A new computer-aided design (CAD) method for automated enhancement of nonlinear device models is presented, advancing the concept of Neuro-space mapping (Neuro-SM). It is a systematic computational method to address the situation where an existing device model cannot fit new device data well. By modifying the current and voltage relationships in the model, Neuro-SM produces a new model exceeding the accuracy limit of the existing model. In this paper, a novel analytical formulation of Neuro-SM is proposed to achieve the same accuracy as the basic formulation of Neuro-SM (known as circuit-based Neuro-SM) with much higher computational efficiency. Through our derivations, the mapping between the existing (coarse) model and the overall Neuro-SM model is analytically achieved for dc, small-signal, and large-signal simulation and sensitivity analysis. The proposed analytical formulation is a significant advance over the circuit-based Neuro-SM, due to the elimination of extra circuit equations needed in the circuit-based formulation. A two-phase training algorithm utilizing gradient optimization is also developed for fast training of the analytical Neuro-SM models. Application examples on modeling heterojunction bipolar transistor (HBT), metal-semiconductor-field-effect transistor (MESFET), and high-electron mobility transmistor (HEMT) devices and the use of Neuro-SM models in harmonic balance simulations demonstrate that the analytical Neuro-SM is an efficient approach for modeling various types of microwave devices. It is useful for systematic and automated update of nonlinear device model library for existing circuit simulators.