<p>Understanding the permeability and transport dynamics of electrically conducting multiphase suspensions of non-Newtonian fluids, particularly Casson fluids, in peristaltic motion is a major challenge in fluid dynamics research. Traditional analytical methods face limitations in solving the coupled nonlinear partial differential equations that arise under the influence of complex parameters such as magnetohydrodynamics, wall compliance, particle concentration, and second-order slip effects. There is a need for advanced computational techniques, such as neural networks, to improve the accuracy and efficiency of modeling such systems for biomedical, industrial, and engineering applications. The primary aim of this study is to investigate the dynamics of electrically conducting Casson fluid under peristaltic transport using both exact analytical techniques and artificial neural networks, specifically multilayer LMS-BPNNs fine-tuned with the Levenberg–Marquardt algorithm. The research seeks to determine how parameters such as Hartman number, particle concentration, wall compliance, second-order slip, and skin friction coefficient influence the velocity profile and flow characteristics. The study considers peristaltic pumping of Casson fluid in a moving frame of reference at steady speed. The governing coupled nonlinear partial differential equations for momentum are formulated under the influences of magnetohydrodynamics, wall compliance, and slip effects. Exact analytical techniques for validation. Artificial Neural Networks: multilayer LMS-BPNNs optimized with the Levenberg–Marquardt method to approximate and predict flow dynamics. Comparative analysis is performed to assess the reliability and predictive accuracy of ANN solutions against exact results. The Casson fluid velocity profile increases with higher values of Hartman number, particle concentration, wall compliance, second-order slip, and skin friction coefficient. The combined effects of particle–fluid interaction, magnetic field, and compliant boundaries contribute significantly to enhancing fluid transport. ANN-based solutions demonstrate strong accuracy and efficiency, closely matching the exact results, while offering a more robust framework for handling nonlinearities. The velocity profile exhibits unique values at each location without streamline crossing, reflecting a well-organized and predictable flow behavior. The integration of advanced artificial neural networks, particularly multilayer LMS-BPNNs with Levenberg–Marquardt optimization, provides a powerful tool for modeling and predicting complex Casson fluid dynamics under peristaltic motion. The results confirm that magnetohydrodynamic effects, wall compliance, slip conditions, and particle concentration collectively enhance fluid velocity and streamline organization. This study establishes a reliable framework for applying ANN-assisted models in biomedical engineering, pharmaceutical transport, and industrial fluid systems requiring precise control over non-Newtonian multiphase flows.</p>