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Neural networks are useful for developing fast and accurate parametric model of electromagnetic (EM) structures. However, existing neural-network techniques are not suitable for developing models that have many input variables because data generation and model training become too expensive. In this paper, we propose an efficient neural-network method for EM behavior modeling of microwave filters that have many input variables. The decomposition approach is used to simplify the overall high-dimensional neural-network modeling problem into a set of low-dimensional sub-neural-network problems. By incorporating the knowledge of filter decomposition with neural-network decomposition, we formulate a set of neural-network submodels to learn filter subproblems. A new method to combine the submodels with a filter empirical/equivalent model is developed. An additional neural-network mapping model is formulated with the neural-network submodels and empirical/equivalent model to produce the final overall filter model. An H -plane waveguide filter model and a side-coupled circular waveguide dual-mode filter model are developed using the proposed method. The result shows that with a limited amount of data, the proposed method can produce a much more accurate high-dimensional model compared to the conventional neural-network method and the resulting model is much faster than an EM model.