Bayesian Optimization for Chemical Synthesis in the Era of Artificial Intelligence: Advances and Applications

Abstract

This review highlights recent advances in the application of Bayesian optimization to chemical synthesis. In the era of artificial intelligence, Bayesian optimization has emerged as a powerful machine learning approach that transforms reaction engineering by enabling efficient and cost-effective optimization of complex reaction systems. We begin with a concise overview of the theoretical foundations of Bayesian optimization, emphasizing key components such as Gaussian process-based surrogate models and acquisition functions that balance exploration and exploitation. Subsequently, we examine its practical applications across various chemical synthesis contexts, including reaction parameter tuning, catalyst screening, molecular design, synthetic route planning, self-optimizing systems, and autonomous laboratories. In addition, we discuss the integration of emerging techniques, such as noise-robust methods, multi-task learning, transfer learning, and multi-fidelity modeling, which enhance the versatility of Bayesian optimization in addressing the challenges and limitations inherent in chemical synthesis.

1. Introduction

Optimization challenges are present in chemical synthesis, ranging from the specific realm of reaction parameter optimization to broader domains, such as molecular design, synthetic route planning, and reaction prediction. Reaction optimization remains a complex, multi-dimensional challenge, even when objectives appear superficially simple, such as yield or selectivity. Within the extensive exploration space of practical chemical synthesis, the complex interactions among variables increase the financial cost of optimization [1,2]. Scientists have been struggling with how to accurately, efficiently, and economically obtain ideal optimization results. In recent years, significant advancements in artificial intelligence (AI) research have accelerated the development of intelligent optimization, offering viable solutions to a wide range of optimization problems [3,4,5]. As a useful tool in machine learning within the field of AI, Bayesian optimization has been widely used by chemists to solve complex and high-cost optimization problems [6,7,8]. Bayesian optimization is a sample-efficient and low-sample-cost global optimization strategy. It leverages probabilistic surrogate models and systematically explores the entire search space to achieve global optimization of complex systems. By iteratively balancing exploration and exploitation through probabilistic predictions, Bayesian optimization not only identifies global optimal solutions in multivariate scenarios but also avoids local optima, as shown in Figure 1 [9].

In principle, Bayesian optimization is a method for optimizing black-box functions that approximates the objective function by constructing probabilistic surrogate models in the chemical space of interest. Acquisition functions (AFs) are utilized to guide the selection of the next sampling points and update the model in Bayesian optimization, with this process repeated until the objective converges, which can be formulated as follows:

$$x^{*}=argmaxf\left(x\right),x\in X$$

(1)

where $X$ represents the chemical space of interest and $x^{*}$ represents the global optimum. Surrogate models construct approximations of the true objective function based on observed data. Gaussian process (GP), the most common surrogate model in Bayesian optimization [10], uses kernel functions to characterize the correlation between input variables and yield probabilistic distributions of objective function values. Additionally, other algorithms are employed as surrogate models, including Random Forests (RFs), Bayesian linear regression, and neural networks (NNs) [11,12,13]. Acquisition functions, another core component of Bayesian optimization, balance the need to explore new regions and exploit existing optimal solutions based on the predictions and uncertainty estimates of the surrogate model, thereby determining the next sampling point. This implies that these regions may harbor solutions superior to the current best-known result. Acquisition functions offer multiple options, including expected improvement (EI), Upper Confidence Bound (UCB), Thompson sampling (TS), q-Noise Expected Hypervolume Improvement (q-NEHVI), etc. [14,15,16,17].

This review systematically discusses the practical applications and the development of various models and algorithms in Bayesian optimization across diverse optimization domains.

2. Bayesian Optimization for Chemical Synthesis

2.1. The Evolution of Optimization Methods

Chemical process optimization is central to breakthroughs in chemical synthesis, while the complexity of chemical reactions remains a key challenge. This complexity arises because reactions are governed by multiple parameters, including temperature, reaction time, additives, solvents, and reactant concentrations. In chemical research, chemists aim to improve yield and optimize efficiency through systematic parameter tuning. Moreover, optimization strategies at different historical stages have shaped the implementation of experimental technologies and the evolution of research models. In the early stages, reaction optimization relied on the trial-and-error method, where researchers adjusted parameters based on experience and intuition. Although this approach reflected the empirical nature of chemical research, it was highly inefficient for multi-parameter reactions and struggled to overcome experiential limitations to achieve globally optimal results, thereby hindering progress in complex synthetic reactions.

To address the shortcomings of the trial-and-error method, the one-factor-at-a-time (OFAT) approach emerged. OFAT fixes other factors and changes only one factor at a time to determine the optimal value of that factor [18,19]. This method provided a structured framework for the optimization process and facilitated a shift from “experience-driven” to “parameterized exploration”. However, OFAT ignores interactions between factors, which leads to biased or suboptimal results and requires numerous experiments in complex systems. As chemical research advances toward the synthesis of complex systems, the demand for systematic optimization methods has become increasingly urgent. The development of machine learning has provided strong technical support for addressing such challenges, enabling data-driven, intelligent optimization of multi-parameter reaction spaces. Building on both local optimization and global optimization paradigms, many algorithms have been developed. For instance, the simplex method and gradient descent method for local optimization adjust parameters through mathematical models, substantially improving the efficiency of searching for local optima and supporting precision-regulated experimental models [20,21]. However, they rely on carefully chosen initial parameters and are often unsuitable for highly nonconvex, noisy, or discontinuous problems.

For global optimization, the developments of Design of Experiments (DoE) and algorithms such as SNOBFIT have enabled the systematic modeling and exploration of multi-parameter interactions [22,23,24]. Among these, DoE, a classical statistical framework, systematically plans experimental schemes, builds models based on experimental data (variables and objectives), and outputs experimental results in a mathematical way [25]. Compared with OFAT and local optimization methods, DoE explicitly accounts for relationships between variables and often achieves higher accuracy in searching for global optima [26]. However, DoE typically requires substantial data for modeling, which raises experimental costs and creates a tension between efficiency and resource constraints.

To address the above issues, Bayesian optimization has gradually been applied to reaction optimization in recent years, owing to its advantages of high efficiency and simplicity. In the following, we mainly introduce the recent studies on Bayesian optimization (BO) for chemical reaction optimization, which have made pivotal contributions to advancing Bayesian optimization and its applications in various optimization domains.

2.2. Applying Bayesian Optimization in Reaction Process Optimization

Reaction process optimization specifically refers to the optimization of continuous variables (e.g., temperature, concentration) and categorical variables (e.g., solvents, catalysts) with known value ranges, which is the most common type of reaction optimization in chemical synthesis. In the early development of Bayesian optimization, reaction parameter optimization served as the most intensively studied and fundamental optimization domain. In the following, we mainly discuss several of the most common acquisition function algorithms, Bayesian optimization frameworks, and supplementary cases that have advanced the development of this field.

2.2.1. The Development of AFs in Bayesian Optimization

Prior to the implementation of Bayesian optimization in practical chemical reaction optimization, extensive theoretical investigations into AFs were conducted within the academic community [14,15,16,17], thereby establishing a robust framework to inform the subsequent selection of such functions in practical applications. Subsequent to the publication of multi-objective Bayesian optimization (MOBO) research by the Lapkin group in 2018, the application of Bayesian optimization in real-world reaction optimization became widespread [27]. Before this, NSGA-II, one of the evolutionary algorithms (EAs), was widely applied to various simulation and realistic problems [28,29]. In 2018, Lapkin et al. first developed the Thompson Sampling Efficient Multi-Objective algorithm (TSEMO), an algorithm employing Thompson sampling with an internal NSGA-II, as an acquisition function and randomly sampled the function of the GP model via spectral sampling [30]. TSEMO was compared in performance with NSGA-II, ParEGO, and EHV, and it exhibited strong competitiveness. Subsequently, two cases were presented to prove the efficiency and accuracy of BO with TSEMO, as shown in Figure 2 [27]. Figure 2a shows the complete framework of BO: (1) A surrogate model is constructed using a small set of initially sampled data. (2) Based on the exploration–exploitation trade-off encoded by the acquisition function, points with the maximum expected improvement (one or several sets of new experiments) are identified. (3) Experiments are performed, and the resulting data are used to update the surrogate model. (4) This process is repeated until the predefined number of iterations is reached or experimental resources are exhausted, at which point the procedure stops. The residence time, equivalence ratio, concentration of reagents, and temperature were taken as variables, while the space–time yield (STY) and the E-factor were taken as the objectives. After 68 and 78 iterations, the Pareto frontiers were obtained. Their work offered valuable guidance for the practical implementation of BO, enabling more effective and efficient applications in relevant domains.

In 2021, the Lapkin group developed a framework named Summit to optimize chemical reactions [31]. They proposed two reaction optimization benchmarks and used them to compare the performance of seven strategies under diverse multi-objective transformation combinations, as shown in Figure 3. The results showed that while TSEMO incurred relatively high optimization costs, it exhibited the best performance across both benchmarks, with particularly strong gains in hypervolume improvement. On this basis, Lapkin et al. continued to explore and deepen the application scenarios of MOBO. They successfully employed TSEMO to conduct multi-objective optimizations on the synthesis of the nanomaterial antimicrobial ZnO and p-cymene [32,33]. In addition, in the optimization of ultra-fast lithium–halogen exchange, they utilized TSEMO as the acquisition function to rapidly develop the decision space and Pareto front within 50 experiments. One of the variables, the residence time, was accurately controlled within the sub-second range, demonstrating the capability of achieving precise control via Bayesian optimization [34]. Lapkin et al. proposed a hybrid optimization framework (TSEMO + DyOS), which was used for multi-objective optimization in pressure swing adsorption [35]. They compared the performance of TSEMO, DyOS, and NSGA-II and found that TSEMO achieved superior optimization results compared to NSGA-II, while DyOS exhibited higher search efficiency than TSEMO near the optima. Therefore, using TSEMO in the early exploration stage can quickly find the area near the optimal solution, and then using DyOS can accurately converge to the optimal solution. This hybrid method achieves fast and more accurate optimization performance at a low cost. A relatively mature process has been established for the Bayesian optimization of chemical reactions.

In the context of complex reactions, the negative impact of noise becomes increasingly pronounced. As reaction systems become more intricate, involving multiple reactants, side reactions, and dynamic reaction conditions, the presence of noise will interfere with the experimental data and hinder the accurate identification of the optimal reaction parameters. q-NEHVI, proposed by Daulton et al., can effectively tackle multi-objective Bayesian optimization problems in noisy environments [36]. Our research group first employed q-NEHVI as the acquisition function to simultaneously optimize three objectives (conversion, energy cost, and selectivity) in the continuous flow synthesis of hexafluoroacetone [37]. Subsequently, we conducted in silico tests to evaluate the noise-handling capabilities of q-NEHVI, q-EHVI, q-NParEGO, TSEMO, and Random. The results showed that q-NEHVI exhibited the best performance [38]. Moreover, we successfully applied it as the acquisition function to optimize the two-step continuous-flow synthesis of hexafluoroisopropanol. Subsequently, in 2024, Lapkin et al. also utilized q-NEHVI as the acquisition function to optimize the Schotten–Baumann reaction in a continuous flow platform [39] and found results similar to ours in terms of both hypervolume improvement and computational time. q-NEHVI offers strong performance in noisy environments and has lower computational costs than TSEMO. However, when tackling complex multi-objective problems, the algorithm does not support decoupled (per-objective) evaluation of individual objective dimensions, which limits its adaptability to the need for independent optimization of separate objectives. In 2025, Lapkin et al. developed a multi-objective Euclidean expected quantile improvement (MO-E-EQI) to identify the optimal reaction conditions under heteroscedastic noise [40]. Compared with q-NEHVI and TSEMO, MO-E-EQI demonstrated superior performance under high-noise conditions in in silico studies. However, this may come at the cost of increasing the number of repeated experimental measurements. In automated experimental platforms or large-scale manufacturing, where inexpensive sensor data can be obtained, MO-E-EQI appears to be a better fit. Continued algorithm development has created multiple routes to solve problems. Selecting an appropriately tailored acquisition function can significantly enhance optimization efficiency and reduce costs.

Table 1. The features of the acquisition function discussed in this section.

Year	AF	Feature	References
2018	TSEMO	the first efficient multi-objective optimization algorithm based on Thompson sampling, suitable for most MOBO	[27]
2021	TSEMO + DyOS	after rapid optimization with TSEMO in the early stage, switch to DyOS for more refined convergence	[35]
2023	q-NEHVI	suitable for multi-objective optimization with multiple parameters	[37,38,39]
2025	MO-E-EQI	exhibits excellent noise resistance performance	[40]

shows the respective features of the aforementioned acquisition functions.

2.2.2. The Development of the Bayesian Optimizer

The Aspuru-Guzik group has made significant contributions to Bayesian optimization. They have developed several Bayesian optimizers that have significantly advanced both the development and the deepened understanding of the field of Bayesian optimization. In 2018, Aspuru-Guzik et al. developed a Bayesian Optimizer, named PHOENICS, that is used for rapidly optimizing the unknown and costly evaluation objective function [41]. Phoenics combines the theory of Bayesian optimization with the concept of Bayesian kernel density estimation (BKDE). It uses a Bayesian neural network (BNN) as the surrogate model and employs expected improvement (EI) and its variants as the acquisition function. This algorithm proposes new conditions based on all previous observations, avoiding redundant evaluations. It achieves efficient parallel search through intuitive sampling strategies and can implicitly favor either the exploration or exploitation of the search space. The authors conducted benchmark tests on Phoenics, comparing it with Spearmint (GP) and SMAC (RF). The results demonstrated that Phoenics is less sensitive to the response surface than the other two algorithms. It provides an effective solution for dealing with problems of objective functions with high evaluation costs.

In 2021, Aspuru-Guzik et al. developed the Gryffin algorithm by extending the PHOENICS approach from continuous to categorical domains, where previous research has been limited [42]. It aims to perform Bayesian optimization on categorical variables by utilizing expert knowledge [43]. By combining kernel density estimation (KDE) and smooth approximations of the categorical distribution, this Bayesian optimizer significantly accelerates the search for promising molecules and materials. In their paper, a comprehensive analysis of Gryffin summarizes its advantages and areas for improvement, providing a viable strategy for optimization tasks of categorical variables in scientific and engineering fields.

The Bourne group collaborated with Lapkin’s group in the early stage of the development of Bayesian optimization [27,44]. In 2021, Bourne et al. proposed MVMOO to explore the application of Bayesian optimization in mixed-variable scenarios [45]. In MVMOO, the GP served as the surrogate model, and the Gower distance metric was utilized as the covariance function to describe the GP [46]. The expected improvement matrix (EIM), a matrix used to evaluate the improvement potential of the search space, served as an acquisition function. Compared to the EI, the EIM is more suitable for comprehensively considering mixed variables [47]. MVMOO was employed to optimize three chemical problems (Discrete VLMOP2, Ordinary Differential Equation catalytic system, and Fuel Injector design) and compared with the random sampling method and the NSGA-II algorithms. The results demonstrate that MVMOO is a feasible and efficient strategy for optimizing expensive multi-objective problems with mixed variables.

2.2.3. Integrating Reaction Constraints with Bayesian Optimization

A multitude of constraints are confronted in the practical implementation of Bayesian optimization. These constraints may include limitations of material properties, hardware restrictions, and safety concerns. To address these constraint issues, Aspuru-Guzik et al. carried out a further expansion of Gryffin, endowing it with the capability to manage any known constraints via an intuitive and flexible Python interface in 2022 [48]. Compared with the Gryffin algorithm, the constrained Gryffin algorithm has the following adjustments: adjusting the kernel precision of the Gaussian process, performing rejection sampling to retain only the samples that meet the restrictive conditions, and adjusting the acquisition function using the Adam algorithm, the Hill algorithm, or the genetic algorithm. In the optimization of o-xylenyl C₆₀ adduct synthesis, the constrained Gryffin algorithm was capable of rapidly optimizing constrained conditions, including the total flow rate of C₆₀ and sultine (10–310 μL/min) and temperature (100–150 °C), as shown in Figure 4. Additionally, in the design of redox-active materials for flow batteries, this algorithm enabled the selection of molecules based on a retrosynthetic accessibility score (RA score > 0.9).

Besides the known constraints, certain constraints are unknown a priori in the realm of chemical process optimization, such as equipment problems and changes in the inherent properties of materials. In response to the problem of unknown constraints, Aspuru-Guzik et al. utilized a variational Gaussian process classifier to learn the constraint function in real-time and combined it with a typical Bayesian optimization regression surrogate to parameterize a feasibility-aware acquisition function [49]. They conducted in-depth discussions and benchmark tests on various strategies for dealing with Bayesian optimization problems involving unknown constraints. For example, in the benchmark test of continuous parameter problems, FCA-0.5 and FIA-1, which are strategies characterized by moderate risk aversion, demonstrated optimal performance. These works provide valuable strategies for dealing with Bayesian problems involving known or unknown constraints and enhance the capability of Bayesian optimization to tackle diverse problem scenarios.

In the study of yield optimization for multi-reactor systems, Grimm developed process-constrained batch Bayesian optimization (pc-BO-TS) and its generalized hierarchical extension (hpc-BO-TS) [50], both of which improve optimization efficiency through a hierarchical parameter structure and recursive tree search. Compared with pc-BO-TS, hpc-BO-TS first optimized the global constraint parameter, i.e., flow rate (5–50 mL/min), using UCB and then optimized the temperatures of four blocks (520–590 °C) to obtain the optimal combination of the flow rate and the four temperatures. In contrast, pc-BO-TS only optimized the four temperatures under a fixed flow rate (30 mL/min). Through 13 iterations and 25 iterations, respectively, pc-BO-TS and hpc-BO-TS improved the initial yield of 75% to 92.3% (30 mL/min and Block 1 = 560 °C, Block 2 = 550 °C, Block 3 = 570 °C, Block 4 = 540 °C) and 95.1% (45 mL/min and Block 1 = 580 °C, Block 2 = 570 °C, Block 3 = 560 °C, Block 4 = 590 °C). Their work effectively addresses hierarchical constrained parameters and provides an efficient framework for multi-reactor systems, promoting the development of digital chemistry.

2.2.4. Comparative Studies with Other Traditional Optimization Methods

Compared with traditional optimization methods, Bayesian optimization exhibits significant advantages in optimization efficiency, owing to its low dependence on black-box functions and the directional search strategy of acquisition functions.

In the design of accelerating formulation, Narayanan et al. optimized eight experimental parameters through Bayesian optimization and the DoE method to obtain formulations with high thermal stability [51]. After optimization, Bayesian optimization converged within 25 experiments, while DoE required 128 experiments to achieve the same optimal result, demonstrating that Bayesian optimization is more efficient in reducing the number of experiments. In a study on the coupling reaction of methyl-4-formylbenzoate and phenyllithium, Lehmann et al. selected the total flow rate and the molar ratio as experimental parameters and employed Bayesian optimization and SNOBFIT, respectively, to optimize the selectivity [52]. Bayesian optimization converges with 14–17 experiments, which was fewer than the over 20 experiments required for SNOBFIT to reach convergence. Similar comparative work by Pickles on the design of cooling crystallization using adaptive Bayesian optimization (AdBO) showed that the number of experiments required by AdBO was less than half of that required by DoE [53]. Without reducing accuracy, Bayesian optimization greatly speeds up experimental development capabilities and decreases experimental costs.

Our group also compared Bayesian optimization with kinetic modeling in optimizing chemical reactions and elaborated on their respective advantages and disadvantages [54,55]. While Bayesian optimization lacks the ability to generate a comprehensive response surface across the entire chemical space, its efficiency and accuracy are undoubtedly commendable compared to the number of experiments required for kinetic modeling.

Table 2. A performance comparison between Bayesian optimization and other methods.

References	Num Parameters	Num Objectives	Num Experiments
			BO	DoE	SNOBFTT	Kinetic Model
[51]	8	3	25	128	/	/
[52]	2	3	14–17	/	>20	/
[53]	2	3	32	70	/	/
[54]	4	1	20	/	/	>50
[55]	4	2	40	/	/	>60

shows a performance comparison between Bayesian optimization and other methods.

2.3. Bayesian Optimization with a Focus on Cost Awareness

In optimization challenges, in addition to optimizing target performance metrics (e.g., yield, selectivity), it is imperative to account for the implicit costs (e.g., temperature, reaction concentration, solvent consumption) embedded in the optimization process. The key to achieving sustainable optimization lies in systematically integrating these multi-dimensional cost factors while ensuring the target performance remains uncompromised.

Corminboeuf et al. proposed a cost-informed Bayesian optimization (CIBO) framework, which introduces experimental costs into the acquisition function [56]. Compared with standard BO, CIBO considers cost factors, including reagent, energy consumption, new reagent purchase, and time costs, rather than immediately adopting new reagents, thus leading to an increase in the number of experiments, as shown in Figure 5. Their study investigates the optimization of two Pd-catalyzed reactions, including direct C-H arylation (DA reaction) and Buchwald–Hartwig cross-coupling (CC reaction), using standard BO and CIBO. It found that in the DA reaction, BO achieved a 99% yield after 25 experiments, while CIBO required 40 experiments to obtain the same yield with a 43% reduction in total cost. For the CC reaction, CIBO significantly reduced costs for different amine nucleophile subsets, as shown in

Table 3. The comparison of cost reduction between standard BO and CIBO in the CC reaction [56].

Amine Nucleophile Subsets	The Cost of Standard BO	The Cost of CIBO	Cost Saved
aniline (An) subset	USD 2474	USD 1124	USD 1350 (54%)
phenethylamine (Ph) subset	USD 2170	USD 142	USD 2028 (93%)
morpholine (Mo) subset	USD 2105	USD 2105	USD 0
benzamide (Be) subset	USD 2144	USD 690	USD 1454 (68%)

.

In addition, Yuan et al. introduced CAPBO [57] and CABO [58], two cost-aware Bayesian optimization frameworks, to minimize experimental costs. By allocating reagent, time, and environmental costs and controlling the weight of these costs through dynamic penalty coefficients in the AF, CAPBO achieves fine-grained management of multi-dimensional costs. Meanwhile, by introducing constraint factors, cost optimization is achieved on the basis of ensuring yield. These works guided how to conduct optimization at a lower cost by systematically integrating multi-dimensional cost factors.

2.4. Integrating Bayesian Optimization into Catalyst Screening

Catalysts are regarded as categorical variables. In some cases, scientists usually screen catalysts within the scope they have specified. For such problems, catalysts are often simply labeled in the form of one-hot encoding [59,60], and Bayesian optimization is used to optimize both continuous variables and categorical variables simultaneously. Our group conducted relevant studies on the screening of catalysts within a specified range [61,62]. In the study of chiral phosphine ligands for the efficient asymmetric hydrogenation of β-keto esters in a continuous flow system, different ligands selected through manual screening are labeled using one-hot encoding. Bayesian optimization is then employed to simultaneously optimize reaction parameters, such as ligand types, temperature, and pressure. While the combination of one-hot encoding and Bayesian optimization shows potential in simplifying catalyst screening within predefined scopes, this approach remains constrained by manually selected candidate pools. This reveals a critical limitation in that the evaluation of the intrinsic properties of catalysts remains inherently inefficient. To overcome the efficiency bottleneck of traditional catalyst screening, an advanced catalyst screening method is urgently required. Mordred [63] and density functional theory (DFT) [64] provide quantitative features for analyzing catalyst properties. Mordred extracts empirical descriptors, such as topological, compositional, and physicochemical properties, from molecular structures. It is fast and has a low computational cost. By contrast, DFT, a quantum chemical calculation method, generates high-fidelity descriptors of molecular physicochemical properties but at a substantially higher computational cost. Together, these approaches offer a promising route to catalyst screening.

In 2021, Doyle et al. developed Experimental Design via Bayesian Optimization (EDBO) [65], a platform that optimizes chemical reactions by optimizing descriptor-based variables (descriptors of physical, chemical, and quantum chemical properties). Doyle et al. employed the GP with the Matérn52 kernel [66] as the surrogate model and EI as the acquisition function. By leveraging descriptor methods, they quantified various parameters (e.g., HOMO/LUMO energies, binding energies in ligands, solvent polarity, dielectric constant) to optimize reactions. This approach enables systematic integration of quantum chemical information into Bayesian optimization, facilitating data-driven discovery of optimal reaction conditions. They compared three descriptor methods (DFT, Mordred, and OHE) and found that DFT performed best. In this platform, they successfully optimized the Mitsunobu and deoxyfluorination reactions with descriptor-based variables (e.g., substrates, ligands, solutions) and general variables (e.g., temperature, reaction time, concentration) to achieve the maximum yield. After only 40 experiments, three sets of Mitsunobu reaction conditions with yields of 99% were obtained from the 180,000 possible combinations in chemical space, surpassing the benchmark result of 60%. Moreover, one of these sets employed an unconventional phosphine reagent (P(Ph)₂Me), which is not typically considered by chemists. In the optimization of the deoxyfluorination reaction, after 50 experiments, conditions with yields of 69% were achieved from the 312,500 possible combinations, surpassing the benchmark result of 36%. EDBO offers an innovative solution for experimental design in chemical synthesis, harnessing the unique advantages of overcoming human experiential limitations and enabling efficient exploration of uncharted reaction spaces.

In 2022, Doyle et al. reported EDBO+, an extended application of EDBO that facilitates the advancement from single-objective to multi-objective optimization [67]. Similar to EDBO, they compared different descriptor methods (DFT, Mordred, and OHE) to visualize ligand information and found that DFT performed best; therefore, they continued to use DFT as the ligand descriptor for subsequent testing. In their work, EI was replaced with q-Expected HyperVolume Improvement (q-EHVI) as the acquisition function [68]. They successfully employed EDBO+ to simultaneously optimize yield and enantioselectivity in a Ni/photoredox-catalyzed enantioselective cross-electrophile coupling of styrene oxide with two different aryl iodide substrates involving 1728 possible combinations (three nickel precatalysts, sixteen bioxazoline and biimidazoline ligands, two additives, three solvents, three concentrations, and two light sources), as shown in Figure 6. EDBO+ optimized the reaction of styrene oxide with 4-iodobenzoate, outperforming 500 manual experiments in just 24 experiments (the yield rose from 70% to 80%, while the % ee was unchanged). For the other substrate, the optimization of 2-fluoro-5-iodopyridine synthesis achieved superior results compared to previously reported ones in just 15 experiments (the yield rose from 49% to 59%, and the % ee rose from 76% to 77%).

In 2024, Doyle et al. studied the stereoconvergent synthesis of trisubstituted alkenes in two steps from simple ketone starting materials. They produced a dataset (96 experiments) including yields and diastereoselectivity results via the parallel screening of 47 monophosphine ligands by High-Throughput Experimentation (THE) [69]. EDBO+ enabled the selection of conditions for E- and Z-alkene formation from over 30,000 reaction combinations within only 25 experiments each. After optimization, the diastereoselectivity for E-alkene formation was improved from 87:13 to 91:9, and the yield increased from 90% to 94%. For Z-alkene formation, the diastereoselectivity was improved from 69:31 to 88:12, with the yield surging from 35% to 92%. This approach reduced the optimization time from the weeks required by OFAT to hours, significantly improving optimization efficiency and reducing experimental costs.

Based on Doyle’s work, Godineau et al. employed EDBO-TS, EDBO-EI, and Automus-UCB to investigate the copper-catalyzed C-N coupling of sterically hindered pyrazines and evaluated their performances. EDBO-EI achieved the highest yield of 87% most rapidly, Automus-UCB demonstrated more stable convergence, and EDBO-TS performed relatively the worst in overall performance [70]. In addition, similar work involved describing catalysts using descriptors to obtain different catalyst formulations and optimizing catalysts and reaction parameters via Bayesian optimization [71,72,73]. The combination of DFT and Bayesian optimization accelerates the development of new catalysts, opening up new avenues for the rational design of catalysts with higher activity.

2.5. Bayesian Optimization Coupled with Transfer Learning

The essence of transfer learning is cross-task knowledge migration, which accelerates the learning of new tasks by reusing existing knowledge. Combining Bayesian optimization with TL can effectively enhance a model’s performance and decision-making capabilities in complex scenarios. Kim et al. proposed a Hybrid Dynamic Optimization (HDO) algorithm, which specifically addresses the cold-start problem of Bayesian optimization by using Message Passing Neural Networks (MPNN), as shown in Figure 7a [74]. MPNN pre-screens over 1 million reaction datasets from the Reaxys database and constrains reaction conditions to narrow the chemical space. Figure 7b shows that HDO significantly accelerates the efficiency of reaction optimization and reduces the total number of experiments required through an intelligent sampling strategy screened by MPNN.

Although the notion of multi-task Bayesian optimization (MTBO) may have been initially conceptualized in prior studies [75,76,77], its practical application in reaction optimization was not successfully realized until 2023 by Lapkin [78]. MTBO simultaneously optimizes multiple related tasks by capturing the dependencies between tasks and making use of knowledge transfer, enabling more accurate modeling, reducing the number of samplings, and enhancing the optimization efficiency. Lapkin et al. successfully used the MTBO algorithm to determine the optimal conditions for C-H activation reactions of different substrates in unseen experiments, which proved that MTBO is an effective optimization strategy.

Pedersen et al. developed an optimization method for carbohydrate protecting group chemistry based on BO and TL [79]. First, BO was employed to optimize the reaction parameters (including solvent, concentration, base, etc., totaling seven parameters) for the monoacylation and diacylation of glucose, generating 96 experimental data points. Subsequently, 71 of these datasets were transferred via TL to optimize the monoacylation and diacylation reactions of α-thiomannoside, achieving convergence in only 23 and 20 experiments, respectively, as shown in Figure 8. Utilizing the 71 sets of glucose experimental data together with the data generated from the α-thiomannoside reactions, TL and BO were applied to optimize the diacylation and monoacylation of β-galactose. Convergence was achieved in just 17 and 21 experiments for the diacylation and monoacylation reactions, respectively. By transferring experimental data from similar reactions, the optimization speed could be significantly accelerated.

In the research on the continuous-flow synthesis of O-methylisourea, our group first optimized the small-scale reaction conditions by Bayesian optimization [80]. Subsequently, by combining transfer learning with Bayesian optimization to perform rapid optimization of the reaction scale-up process, we enhanced the reaction productivity to 10 times its original level in just 10 iterations, marking a significant breakthrough.

2.6. Bayesian Optimization in the Context of Molecular Design

Screening for molecules with specific properties is one of the core challenges in drug discovery. Traditional high-throughput screening methods, while effective, tend to demand vast amounts of time, resources, and experimental data. However, the development of Variational Autoencoders (VAEs) [81] has provided chemists with a powerful tool for efficiently exploring chemical space. Based on VAEs, Jin et al. proposed a molecular generation method named JT-VAE and screened molecules with desired chemical properties through Bayesian optimization [82]. The sparse Gaussian process (SGP) for Bayesian optimization was trained using the latent vectors of 250,000 molecules in the ZINC database and property data, such as logP and SA score. By using the EI as the acquisition function and iterating five runs, more than 50 high-potential molecules with logP scores over 3.5 were successfully discovered.

In 2020, Griffiths et al. proposed a molecular generation method based on constrained Bayesian optimization [83]. They trained a VAE on 249,456 molecules from the ZINC database to generate molecular libraries and constructed a BNN as the AF to evaluate the probability of generating valid molecules at latent points. Using objective functions such as logP and QED, after 20 iterations, the validity of the generated molecules improved from 12–51% in the baseline model to 86–97%. Bayesian optimization enables an efficient search for specific molecules in the latent space of VAEs, accelerating the discovery of novel molecules with optimized properties.

In 2025, Jensen’s team first showed the multi-fidelity Bayesian optimization (MFBO) method in an autonomous molecular discovery platform for the prospective search of novel histone deacetylase inhibitors, as shown in Figure 9 [84]. In their work, Jensen et al. first compared the performance among different surrogate models (GP, Random Forest (RF), and Natural Gradient Boosting) and determined that the GP with Morgan fingerprints [85], using a Tanimoto Kernel [86], performed the best. Meanwhile, the EI was used as the acquisition function. They obtained original data from public databases (ChEMBL) and constructed a low-fidelity database and a medium-fidelity database using DiffDock docking and the Hill equation, respectively. Subsequently, MFBO was employed to identify low-fidelity and medium-fidelity databases to generate high-fidelity candidates within an autonomous molecular discovery platform. To acquire a dose-response curve, which is a direct measurement of potency, they synthesized high-fidelity candidates manually and determined their pharmacological effects. After several rounds of iteration to continuously refine the search results, conducting manual synthesis, and measuring dose–response curves, a few new and effective histone deacetylase inhibitors were discovered. This autonomous molecular discovery platform, leveraging multi-fidelity data and MFBO, rapidly screens high-potential molecules, broadening the application and power of Bayesian optimization.

2.7. Leveraging Bayesian Optimization in Synthetic Route Planning

The optimization and innovation of chemical reaction routes essentially pursue efficiency and sustainability. An efficient synthesis route enables researchers to shorten the production cycle, reduce costs, and accelerate the research and development of new compounds. Data-driven approaches based on AI have demonstrated remarkable auxiliary efficacy in the field of route planning [87,88,89]. Despite the excellent performance of Bayesian optimization in various fields, as previously described, there remains room for improvement in its development for synthetic route planning.

Retrosynthesis poses more challenges than forward synthesis. The precision of the deduced routes is relatively low, and there is a risk of dimensional explosion [90]. However, it is certain that the diversity of the inferred routes far exceeds that of forward synthesis. Regarding this, Yoshida et al. proposed a Bayesian retrosynthesis framework that generates target molecule products by training a forward model and uses Bayes’ theorem to inversely search reactant databases for feasible synthetic routes [91]. By using a forward model as a probability calculator for retrosynthesis to evaluate whether the reverse-derived reactant combinations can generate the target product, this strategy has greatly improved the reliability and efficiency of retrosynthetic pathways. The algorithm employs Gradient Boosting Regression (GBR) as a surrogate model and integrates Sequential Monte Carlo (SMC) to assist the AF in iteration. Optimization results show that it achieves an 81.8% top-10 accuracy in single-step reactions, reproduces 33.3% of known routes in two-step reactions, and generates thousands of new routes verified as feasible by experts.

Westerlund et al. utilized Optuna [92], a Bayesian optimization framework, to optimize the Component of the Monte Carlo Tree Search (MCTS) strategy, a key pathway in the AiZynthFinder retrosynthesis tool [93]. Although the final testing revealed that parameters optimized via Optuna exhibited superior optimization speed compared to systematic grid search (a manual analytical approach), their ultimate performance remained inferior to manually determined parameter values. Nevertheless, their study provided a new methodological exploration for the Bayesian optimization of route planning parameters.

2.8. Bayesian Optimization Integrated with Self-Optimization Platforms

Self-optimization is an automated improvement process achieved through a closed-loop feedback mechanism, capable of receiving and executing reaction conditions without human intervention. The core of this approach lies in integrating Process Analytical Technologies (PATs), automation technology, and reaction optimization algorithms to build a complete cycle of “perception–analysis–decision–execution” in a self-optimizing system. This integration enables dynamic tuning of chemical reactions or catalytic processes.

The self-optimizing platform developed by Lapkin in 2020 demonstrated remarkable efficiency in optimizing the Sonogashira reaction, achieving excellent results in terms of the three objectives: purity, STY, and reaction mass efficiency (RME) [44]. The self-optimizing platform integrated Bayesian optimization and automated control technologies. Leveraging TSEMO as the acquisition function, the self-optimizing platform achieved optimization of the Sonogashira reaction in just 13 h. Compared to conventional optimizations, which required weeks to complete, this platform significantly enhanced the efficiency of optimization.

Kappe’s team has long been dedicated to the research of continuous flow reactions [94,95,96,97,98]. As the concept of self-optimization continues to deepen, Bayesian optimization, as an effective strategy for self-optimization, has become increasingly important. Kappe et al. published research stating that PATs, as a crucial bridge connecting self-optimization and Bayesian optimization, play an indispensable role in providing real-time feedback data for Bayesian optimization [99,100]. Owing to the substantial prior research efforts dedicated to Bayesian optimization, Bayesian optimization reaches a level of accessibility that allows researchers with diverse backgrounds to engage with it relatively easily.

In 2022, Kappe et al. developed a closed-loop experimental platform for reaction self-optimization and tested it for single-step and multi-step reaction self-optimization, as shown in Figure 10 [101]. In this platform, they used the GP and TSEMO as a surrogate model and the AF, respectively, and selected the SNAr reaction between morpholine and 3,4-difluoronitrobenzene as the single-step self-optimization reaction test. The conversion and the STY were used as optimization objectives, and four variables were optimized simultaneously: concentration, temperature, residence time, and equivalents of morpholine and triethylamine base. After self-optimization, the final conversion was >95% and the STY was >4.3 kg L⁻¹ h⁻¹. The two-step synthesis of edaravone was selected as a multi-step self-optimization test. To test the optimization limits of the closed-loop experimental platform, they simultaneously optimized the two steps of the reaction, integrated seven optimization variables into a chemical space, and set three optimization goals (maximizing solution yield, maximizing the STY of edaravone, and minimizing overall equivalents of reagents used). After 85 iterations, the trade-off relationship among the three was obtained. Their work demonstrated that the self-optimization platform exhibited remarkable capabilities when faced with complex chemical spaces. Following this, the Kappe group advanced the field of reaction self-optimization through a series of publications leveraging Bayesian optimization [102,103]. These works have enriched the practical experience and theoretical framework of self-optimization platforms for subsequent applications.

Subsequently, Bourne et al. built a self-optimizing continuous flow platform equipped with MVMOO to automatically optimize nucleophilic aromatic substitution (S_NAr) and Sonogashira cross-coupling reactions [104]. In the optimization of the S_NAr reaction, the solvent was regarded as a categorical variable, and temperature, residence time, equivalents, and concentration were chosen as continuous variables. After 74 iterations in 18 h without human intervention, a trade-off curve for the formation of ortho-isomer and para-isomer was obtained. In the Sonogashira reaction, a series of monodentate phosphine ligands were selected as categorical variables, and residence time, equivalents, and temperature were selected as continuous variables. The optimal ligand and the STY were obtained through 69 experiments completed within 22 h. The combination of Bayesian optimization and automation technology greatly accelerated the optimization. In the subsequent years, Bourne and colleagues devoted their efforts to investigating the development of self-optimization platforms [105,106,107,108,109], as shown in Table 3. Within this research framework, Bayesian optimization, as a self-optimization strategy, demonstrates remarkable adaptability.

Jensen et al. conducted self-optimization of the multiphase diastereoselective metallaphotoredox cross-coupling reaction [110] via the Dragonfly open-source package [111,112]. The GP was used as a surrogate model, and UCB and TS are used as acquisition functions. The UCB or TS acquisition function was selected with equal probability to generate new experiments. They input two types of photocatalysts as categorical variables and temperature, residence time, and solvent composition as continuous variables, aiming to optimize yield and diastereoselectivity. The self-optimization process concluded after 15 runs, during which an operational error took place in the eighth run. However, the algorithm still obtained results close to the true Pareto front, demonstrating the robustness and high efficiency of the algorithm.

Likewise, using the Dragonfly Bayesian framework, Viswanathan developed the automatic experimental platform Clio and optimized non-aqueous lithium battery electrolytes. Six electrolytes meeting the expectations were screened out through 42 experiments within two working days [113]. Similar to Jensen’s work [110,114], their study demonstrated a successful implementation of fully automated experimentation by integrating the Dragonfly framework with advanced automation technologies, enabling efficient reaction optimization. Self-optimization technology is an integrated product of experimental design, process control, and result analysis, which significantly enhances the optimization efficiency and precision of complex systems while greatly reducing experimental and labor costs.

Table 4. Research on self-optimization platforms.

Year	Case	Optimization Parameters	Optimization Objectives	AFs or Optimizer
2022	Autonomous multi-step and multi-objective optimization facilitated by real-time process analytics [101]	temperature; concentration; residence time; equivalents	conversion; STY	TSEMO
2024	Self-optimization platform with Multiple Process Analysis [102]	loading of amine and catalyst; equivalents; concentration; temperature	STY; yield; cost	TSEMO
2024	Three AFs compared in the self-optimization system [103]	equivalents; concentration; temperature; residence time; coupling reagents	yield	EI; TSEMO; BOAEI
2023	Self-optimization of mixed variable chemical systems [104]	solvent; ligands; temperature; equivalents; concentration	STY; RME; optimal ligand;	MVMOO
2022	Closed-loop optimization of polymer synthesis [105]	temperature; residence time; types of RAFT agents; initiator concentration	monomer conversion; molar mass dispersity	TSEMO
2023	Autonomous synthesis optimization for 1-methyltetrahydroisoquinoline C5 functionalization precursor [106]	temperature; residence time; equivalents; flow rate ratio	yield	BOAEI
2024	Self-optimization of two-step synthesis of Paracetamol [107]	temperature R1; temperature R2; nitrophenol flow rate; flow rate ratio	yield	BOAEI
2024	Operator-free HPLC method development guided by Bayesian optimization [108]	initial organic modifier; concentration; gradient time	number of peaks; resolution; the elution time of the last peak	TSEMO/BOAEI *
2025	Self-optimizing purification of DEHiBA [109]	solvent ratio; acid concentration; alkali concentration	purity; recovery rate	BOAEI *
2022	Continuous stirred-tank reactor cascade platform for self-optimization of reactions involving solids [110]	photocatalysts; temperature; residence time; solvent composition	yield; diastereoselectivity	Dragonfly
2022	Autonomous optimization of non-aqueous Li-ion battery electrolytes [113]	ternary solvent combination; concentration	ionic conductivity	Dragonfly

* BOAEI conducts single-objective optimization after performing a weighted treatment on multiple objectives.

shows the key details of research on self-optimization platforms.

2.9. Bayesian Optimization in Self-Driven Laboratories (SDLs): Intelligent Agents

SDLs mark a paradigm shift toward full automation of the scientific workflow. Unlike self-optimization platforms that focus solely on process optimization, SDLs act as intelligent agents, spanning hypothesis generation, experimental planning, execution, and analysis. SDLs represent the future direction of scientific experiments and are regarded as the next-generation cutting-edge technology for autonomous scientific experimentation. SDLs are typically equipped with robotic arms or robots for automated execution of experimental operations, which can simulate the hand movements of lab technicians to achieve truly unmanned experimental procedures. The functional scope of SDLs not only covers reaction optimization but also extends to more comprehensive scientific research areas such as catalyst screening and specific molecule discovery.

Designing ternary blends was important for improving the efficiency and stability of organic photovoltaics (OPVs). In 2019, Aspuru-Guzik et al. established an SDL to study quaternary blends and further enhance the stability of OPVs, as shown in Figure 11 [115]. However, when facing highly complex optimization problems in a multi-dimensional composition space with hundreds of potential candidate performance-enhancing additives, it was costly to optimize this problem. They employed HTE technology, introducing an automatic film-forming method and a robotic drop-casting technique to rapidly conduct a large number of experiments. This technology is capable of preparing up to 6048 sets of films with different compositions per day. By leveraging Bayesian optimization, with the BNN serving as the surrogate model, the system autonomously evaluated and designed subsequent experiments, accelerating process optimization and material discovery. In the complex operational scenarios of SDLs, Bayesian optimization demonstrates remarkable adaptability and high practicality.

Additionally, Aspuru-Guzik et al. developed Atlas, a Python library for Bayesian optimization, which was designed to precisely meet the requirements of SDLs [116]. As open-source software, Atlas integrates previous Bayesian optimization algorithms, such as multi-objective, multi-fidelity, and constrained Bayesian optimization, and includes documentation that discusses most of the previous cases. This provides a systematic approach to Bayesian optimization parameter tuning and practical optimization parameter configuration strategies, enabling the provision of technical support for SDLs.

The Aspuru-Guzik team has constantly explored the field of SDLs. Based on previous work, they deeply analyzed the current situation of SDLs and applications of SDLs in different disciplines. They also summarized Bayesian optimization methods as planning strategies in SDLs and possible challenges in software or hardware [117]. In 2025, Aspuru-Guzik et al. developed an AFION lab, which could synthesize plasmonic nanoparticles (NPs) according to different requirements without human intervention [118]. The AFION lab integrated continuous flow technology, online spectral NP characterization, and machine learning technology, carrying out photochemical synthesis according to the set conditions to obtain the desired spectral characteristic targets. In the AFION lab, the model was updated, and the experimental conditions for the next run were determined by the Gryffin and Chimera algorithms. This cycle continued until the target was reached. By setting different spectral targets, the AFION laboratory successfully synthesized eight types of NPs, and the shapes, sizes, and compositions all met expectations. Seven initial parameters were set, including the concentrations of four reagents, reaction time, light intensity, and slug oscillation speed. On average, the optimal reaction conditions for each type of NP could be found with less than 30 experiments and within 30 h, demonstrating the outstanding efficiency of the AFION lab. Their work drives the development of the nanomaterial synthesis field and enriches the content of SDLs.

An increasing number of research teams are engaging in the development of SDLs equipped with BO. Noël et al. reported that the structure of SDLs involves coordination and compatibility between software and hardware and pointed out that Bayesian optimization serves as an effective optimization approach [119]. Meanwhile, Noël et al. developed a robotic platform called RoboChem for the self-optimization, intensification, and scaling-up of photocatalysis using BO as the optimization method [120]. Their work improves operational safety and liberates researchers as well. Additionally, Choi et al. developed an SDL, called Synbot, which incorporates multiple functional modules, as shown in Figure 12 [121]. Synbot planned synthetic pathways and defined reaction conditions, subsequently iteratively refining these plans using feedback from the experimental robot to gradually optimize the recipe using BO. This process successfully established the synthetic recipes for three target organic compounds. The development of Synbot is expected to accelerate the innovation process in fields such as new drug development and functional material research. Bayesian optimization guides SDLs to prioritize high-potential experiments, serving as a key technical driver that pushes SDLs toward autonomous and efficient scientific exploration.

3. Conclusions

This review highlights the innovative applications and recent advances of Bayesian optimization for chemical synthesis in the era of AI. Bayesian optimization offers remarkable advantages: by building probabilistic surrogate models and using acquisition functions to dynamically balance exploration and exploitation for an efficient search, Bayesian optimization significantly improves experimental efficiency, reduces costs, and mitigates the limitations of traditional heuristics. As discussed above, Bayesian optimization has been widely adopted for reaction optimization. Meanwhile, Bayesian optimization is highly scalable and has shown strong performance in adjacent areas, including molecular design, synthetic route planning, catalyst screening, and the integration of automation technologies. These integrations are accelerating the shift from labor-intensive, iterative experimentation to data-driven, AI-enabled paradigms in chemical synthesis, opening new pathways to address complex chemical challenges.

The future of laboratories points toward greater intelligence. With applications in reaction optimization maturing, a key direction is the development of more efficient, intelligent, and accurate chemical foundation models grounded in Bayesian optimization [122]. By leveraging transfer learning to extract knowledge and features from databases, such models can achieve strong generalization and high reliability, enabling rapid adaptation to sub-tasks within a domain and facilitating knowledge transfer across diverse scenarios. These foundation models are expected to address a wide range of problems across fields, including chemical-related tasks, such as predicting yields, inferring compound structures and properties, and discovering new materials and catalysts [123,124]. In parallel, automated hardware requires urgent upgrades. Establishing standardized and integrated hardware frameworks is crucial for enabling the convergence of interdisciplinary technologies and breaking down technical barriers in chemical synthesis. A tightly integrated software–hardware experimental platform will propel chemical synthesis into a new era of intelligent optimization.