Constrained Modeling with Response Features

The necessity of employing surrogate modeling techniques for high-frequency design have been instigated by high computational cost of direct simulation-driven design. Yet, it turns out that conventional surrogate modeling techniques exhibit considerable difficulties in setting up reliable models caused primarily by the curse of dimensionality and high nonlinearity of system characteristics. This has encouraged researchers to seek alternative modeling paradigms. One of them is a performance-driven modeling concept, in which the surrogate domain is contentiously delimited, so that it coincides with the most important regions of the design space, where high-quality designs reside. The two main techniques following the performance-driven (constrained) modeling paradigm include the nested kriging modeling technique and the two-stage modeling technique based on random observables. Both approaches permit a significant reduction of training data acquisition cost with regard to standard modeling procedures. Subsequent sections outline specific modeling techniques following the performance-driven concept. The chapter starts from the delineation of the earliest framework, namely, nested kriging modeling technique, which is followed by the description of its later developments: nested kriging with response features and feature-based nested kriging with explicit dimensionality reduction. All of these procedures require pre-optimized reference designs for domain definition purposes, which in some cases could be available from the previous work with a given high-frequency structure. If, however, such a database is not readily accessible, an alternative approach is offered by the two-stage modeling technique. Therein, the surrogate model domain is delimited using randomly acquired observables, whose quality is assessed based on the response features extracted from the respective system responses. The employment of the features for design quality estimation permitted improving computational efficiency of performance-driven modeling frameworks. Further cost reduction has been achieved by carrying out the modeling process directly at the level of the response features rather than complete characteristics. The last two sections of this chapter describe observable-based constrained modeling technique and its feature-based version.