# Accelerated Simulation of Discrete Event Dynamic Systems via a Multi-Fidelity Modeling Framework +
## 3 Literature Review  
Over the last decade, several studies have sought to use multi-fidelity M&S to speed up simulations. The fundamental concept for these studies is multi-fidelity optimization, where lower-fidelity simulations are used to approximate the behavior of the high-fidelity simulation. Figure 4: Interest region in a single simulation scenario: Target attacking scenario of an unmanned underwater vehicle (UUV). For example, [PERSON] et al. [30] used multi-fidelity approximations combined with heuristic methods for the optimal design of aircraft pressure bulkheads. They coupled nonlinear high-fidelity analysis and linear low-fidelity analysis with four methods (i.e., ant colony optimization, genetic algorithm, particle swarm optimization, and life cycle model). [PERSON] et al. [31] introduced several applications, such as an airfoil wing simulation, car crash simulation, and an artificial neural network, etc., which were achieved with multi-fidelity modeling and an approximation management framework. [PERSON] et al. [32] proposed a two-stage multi-fidelity procedure for solving crashworthiness design for cellular structures and materials. In the first stage of their proposed work, a correction response surface was constructed based on the ratio between high-fidelity and low-fidelity analyses at a few sample points. In the second stage, low-fidelity analysis is replaced with a radial bias function approximation. [PERSON] et al. [33] presented an ordinal transformation approach to transform the original solution space into a one-dimensional space based on the rankings of solutions using the low-fidelity model. After that, they used an optimal sampling approach to search solutions in the transformed one-dimensional space for optimal solutions using high-fidelity simulations. One of the common points of the above-mentioned studies is to drive the preliminary design process using low-fidelity models as surrogates for expensive high-fidelity simulations. Then, high-fidelity models are employed in the final design stages to refine the design. In this case, the multi-fidelity technique is to utilize initial design points determined from a low-fidelity simulation to correct the simulation at other design points. This means that the fidelity did not change dynamically during the same simulation scenario. In addition, because these studies have focused on application-based approaches to resolve practical issues, there has been no formal representation of the multi-fidelity model and no model reusability of existing simulation models. [PERSON] and [PERSON] [34] presented a modeling framework for dynamically changing the fidelity of component models throughout a single scenario-the approach most similar to our own. For a dynamic change of fidelity, they proposed the following design concepts: (1) a supervisor filter to analyze and determine which inputs trigger a switch to low- and high-fidelity models and (2) a dwell time that provides a buffer during fidelity switching. The proposed framework was demonstrated for a finite-volume model of a vapor compression system where the model fidelity is based on the number of volumes used for the evaporator. Although the authors regarded dynamic changes of the fidelity, this study also suffers from an insufficient representation of behaviors of the event-based system. For example, the authors did not consider internal discrete events of the model but focused on exogenous signals; thus, the modeling form used in [PERSON] and [PERSON]'s study also makes it difficult to directly apply it to the discrete event dynamic system. In common with most M&S methods, multi-fidelity M&S inevitably involves behavioral errors of the developed models due to their approximations. [PERSON] et al. [35] classified them into two types. The first error is directly connected to the translation of the real system into a simulation model; the second one is related to the transformation of the simulation models.