  The identification of synthetic routes that end with a desired product has
been an inherently time-consuming process that is largely dependent on expert
knowledge regarding a limited fraction of the entire reaction space. At
present, emerging machine-learning technologies are overturning the process of
retrosynthetic planning. The objective of this study is to discover synthetic
routes backwardly from a given desired molecule to commercially available
compounds. The problem is reduced to a combinatorial optimization task with the
solution space subject to the combinatorial complexity of all possible pairs of
purchasable reactants. We address this issue within the framework of Bayesian
inference and computation. The workflow consists of two steps: a deep neural
network is trained that forwardly predicts a product of the given reactants
with a high level of accuracy, following which this forward model is inverted
into the backward one via Bayes' law of conditional probability. Using the
backward model, a diverse set of highly probable reaction sequences ending with
a given synthetic target is exhaustively explored using a Monte Carlo search
algorithm. The Bayesian retrosynthesis algorithm could successfully rediscover
80.3% and 50.0% of known synthetic routes of single-step and two-step reactions
within top-10 accuracy, respectively, thereby outperforming state-of-the-art
algorithms in terms of the overall accuracy. Remarkably, the Monte Carlo
method, which was specifically designed for the presence of diverse multiple
routes, often revealed a ranked list of hundreds of reaction routes to the same
synthetic target. We investigated the potential applicability of such diverse
candidates based on expert knowledge from synthetic organic chemistry.
