the next experiment, based on the predicted mean µt(x) and the uncertainty σt(x).

This surrogate model is built and continuously refined using data from previous experiments, enabling informed decision-making for subsequent explorations.
Meta’s open-source Ax platform [2] was used as an interface in this work for defining, running, and analyzing Bayesian Optimization (BO) experiments. Thanks to the robust capabilities of BoTorch, Ax effectively abstracts the complexities associated with optimization tasks, reducing the necessity for in-depth exploration of algorithmic intricacies by the user. Both Ax and BoTorch, being Python libraries, required a Python environment, which was established in this work using an Ubuntu installation on the Windows Subsystem for Linux (WSL) feature.
The dataset used in this study was originally generated using a one-variable-at-a-time (OFAT) method [3]. Subjecting a rhodium surface in alkaline solution to a repetitive triangular potential sweep over the range 0-1.55 V (RHE) generated a thick, hydrous oxide film which exhibited appreciable charge storage effects at about 1.2–1.5 V, attributed to a bulk redox process enabled by proton transfer. Oxide growth rate depended on variables such as hydroxide ion concentration, potential sweep limits, and temperature, sometimes in a nonlinear manner.
The goal of this BO study was to maximize the value of the oxide’s redox charge capacity at a fixed sweep rate of 15.4 V/s for 300 cycles; the previously measured data [3] was used to validate the predicted values. Figure 1 shows a summary of the experimental parameter ranges used here and the creation of an experiment protocol within Ax to optimize parameters towards a specific goal, maximizing charge capacity. Figure 2 shows a GenerationStrategy (GS) user code snippet that interacts with its underlying engine (the “Service API”). A user generated instance of AxClient, a user-friendly interface to the Ax library, uses the GS instance to generate new trials and log trial results.
Figure 3 shows historical trial information added to the newly created “Rh_experiment” (Fig. 1) to aid trial prediction. As new trials proceeded, and their information dynamically fed back to the GPEI model, the accuracy of the trials’ predictions improved, the actual Q value reached the maximum values expect from the original data [3]. The variance values also decreased, confirming more accurate predictions.
Figure 4 lists historical trial information for a GenerationStrategy with two GenerationSteps, the first containing Sobol, the second GPEI models; the Sobol model in Ax GenerationStrategy is primarily used for initial exploration in a quasi-random manner without assuming any prior knowledge. In the trial examples shown in Fig. 4, the actual Q value reached the expected maximum Q values faster on switching to the GPEI model than in Fig. 3, mainly due to the fortuitous predictions resulting from the Sobol model.
This study underscores the effectiveness of BO through its adaptive exploration-exploitation strategy, used here through the Ax platform [2], in streamlining the path from early experimentation to data-driven decision-making in rapid technology development.
[1] See, e.g., Greenhill et al. (2020). Bayesian Optimization for Adaptive Experimental Design: A Review. IEEE Access. PP. 1-1. 10.1109/ACCESS.2020.2966228.
[2] https://ax.dev/
[3] L.D. Burke and EJ.M. O’Sullivan, J. Electroanal. Chem., 93 (1978) 11-18.

Figure 1