# Investigating Supercomputer Performance with Sustainability in the Era of Artificial Intelligence
## 5 Results and Discussion
### Performance (Rmax) Analysis  
Table 5 presents a statistical analysis of the performance of top-performing supercomputers. The worst-case scenario refers to the supercomputer with the lowest performance, typically ranked in the 10 th position, whereas the best-case scenario represents the top-performing supercomputer, consistently occupying the 1 st position in the top 10. An analysis of the worst-case scenario suggests performance improvement. A similar trend is observed in the best-case scenario, where performance shows a rapid increase, particularly in recent periods compared to the earlier periods (June20, Nov20, June21 and Nov21). In the early periods, the performance levels were relatively low, especially in the worst case, with slight improvements in both the worst case and the best case. The performance continued to improve modestly with stable variability, as indicated by the standard deviation. The worst-case performance improvement suggests improvements in the top lower-performing supercomputers. A significant jump in performance is observed starting \begin{table}
\begin{tabular}{l l l l l l l l l l} \hline \hline  & **Nov24** & **June24** & **Nov23** & **June23** & **Nov22** & **June22** & **Nov21** & **June21** & **Nov20** \\ \hline June24 & 0.984 & & & & & & & & \\ Nov23 & 0.987 & 0.975 & & & & & & & \\ June23 & 0.971 & 0.966 & 0.991 & & & & & & \\ Nov22 & 0.939 & 0.967 & 0.923 & 0.922 & & & & & \\ June22 & 0.972 & 0.974 & 0.952 & 0.949 & 0.930 & & & & \\ Nov21 & 0.904 & 0.945 & 0.909 & 0.899 & 0.950 & 0.863 & & & \\ June21 & 0.928 & 0.962 & 0.933 & 0.930 & 0.963 & 0.932 & 0.934 & & \\ Nov20 & 0.858 & 0.892 & 0.871 & 0.890 & 0.915 & 0.907 & 0.826 & 0.926 & \\ June20 & 0.904 & 0.947 & 0.917 & 0.904 & 0.936 & 0.892 & 0.954 & 0.987 & 0.872 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Correlation analysis of most energy-efficient supercomputers. \begin{table}
\begin{tabular}{l l l l} \hline \hline  & **Worst Case (Rmax)** & **Best Case (Rmax)** & **Mean** & **Std. Deviation** \\ \hline Nov24 & 208.10 & 1742.00 & 685.2010 & 512.92329 \\ June24 & 121.40 & 1206.00 & 455.7410 & 373.37786 \\ Nov23 & 94.64 & 1194.00 & 390.3790 & 336.75663 \\ June23 & 61.44 & 1194.00 & 271.5830 & 347.76592 \\ Nov22 & 61.44 & 1102.00 & 255.9830 & 321.98705 \\ June22 & 46.10 & 1102.00 & 227.4030 & 328.35762 \\ Nov21 & 30.05 & 442.01 & 108.3650 & 122.27634 \\ June21 & 23.52 & 442.01 & 107.0840 & 122.98281 \\ Nov20 & 22.40 & 442.01 & 102.8650 & 125.30433 \\ June20 & 21.23 & 415.53 & 94.2640 & 120.53683 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: The performance (Rmax) of top-performing supercomputers. from June22, especially in the best case. The performance keeps increasing continuously. The likely reason for this surge is the entry of the first exascale system, _Frontier_, into the list in June 2022. The performance for the top system does not evolve in a smooth, linear manner, but rather in \"jumps\" each time a new top machine is deployed. The values remain constant for a period, as shown in Table 5, because it takes time for the next best system to be deployed. Moreover, for a new system to claim the top position, it must outperform the previous state-of-the-art top performer. The standard deviation remains high, highlighting the diversity in supercomputing performance levels. The mean performance exhibits a consistent improvement throughout the observed period, highlighting the relentless race for higher performance. The period under study indicates that exascale supercomputers dominated the number one spot in the top-performing group. Exascale supercomputers have held the number one position since June22, indicating a new benchmark in high-performance computing. This trend suggests that, moving forward, any supercomputer aiming for the top spot must operate at the exascale level. The substantial leap in performance also signals the beginning of the race toward zettascale computing. Table 6 presents the correlation analysis for the performance of top-performing supercomputers across the five-year period.