  The interpretability of machine learning, particularly for deep neural
networks, is crucial for decision making in real-world applications. One
approach is replacing the un-interpretable machine learning model with a
surrogate model, which has a simple structure for interpretation. Another
approach is understanding the target system by using a simulation modeled by
human knowledge with interpretable simulation parameters. Recently, simulator
calibration has been developed based on kernel mean embedding to estimate the
simulation parameters as posterior distributions. Our idea is to use a
simulation model as an interpretable surrogate model. However, the
computational cost of simulator calibration is high owing to the complexity of
the simulation model. Thus, we propose a ''model-bridging'' framework to bridge
machine learning models with simulation models by a series of kernel mean
embeddings to address these difficulties. The proposed framework enables us to
obtain predictions and interpretable simulation parameters simultaneously
without the computationally expensive calculations of the simulations. In this
study, we apply the proposed framework to essential simulations in the
manufacturing industry, such as production simulation and fluid dynamics
simulation.
