Electromagnetics-based Design through Inverse Space Mapping Techniques

Inverse space mapping algorithms for designing with accurate but computationally expensive simulators are described and contrasted in this presentation. Neural Inverse Space Mapping (NISM) optimization was the first space mapping algorithm that explicitly made use of the inverse of the mapping from the fine to the coarse model parameter spaces. NISM follows an aggressive formulation by not requiring a number of up-front fine model evaluations to start building the mapping. An statistical procedure to parameter extraction (PE) is employed in NISM to avoid the need for multipoint matching and frequency mappings. An artificial neural network (ANN) whose generalization performance is controlled through a network growing strategy approximates the inverse mapping at each iteration. The ANN starts from a 2-layer perceptron and automatically migrates to a 3-layer perceptron when the amount of nonlinearity found in the inverse mapping becomes significant. The NISM step consists of evaluating the current neural network at the optimal coarse model solution. Linear Inverse Space Mapping (LISM) follows a piece-wise linear formulation to implement the inverse of the mapping, avoiding the use of neural networks. LISM approximates the inverse of the mapping function at each iteration by linearly interpolating the last n + 1 pairs of coarse and fine model design parameters, where n is the number of optimization variables. The same statistical procedure to PE is used in LISM as in NISM. LISM also follows an aggressive formulation in the sense of not requiring up-front fine model evaluations. LISM has been applied to design linear circuits in the frequency domain and nonlinear circuits in the time domain transient-state. A rigorous comparison between Broyden-based direct space mapping, neural (NISM) and linear (LISM) inverse space mapping is realized using a synthetic example. Two industrially relevant microwave design problems are efficiently solved using inverse space mapping techniques