Figure Design of synthetic reaction networks using the SMC calculation based on sequential stacking algorithm. In the current step, all sampled reaction networks and their products are added to the reactant pool in the next step. By searching for single-step reactions from this expanding pool of reactants, the network can be built up recursively. resampling based on the goodness-of-fit of the current set of reactants, (2) updating the set of hypothetical reactants based on the proposed distribution, and (3) calculating the goodness-of-fit importance weights. All reactant sets generated from the proposal distribution are handed over to the forward model module to generate the predicted products and characterize their properties. All the products generated in this module are successively added to the pool of candidate reactants B t in the SMC module. The monotonically growing reactant pool B t contains the intermediate products calculated from the reaction prediction model. Therefore, throughout the search for single-step reactions in SMC, reaction networks with various structures can be constructed by sampling and stacking intermediate products for which their reaction networks have already been calculated. The computational complexity of the neighborhood search owing to the monotonic growth of B t is suppressed by pre-clustering the set of reactants using the GTM. In summary, the algorithm is based on four ideas: (1) the recurrent algorithm for the network search, which is based on the sequential expansion of the reactant pool, (2) the avoidance of the neighborhood search from large reactant pools using GTM clustering, (3) efficient computation of the forward cascade model using a surrogate model, and (4) the asynchronous parallel computation algorithm.