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Title Design of Mexican Hat Wavelet Artificial Neural Network for solving Lorenz Model.

Author(s) Anika Fayyaz

Abstract Artificial Neural Networks (ANNs) have become a highly effective technique for addressing complex mathematical and scientific challenges, thanks to their remarkable learning and approximation abilities. One essential area of study within computational mathematics and dynamical systems is the Lorenz model, which consists of nonlinear differential equations. This thesis introduces a novel computational strategy that integrates artificial neural networks with a hybrid optimization framework to explore the chaotic dynamics characterized by the Lorenz model. In order to precisely approximate the solutions of the Lorenz model, a hybrid optimization technique that combines Particle Swarm Optimization (PSO) and Active Set Algorithm (ASA) is devised in this study. The model’s learning efficiency is increased by using a feedforward ANN structure with a Mexican Hat activation function. The proposed ANN-PSO-ASA approach, with its ability to manage the complexity of chaotic systems, appears to be a promising tool for modeling complex dynamical behaviors. For every Lorenz model test case, 50 experimental runs were conducted in order to evaluate the suggested ANN-based framework’s consistency, accuracy, and robustness. Superior convergence dependability, numerical stability, and prediction accuracy were demonstrated by the hybrid PSO-ASA optimized ANN model, which continuously outperformed other hybrid optimization techniques as well as conventional numerical methods. Statistical measures including Mean Squared Error (MSE) analysis and Mean Absolute Deviation (MAD) were used to validate these results. All things considered, this study demonstrates how well new revolutionary methods work to solve nonlinear differential equations related to chaotic systems. A flexible, adaptive, and computationally effective method for simulating intricate dynamical events is the PSO-ASA optimized ANN framework, which incorporates the Mexican Hat activation function.

Type Thesis/Dissertation MS

Faculty Engineering and Computer Science

Department Mathematics

Language English

Publication Date 2025-11-25

Subject Mathematics

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