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A spectral-approximation-based intelligent modeling approach is proposed for the distributed thermal processing of the snap curing oven that is used in semiconductor packaging industry. The snap curing oven can be described by a nonlinear parabolic distributed parameter system (DPS) in the time-space domain. After finding a proper approximation of the complex boundary conditions of the system, the spectral methods can be applied to time-space separation and model reduction, and neural networks (NNs) can be used for state estimation and system identification. With the help of model reduction techniques, the dynamics of the curing process derived from physical laws can be described by a model of low-order nonlinear ordinary differential equations with a few uncertain parameters and unknown nonlinearities. A neural observer can then be designed to estimate the states of the ordinary differential equation model from measurements taken at specified locations in the field. Using the estimated states, a hybrid general regression NN is trained to be a nonlinear model of the curing process in state-space formulation, which is suitable for the further application of traditional control techniques. Real-time experiments on the snap curing oven show that the proposed modeling method is effective. This modeling methodology can be applied to a class of nonlinear DPSs in industrial thermal processing.