High-Dimensional Metamodeling for Prediction of Clock Tree Synthesis Outcomes

Abstract—Clock tree synthesis (CTS) is a key aspect of on-chip interconnect, and major consumer of IC power and physical design resources. In modern sub-28nm tools and flows, it has become exceptionally difficult to satisfy skew, insertion delay and transition time constraints within power and area budgets, in part because commercial tools (with their many knobs) have become highly complex. This complexity, along with the complicated structure of real-world CTS instances (hierarchy, dividers, etc.) and floorplan contexts (aspect ratios, obstacles, etc.) make it very difficult to predict skew, power and other important metrics of CTS outcomes. In this work, we study CTS estimation in the high-dimensional parameter space of instance constraints and floorplan contexts. Using two leading commercial CTS tools as our testbed, we develop predictors, classifiers and “field of use ” characterizations that can enable IC design teams to achieve required CTS solution quality through understanding of appropriate parameter subspaces. Our hierarchical hybrid surrogate modeling approach mitigates challenges of parameter multicollinearity in high dimensions. It achieves, e.g., worst-case estimation errors of 13 % in contrast to 30 % errors in [17]. We demonstrate use of a 94%-accurate “oracle ” classifier and estimation models to predictably achieve CTS outcomes that meet specified constraints and target metrics. I