Application of factorization machine with quantum annealing to hyperparameter optimization and metamodel-based optimization in granular flow simulations

This study examined the applicability of factorization machines with quantum annealing (FMQA) to the field of landslide risk assessment for two specific black-box optimization problems, hyperparameter optimization (HPO) for metamodeling and metamodel-based simulation optimization (MBSO) targeting granular flow simulation using discrete element method (DEM). These two optimization problems are solved successively: HPO is first performed to determine the hyperparameters of the Gaussian process regression (GPR) metamodel, which is then used as a low-cost, fast approximate solver of granular flow simulations for MBSO. After conducting a series of granular flow simulations using DEM, a metamodel is created that outputs a risk index of interest, the run-out distance, from its input parameters by employing GPR with two hyperparameters, length-scale and signal variance. Subsequently, HPO is performed to obtain the optimal set of hyperparameters by applying FMQA and other optimization methods using another set of hyperparameters determined using the gradient-ascent method as the reference solution. Finally, using the metamodel created by each optimization method as an approximate solver for DEM simulations, MBSO is performed to find the optimal target output, the maximum run-out distance, in the space of physical input parameters for risk assessment. A comparison of the performance of FMQA with that of other methods shows that FMQA is competitive in terms of efficiency and stability with state-of-the-art algorithms such as Bayesian optimization.