Evaluating Linear Regression for Temperature Modeling at the Core Level

Temperature issues have become a first-order concern for modern computing systems. There are several approaches for dynamic thermal management, including reacting based on some threshold temperature, predicting based on history, or estimating localized temperatures based on performance counters. One possibility for more proactive management is to predict temperatures based on the upcoming instruction stream or performance counters. A logical approach is to use linear regression to generate a model based on the instruction stream, performance counters, or a combination of the two to predict temperatures at the next time step. However, we show in this paper that linear regression is unsuitable for predicting temperatures at the core level. This is primarily due to the fact that temperature at a time step is dependent upon both the processor activity and the temperature at the previous time step. As a result, application phases have long periods with similar instruction streams and performance counter values per time step but with different temperatures, which leads to prediction errors elsewhere in the phase. Incorporating temperature history as an input to the regression essentially leads to a last value predictor, which predicts the temperature will always be the same as the last time step. Thus, neither approach is truly suitable for predictive thermal management.