# Agnostic Energy Consumption Models for Heterogeneous GPUs in Cloud Computing
## 5 Discussion
According to Table 10, the minimum mean error percentage of all power models on both VMs was 9%, for DNN models with hybrid inputs in both VMs, and the minimum greatest error percentage of all power models was 23%, for the DNN model with hybrid inputs in the VM connected with Kepler K40c. This indicates that adding both the utility percentage of GPU usage and the memory usage improves the model's accuracy. (2) Energy Consumption Models  
The outliers in the energy DNN model results do not exist when compared with the actual energy values in both VMs, as shown in the energy models' section. In comparing the energy models having standard inputs and the agnostic model that has the common inputs in the VM connected with the Fermi GPU, the overall accuracy in the agnostic energy model performed slightly better than the energy model with standard inputs with a mean error of 8.6% compared with a 9.1% mean error in the standard energy model. In terms of individual accuracy, the maximum percentage error in the DNN energy model with standard inputs was 25% (H8192), while the greatest error in the agnostic DNN energy model with the common inputs was 15.4% (SC 1048576). In a VM connected with the Kepler GPU, the agnostic energy model performance is slightly better than the energy model with standard inputs with a mean error of 6.3% compared with 6.5% in the energy model with standard inputs. Moreover, the maximum individual percentage error in the DNN energy model with standard inputs is 23.6% (H8192), while the highest individual percentage error in the DNN agnostic energy model is 24.3% (H8192). Therefore, the agnostic DNN energy model has exhibited a better performance in terms of the mean error and the maximum individual error percentage. Table 11 summarizes the mean error and the greatest error percentages of energy models in both VMs. According to Table 11, for a comparison of both VMs, the best mean percentage error for the energy prediction model was found on the VM connected with the Kepler K40c GPU (6.3%), while the VM that connected with the Fermi C2075 GPU had the minimum greatest individual error (15.4%). Thus, the energy agnostic model has a better performance and allows us to reduce the input parameters required, which contributes to a reduction in the cost of data collection. Another interesting finding is that the agnostic model provides an unintended level of bias in some cases. For example, the overall performance (measured by the mean) of the agnostic model in the Kepler GPU is better than the Fermi GPU. However, the Fermi GPU is better in terms of the greatest error. Therefore, there is a trade-off between accuracy and the cost of data collection in agnostic models. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Power Models** & **VM with Fermi C2075 GPU** & \multicolumn{2}{c}{**VM with Kepler K40c**} \\ \cline{2-5}
**Mean Error** & **Greatest Error** & **Mean Error** & **Greatest Error** \\ \hline
**Performance Counters Inputs** & 45 & 137 & 27.4 & 56.3 \\
**(Shallow)** & & & & \\ \hline
**Performance Counters Inputs** & 18.1 & 38.1 & 17 & 82 \\ \hline
**Hybrid Inputs (Shallow)** & 12.5 & 40 & 10 & 29 \\ \hline
**Hybrid Inputs (Deep)** & **9** & **28.3** & **9** & **23** \\ \hline \hline \end{tabular}
\end{table} 
Table 10: The mean errors and greatest errors values summary of power consumption models on Both VMs. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Energy Models** & **VMs** & **VM with Fermi C2075 GPU** & \multicolumn{2}{c}{**VM with Kepler K40c**} \\ \cline{2-5}  & **Mean Error** & **Greatest Error** & **Mean Error** & **Greatest Error** \\ \hline
**DNN with Standard Inputs** & 9.1 & 25 & 6.5 & 24.3 \\ \hline
**DNN with Common Inputs** & 8.6 & **15.4** & **6.3** & 23.6 \\ \hline \hline \end{tabular}
\end{table} 
Table 11: The mean errors and greatest errors values summary of energy models for both VMs.