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An artificial intelligent neural network improved particle swarm optimization algorithm is proposed for the inverse design of semiconductor optical amplifier. Seven input parameters, current-gain curve and saturation output power curve are selected to form the data set based on the physical model of semiconductor optical amplifier. The effectiveness of forecasting performance is improved by contrasting two back propagation neural network techniques (Scaled Conjugate Gradient and Levenberg-Marquardt) and operational settings (Central Processing Unit and Graphics Processing Unit). Higher accuracy is achieved through feedback analysis of neuron number optimization and test error. The addition of a unique backpropagation neural network can make the fitness of particle swarm algorithm mostly converge below $2\times 10^{-4}$. The relative difference between original performances and inverse predictions is close to 0%, which proves the effectiveness of parameter extraction. This method can take advantage of neural networks to improve accuracy and speed of particle swarm optimization algorithms for efficient semiconductor optical amplifier inverse design and multi-solution analysis.