Regression based analog performance macromodeling: Techniques and applications

Regression based techniques, when applied to performance macromodeling, have obvious advantages over other approaches: higher degree of automation, no need for simulator whatsoever, applicable to any performance parameter and topology. On the other hand, regression techniques usually suffer from "the curse of dimensionality", which refers to the phenomenon that the sample size needed to cover a high dimensional space grows exponentially with the dimension. This thesis provides a few novel techniques to cope with this problem based on the specific needs by analog performance macromodeling, falling into two categories: adaptive sampling and design space reduction.;Initial effort has been dedicated to developing an adaptive sampling algorithm to reduce training set size while maintaining high model accuracy. The proposed adaptive sampling algorithm is called adaptive grid refinement algorithm. The algorithm first constructs a regression model in the entire design space, a hypercube, using training data set generated from a two level full factorial design. The hypercube is then split into equal-sized smaller hypercubes if the model has error exceeding user defined bound. Within each smaller hypercube a local regression model is constructed and validated. Splitting stops only if all the local models have validation errors within the error bound. The final model is a set of local regression models.;Although it is desirable to model the entire design space accurately, only part of the design space called the feasible design space is worth exploring by an analog sizing tool. A feasibility model is needed to identify the feasible design space. Feasibility modeling is treated as a two class classification problem in our case. The small size of the feasible design space, however, challenges the state-of-the-art classification techniques such as Support Vector Machines when uniform randomly distributed instances are used for model training. We thus propose an active learning scheme to improve the feasibility classifier's accuracy more efficiently. The performance regression macromodels are built and validated within the feasible design space. Experiments show that they are more accurate compared to those valid within the entire design space when equal sized training sets are used. The resulting performance macromodel is essentially a combined model: a feasibility classifier and a set of performance regression models.;The third technique is designed to further reduce modeling cost of the combined model. More efficient feasibility model generation is achieved by introducing a sequential design space decomposition algorithm. Performance regression models are developed similarly. The sequential design space decomposition algorithm decomposes the initial design space into smaller partitions and constructs one feasibility classifier for one subsequent significant partition that includes most of the feasible designs. The final feasibility model is composed of a set of classifiers, each of which has its own applicable region. By sequentially decomposing the design space and exploring the significant partitions, we are able to build feasibility model of high precision with much lower modeling cost. (Abstract shortened by UMI.)...