This paper presents research combining an agent-based modeling and simulation paradigm with game theory for an in silico historical analysis of the Bay of Biscay submarine war during WWII. The U-boat threat was of great concern to the Allies, prompting initial operational research efforts to devise counterstrategies. Focusing search efforts in the Bay of Biscay enabled an effective Allied response. Using the historical record as a means to create a reasonably accurate model of the U-boat campaign, we allow the resulting agents within the model to adapt their strategies to counteropposition strategies. Model output data are examined with respect to the historical record and game theory. The results hold promise for extending the agent-based modeling paradigm into more complex military-based domains.
Combat, unlike many real-world processes, tends to be singular in nature. This makes statistical analysis of the combat data problematic. Building stochastic simulation models of combat scenarios provides a means of studying in some detail the particulars of a combat scenario provided that the model accurately captures the scenario. The scenario of interest in this paper is the WWII Bay of Biscay U-boat campaign, and the model is an agent-based simulation. The challenge is how to validate, or ensure the adequacy of, the simulation representation of the combat scenario with the actual scenario on the basis of comparing simulation output to typically small-sample-size actual combat data. In this paper we give the details of a new statistical methodology for use in validating a mission-level, agent-based model of a historical combat scenario. We use the Bay of Biscay agent-based simulation and develop a bootstrapping technique applied to the small-sample-size actual data from the Bay of Biscay campaign. Results from this bootstrapping statistical technique are compared with commonly used statistical techniques and are shown to improve the comparison of agent-based simulation output to actual real-world data.
Long-duration logistical wargames within the Air domain are complex and highly dynamic events that are driven by aircraft availability. In order to gain insight into the impact of aircraft use, this research developed a simulation tool that uses a stepwise approach for adjudication and provides the user many capabilities including, but not limited to, the ability to have multiple bases and types of aircraft. Daily aircraft availability and missions accomplished are two critical metrics of interest. Within the simulation, the user has the ability to control types of part failures, control parts availability, control maintenance capabilities, and control number of mission scheduled. Finally, the user can account for the possibility of attrition along with the effects of numerous major events present in real-life scenarios. This tool is validated through application of a space covering design along with regression modeling and shows that the tool is well-behaved, functions as expected, and can quickly provide meaningful insights into operational scenarios.
In recent years, real-valued neural networks have demonstrated promising, and often striking, results across a broad range of domains. This has driven a surge of applications utilizing high-dimensional datasets. While many techniques exist to alleviate issues of high-dimensionality, they all induce a cost in terms of network size or computational runtime. This work examines the use of quaternions, a form of hypercomplex numbers, in neural networks. The constructed networks demonstrate the ability of quaternions to encode high-dimensional data in an efficient neural network structure, showing that hypercomplex neural networks reduce the number of total trainable parameters compared to their real-valued equivalents. Finally, this work introduces a novel training algorithm using a meta-heuristic approach that bypasses the need for analytic quaternion loss or activation functions. This algorithm allows for a broader range of activation functions over current quaternion networks and presents a proof-of-concept for future work.
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