Physics-based algorithms are the gold standard for Modeling and Simulation (M&S) of a System of Systems (SoS); however, high-fidelity physics M&Ss can be cost prohibitive, slow, and/or exceedingly complex. Further, physics-based algorithms are often not considered useful until they pass a threshold of “realness,” this adds to cost and delays the readiness of M&S. Given the costs, development delays, and run speed of physics-based M&S they are often used sub-optimally, introduced too late to be used to aid design, or simply not implemented at all. 

Stochastic algorithms are inexpensive as the same algorithm can be used for each component in an SoS. These algorithms use a random number generator making them faster and less hardware intensive than physics-based algorithms. Finally, the parameters used in a stochastic model or simulation can be changed and refined over time, while still providing actionable insights early on in the design process. However, one drawback of stochastic models is that they do not have the fidelity of their physics-based counterparts. With this understanding, we assert that the M&S environment could greatly benefit from more extensive use of stochastic M&S. This is particularly true for aiding design, as fault identification, and as a guide for better utilization of higher-fidelity M&S tools.  

This paper describes the use and benefits of stochastic M&S for SoSs. We compare the capabilities of stochastic M&S to physics-based M&S using a simplified threat/intercept scenario. We explore how stochastic simulations can aid in optimization of physics-based M&S by constraining the input space for physics-based M&S. We introduce the concept of a digital caricature (a stochastic digital twin) and how this can be used in conjunction with real-world data and existing digital twins. Finally, we describe other avenues of interest for stochastic M&S to aid design, training, and operations of real-world systems.