This chapter explores Particle Swarm Optimization (PSO) as a bio-inspired metaheuristic for neural network training, addressing limitations of gradient-based methods like local minima convergence. It presents the fundamental PSO algorithm with velocity and position update equations, and extends the methodology through integration with gray correlation analysis for network structure optimization and Bayesian regularization for enhanced generalization. The chapter demonstrates practical implementation through Python code that minimizes the Sphere function, showing PSO’s effectiveness in multidimensional optimization. Experimental results reveal PSO’s superior performance over standard and adaptive BP algorithms, achieving significantly lower test error rates. The comprehensive approach combines structural optimization, regularization techniques, and swarm intelligence to create robust neural network training frameworks with improved convergence and generalization capabilities.