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This letter presents a simple and efficient high-dimensional parametric model of microwave cavity filters utilizing a modular neural network technique. The filter structure is decomposed into several parts, and a set of neural networks are trained to learn the behavior of the filter parts. These neural networks considered as submodels, are then combined and incorporated into the final model structure. A frequency-space mapping module is introduced to align the combined model to match the overall filter behavior. The proposed method allows the overall model be developed with limited training data of the overall filter. Once trained, the model provides an accurate and fast prediction of EM behavior of filters with high-dimensional geometry parameters as variables. The proposed model is used for fast design optimization of filters. Numerical examples and comparisons with direct EM simulation and optimization are included to demonstrate the merits of the proposed technique.