# Agnostic Energy Consumption Models for Heterogeneous GPUs in Cloud Computing
## 5 Discussion  
Several models have been developed to predict power and energy consumption on heterogeneous GPUs connected with VMs in a cloud environment; each GPU has different characteristics. The absolute percentage error has been calculated to measure the overall accuracy in the testing set. (1) Power Consumption Models  
A comparison between shallow neural networks and DNNs to validate DNN models has been performed in power consumption models. Acceptable accuracy differences between actual and predicted power values have been conducted using neural networks (shallow and deep) by merely using performance counters as models' inputs. According to the power models' results on heterogeneous VMs, DNN models systematically produce a better accuracy compared with shallow networks in both VMs connected with heterogeneous GPUs. In power consumption models' results on a VM with the Fermi C2075 GPU, the outliers of power consumption values in Nbody, Mri-q, and Streamcluster applications produced by shallow networks have been dramatically decreased in the DNN model. Additionally, the overall accuracy in the DNN GPU power model has exhibited better accuracy than shallow networks with a mean error of 18.1% compared with 45% in shallow networks. Furthermore, in the power consumption model results on a VM with the Kepler K40c GPU, many power consumption outliers have been produced by the shallow network in ConvolutionTexture, FastWalshTransform, Nbody, and Cutcp applications, while these outliers have been mitigated in the DNN power model, as shown in Figure 6.  
The overall accuracy of the DNN model is also greater than the shallow network with 17% in comparison with the 27.4% mean error in the shallow network. A significant accuracy improvement has occurred when the utility percentage of GPU and memory have been added with the selected performance counters--hybrid inputs--for the power consumption prediction in both heterogeneous GPUs connected with two different VMs. In the power consumption model's results on a VM with the Fermi C2075 GPU, the accuracy of shallow networks has been improved with a mean error of 12.5% compared with 45% in the performance-counters-only model. Similarly, the DNN power model's accuracy has been improved from 18.1% in the performance counters model to 9% in the hybrid inputs model. In terms of the accuracy of each application individually, the greatest absolute percentage error has been dropped by adopting hybrid inputs from 38.1% (Histo) to 28.3 (Streamcluster) in the DNN model. However, in the shallow networks model, the greatest absolute percentage error has been reduced from 137% (Streamcluster) to 40% (Grad) on the VM connected with Fermi C2075. However, the accuracy of the DNN was better than shallow networks with a 9% mean error and 12.5% for shallow networks. In the power consumption results on a VM with the Kepler K40c GPU, an improvement of the overall accuracy has occurred in the shallow networks model from a 27.4% mean error with the only-performance-counters-inputs model to a 10% mean error in the hybrid inputs model. Moreover, the overall accuracy in DNN has been enhanced from a 17% mean error in only-performance-counters-inputs to a 9% mean error in hybrid inputs. Although the accuracy of the shallow networks has been improved in hybrid inputs, the DNN model has performed better than the shallow networks model with 9% compared with a 10% mean error in the shallow network model. For individual evaluation, the greatest absolute percentage error has been decreased from 82% (Bfs) to 23% (Cutcp) in the DNN model with hybrid inputs. Similarly, in the hybrid inputs model, the greatest absolute percentage error value in shallow networks has dropped from 56.3% (Cutcp) to 29% (Cutcp). Table 10 summarizes the mean errors and the greatest error percentages of the GPU power consumption models on both VMs.