Deep Kernel Learning for Reaction Outcome Prediction and Optimization

Chemical reaction optimization is crucial for organic synthesis, but exploring the vast multidimensional chemical space (reaction variables like catalyst, solvent, temperature, etc.) is challenging. Traditional approaches rely on chemical intuition, while data-driven methods offer efficient exploration. Accurate prediction of reaction outcomes (e.g., yield, enantiomeric excess) is essential to save resources by identifying low-yield reactions before conducting wet-lab experiments. Machine learning (ML), particularly deep learning (DL), has shown great potential in chemistry. Early efforts used hand-crafted features like physical organic descriptors and molecular fingerprints with conventional ML methods (e.g., random forests), achieving good results. However, recent advances in DL enable learning representations directly from molecular structures (SMILES, molecular graphs), with chemical language models and GNNs showing promise in reaction outcome prediction. Uncertainty quantification is vital for reaction optimization, particularly when using Bayesian optimization (BO), which uses uncertainty estimates to suggest new experiments. Gaussian processes (GPs) naturally provide uncertainty estimates, but their fixed kernels limit their ability to learn representations from the data, unlike NNs. This research addresses this limitation by combining the strengths of NNs (feature learning) and GPs (uncertainty quantification) within a DKL framework to create a robust and efficient model for reaction outcome prediction and optimization.

Existing machine learning models for reaction outcome prediction are typically tailored to either non-learned (molecular descriptors, fingerprints) or learned (SMILES, graphs) molecular representations. The authors review prior work highlighting the success of random forests with hand-crafted features and the emerging potential of deep learning methods like transformers and GNNs that directly learn representations from molecular structures. They emphasize the importance of uncertainty quantification for reaction optimization, particularly in Bayesian optimization, while noting the limitations of GPs in handling learned representations. The literature review sets the stage for the introduction of the DKL model as a solution that bridges the gap between representation learning and uncertainty quantification.

The authors propose a DKL model that integrates NNs and GPs to predict reaction outcomes with associated uncertainties. The model is tested on the Buchwald-Hartwig cross-coupling reaction dataset, encompassing various combinations of aryl halides, ligands, bases, and additives (3955 reactions). The study explores two main scenarios: DKL with non-learned and learned representations. For non-learned representations (molecular descriptors, Morgan fingerprints, and DRFP), a feed-forward NN with two fully connected layers extracts features from the concatenated input representation of the reaction components, which are then fed into a GP for prediction. For learned representations (molecular graphs), a message-passing GNN learns graph embeddings for each reactant, these embeddings are summed to obtain a reaction embedding, which is then processed by a feed-forward NN and fed into a GP. In both cases, the model is trained by jointly optimizing NN and GP parameters using the log marginal likelihood as the objective function. The model's performance is evaluated using RMSE, MAE, R-squared, and NLPD (negative log predictive density). Bayesian Optimization (BO) is then employed using the DKL model as a surrogate model, with expected improvement as the acquisition function. The BO process iteratively selects new reaction conditions from a held-out set, aiming to maximize the reaction outcome. The performance of BO using DKL is compared with BO using standard GPs and random search.

The DKL model significantly outperforms standard GPs across all input representations (molecular descriptors, Morgan fingerprints, DRFP, and molecular graphs), achieving lower RMSE values. For molecular descriptors, the DKL model achieves an RMSE of 4.87 ± 0.07, compared to 8.58 ± 0.06 for the standard GP. Similar improvements are observed for other representations. The DKL model’s performance is comparable to GNNs, but with the added benefit of uncertainty quantification. The negative log predictive density (NLPD) shows that DKL provides better predictive uncertainty estimations than standard GPs across all molecular representations. The correlation between absolute prediction error and uncertainty estimates in the MorganFP-DKL model is comparable to an ensemble of GNNs. Even with limited training data, DKL models generally outperform standard GPs. Feature analysis reveals that the DKL model extracts features more relevant to predicting yield compared to the original non-learned representations. In Bayesian optimization, the DKL model demonstrates superior performance compared to standard GPs and random search, effectively optimizing reaction conditions by selecting promising candidates based on the uncertainty estimates. The study shows that DKL is applicable to both learned and non-learned representations.

The DKL model successfully addresses the limitations of previous approaches by combining the representation learning power of NNs with the uncertainty quantification of GPs. The consistent improvement over standard GPs and the comparable performance to GNNs, along with the provision of uncertainty estimates, highlights the model's versatility and robustness. The successful application of the DKL model within a Bayesian optimization framework demonstrates its potential for accelerating reaction discovery and optimization. The feature analysis further supports the model's ability to extract task-relevant information, enhancing its predictive power. The findings suggest that DKL can be a valuable tool for chemists to improve reaction development and accelerate the discovery of optimized reaction conditions.

This research introduces a novel DKL model for reaction outcome prediction and optimization, demonstrating superior performance and uncertainty quantification compared to standard GPs and comparable results to GNNs. The model's applicability to both learned and non-learned molecular representations, along with its seamless integration into Bayesian optimization, positions it as a powerful tool for accelerating reaction discovery and optimization. Future work could explore other kernel functions, NN architectures, and acquisition functions to further enhance the model’s capabilities. Investigating the model's performance on a broader range of reaction types would also be valuable.

While the DKL model demonstrates significant improvements, its performance is dataset-specific. The study focused on the Buchwald-Hartwig cross-coupling reaction; further validation with other reaction types is necessary to establish broader applicability. The computational cost of training the DKL model, especially with learned representations, might be a limiting factor for very large datasets. The interpretation of the learned features within the DKL framework could be further explored to improve model interpretability.