以高效能計算平台加速蒙地卡羅模擬

Abstract

蒙地卡羅方法被廣泛地使用於進行核物理等具有內在隨機性的問題模擬，藉由電腦運算能力直接模擬問題內的隨機過程。在腫瘤醫學的放射性療法中，需要先針對劑量分佈進行模擬，以提昇療效並減低對正常細胞的影響。但蒙地卡羅方法需要反覆大量的計算才能得出精準的模擬結果。但以蒙地卡羅方法進行模擬需要反覆、大量的計算才能得出精準的模擬結果。為了進行療程規劃，更需要多次調整各項模擬參數，進行多次模擬，以便挑選出適當的療程，使得模擬程式的執行效率更顯其重要。現存研究中，便有團隊曾利用通用計算圖形處理器、向量處理機及現場可程式邏輯閘陣列試圖加速蒙地卡羅模擬程式。 在本論文中，我們延續先前的研究，將使用蒙地卡羅方法的光子模擬程式 MCML 移植到高效能計算平台上以加速模擬進行。我們比較了兩個不同的平台， Intel Xeon Phi 處理器及 Intel CPU + FPGA 軟體開發平台，分別以其進行加速並進行比較其加速成果。在 Xeon Phi 處理器上，我們以 OpenMP 進行平行化，並利用其提供的 AVX-512 向量指令集來進行向量化；在 Intel 的 CPU + FPGA 軟體開發平台上，我們透過 OpenCL 以運用 FPGA 進行計算，並利用其 CPU 與 FPGA 共用實體記憶體的特點達到進一步加速。相對於傳統的中央處理單元，我們在 Xeon Phi 處理器和 Intel CPU + FPGA 軟體開發平台上分別獲得了約 47.8 和 3.1 倍的加速。

Monte Carlo methods are widely used in solving problems with stochastic properties, such as the process of radiation from atoms in nuclear physics. By using Monte Carlo method, the stochastic processes can be directly simulated. In radiation oncology, it is required to simulate the dose distribution in advance, in order to provide higher efficacy and lower the side effects on healthy tissues. However, Monte Carlo simulation requires a lot of intensive computation to deliver the accurate result. Moreover, it is required to examine different configurations and use the simulation results to find out a proper treatment plan. Thus, the execution efficiency is an important issue in Monte Carlo simulation. Based on our previous works, this thesis further explores the performance of a Monte Carlo simulation program on high-performance computing platforms. We compare two different platforms, Intel Xeon Phi processor and Intel CPU + FPGA Software Development Platform, accelerate the program on them, and compare the acceleration results. We use OpenMP to parallelize the program, and use the AVX-512 vector instruction set to vectorize it on a Xeon Phi processor. We use FPGA to accelerate the program with OpenCL, and leverage the shared physical memory between CPU and FPGA to speed up the simulation on Intel CPU + FPGA Software Development Platform. As a result, we get a speedup of 47.8 times on Xeon Phi and 3.1 times on Intel CPU + FPGA Software Development Platform with respect to the CPU.