School of Computer Science and Applied Mathematics (ETDs)

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Browsing School of Computer Science and Applied Mathematics (ETDs) by SDG "SDG-17: Partnerships for the goals"

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    Comparing the effectiveness of LSTM, ARIMA, and GRU algorithms for forecasting customer charging behavior in the electric mobility industry in Europe
    (University of the Witwatersrand, Johannesburg, 2023) Pelwan, Robyne Chimere
    Forecasting, a powerful technique for unveiling potential future events, relies on historical data and methodological approaches to provide valuable insights. This dissertation delves into the domain of electric mobility, investigating the effectiveness of three distinct algorithms—Long Short-term Memory (LSTM), Autoregressive Integrated Moving Average (ARIMA), and Gated Recurrent Unit (GRU)—for predicting customer charging behavior. Specifically, it focuses on forecasting the number of charges over a 7-day period using time-series data from European electric mobility customers. In this study, we scrutinize the interplay between algorithmic performance and the intricacies of the dataset. Root mean squared error (RMSE) serves as a metric for gauging predictive accuracy. The findings highlight the supremacy of the ARIMA model in single-variable analysis, surpassing the predictive capabilities of both LSTM and GRU models. Even when additional features are introduced to enhance LSTM and GRU predictions, the superiority of ARIMA remains pronounced. Notably, this research underscores that ARIMA is particularly well-suited for time series data of this nature due to its tailored design. It contributes valuable insights for both researchers and practitioners in the electric mobility industry, aiding in the strategic selection of forecasting methodologies.
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    Estimating skills in discrete pursuit-evasion games
    (University of the Witwatersrand, Johannesburg, 2023) Gomes, Byron John; Rosman, Benjamin
    Game Theory is a well-established field in mathematics, economics, and computer science, with a rich history of studying n-person, zero-sum games. Researchers have utilized the best computational power of their time to create computational players that are able to beat the best human players at complex two-player, zero-sum games such as Chess and Go. In the field of Reinforcement Learning and Robotics, these types of games are considered useful environments to conduct experiments about agent behavior and learning. In this research report we explore a subset of discrete skill-dependent pursuit-evasion games upon which we build a framework to estimate player skills. In this game environment a player’s skill determines the actions available to them in each state and the transition dynamics resulting from the chosen action. The game offers a simplified depresentation of more complex games which often have vast state and action spaces, making it difficult to model and analyze player behavior. In this game environment we find that players with incorrect assumptions about an opponent’s skill perform sub-optimally at winning games. Given that knowledge of an opponent’s skill impacts on player performance, we demonstrate that players can use Bayesian inference to estimate their opponent’s skill, based on the action outcomes of an opponent. We also demonstrate that skill estimation is a valuable exercise for players to undertake and show that the performance of players that estimate their opponent’s skill converges to the performance of players given perfect knowledge of their opponent’s skill. This research contributes to our understanding of Bayesian skill estimation in skill-dependent pursuit-evasion games which may be useful in the fields of Multi-agent Reinforcement Learning and Robotics.
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    Overlapping multidomain paired quasilinearization methods for solving boundary layer flow problems
    (University of the Witwatersrand, Johannesburg, 2024) Nefale, Mpho Mendy; Otegbeye, Olumuyiwa; Oloniiju, Shina Daniel
    There is a constant and continuous need to refine current numerical approaches used to solve non-linear differential equations, which are employed to model real- world problems that often do not have analytical solutions. Spectral-based techniques have proven to be one of the most efficient numerical techniques for finding solutions of differential equations. Numerous spectral-based linearization techniques have been developed, such as the spectral relaxation (SRM), the spectral local linearization (SLLM), the spectral quasilinearization (SQLM), and the paired quasilinearization (PQLM) methods, among others. Previous research suggests that the PQLM is an efficient approach for solving complex non-linear systems of ordinary (ODEs) and partial differential equations (PDEs). However, it has been observed that this method requires further enhancement when utilized for problems described over a large domain, be it temporal or spatial. This research aims to address this limitation by proposing a modified version of the PQLM called the overlapping multi-domain paired quasilinearization method (OMD-PQLM), that enhances the accuracy and convergence speed of the original approach. The new approach entails solving a system by a technique that involves decoupling the system into pairs of equations and partitioning the large domain into smaller overlapping sub-domains. A comparison between the OMD-PQLM and the PQLM is conducted by solving systems of ODEs and PDEs. The proposed numerical approach is evaluated based on the norms of the residual and convergence errors, computational time, and the influence of the number of grid points and sub-domains on the convergence speed of the iterative scheme and the accuracy of the solutions. The findings demonstrate that the OMD-PQLM remarkably improves the accuracy of the solution compared to the PQLM, suggesting that partitioning the problem domain into overlapping multiple-domains optimizes the performance of the PQLM.