Temperature-to-power mapping

Accurate power maps are useful for power model validation, process variation characterization, leakage estimation, and power optimization, but are hard to measure directly. Deriving power maps from measured thermal maps is the inverse problem of the power-to-temperature mapping, extensively studied through thermal simulation. Until recently this inverse heat conduction problem has received little attention in the microarchitecture research community. This paper first identifies the source of difficulties for the problem. The inverse mapping is then performed by applying constraints from microarchitecture-level observations. The inherent large sensitivity of the resultant power map is minimized through thermal map-filtering and constrained least-squares optimization. Choices of filter parameters and optimization constraints are investigated and their effects are evaluated. Furthermore, the paper highlights the differences between the grid and block modeling in the inverse mapping which were often ignored by previous schemes. The proposed methods reduce the mapping error by more than 10× compared to unoptimized solutions. To our best knowledge this is the first work to quantitatively evaluate and minimize the noise effect in the temperature to power mapping problem at the microarchitecture level for both grid and block mode, and for the steady and transient case.