Surface spline interpolation method for thermal reconstruction with limited sensor data of non-uniform placements

With the characteristic size reducing as well as the power densities exponentially increasing, elevated chip temperatures are true limiters to the performance and reliability of integrated circuits. To address these thermal issues, it is essential to use a set of on-chip thermal sensors to monitor temperatures during operation. These temperature sampling results are then used by thermal management techniques to appropriately manage chip performance. In this paper, we propose a surface spline interpolation method to reconstruct the full thermal characterization of integrated circuits with non-uniform thermal sensor placements. We construct the thermal surface function using the mathematical tool of surface spline with the matrix calculation of the non-uniform sample data. Then, we take the coordinates of the points at grid locations into the surface function to get its temperature value so that we can reconstruct the full thermal signals. To evaluate the effectiveness of our method, we develop an experiment for reconstructing full thermal status of a 16-core processor. Experimental results show that our method outperforms the inverse distance weighting method based on dynamic Voronoi diagram and spectral analysis techniques both in the average absolute error metric and the hot spot absolute error metric with short enough runtime to meet the real-time process demand. Besides, our method still has the advantages such as its mathematical simplicity with no need of pre-process.