PowerField: A Probabilistic Approach for Temperature-to-Power Conversion Based on Markov Random Field Theory

Temperature-to-power technique is useful for post-silicon power model validation. However, the previous works were applicable only to the steady-state analysis. In this paper, we propose a new temperature-to-power technique, named PowerField, supporting both transient and steady-state analysis based on a probabilistic approach. Unlike the previous works, PowerField uses two consecutive thermal images to find the most feasible power distribution that causes the change between the two input images. To obtain the power map with the highest probability, we adopted maximum a posteriori Markov random field (MAP-MRF). For MAP-MRF framework, we modeled the spatial thermal system as a set of thermal nodes and derived an approximated transient heat transfer equation that requires only the local information of each thermal node. Experimental results with a thermal simulator show that PowerField outperforms the previous method in transient analysis reducing the error by half on average. We also show that our framework works well for steady-state analysis by using two identical steady-state thermal maps as inputs. Lastly, an application to determining the binary power patterns of an FPGA device is presented achieving 90.7% average accuracy.