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Space mapping is a recognized method for speeding up electromagnetic (EM) optimization. Existing space-mapping approaches belong to the class of surrogate-based optimization methods. This paper proposes a cognition-driven formulation of space mapping that does not require explicit surrogates. The proposed method is applied to EM-based filter optimization. The new technique utilizes two sets of intermediate feature space parameters, including feature frequency parameters and ripple height parameters. The design variables are mapped to the feature frequency parameters, which are further mapped to the ripple height parameters. By formulating the cognition-driven optimization directly in the feature space, our method increases optimization efficiency and the ability to avoid being trapped in local minima. The technique is suitable for design of filters with equal-ripple responses. It is illustrated by two microwave filter examples.Index Terms-Cognition-driven design, computer-aided design (CAD), electromagnetic (EM) optimization, microwave filters, modeling, space mapping (SM).