面向大规模蒙特卡罗科学计算的FPGA加速关键技术研究与应用

The Monte Carlo method is widely used in a large number of scientifical applications, including molecular physics simulation, financial modeling and biomedical simulation. With rapid development of science, the practical problems become increasingly complicated, causing the Monte Carlo computations to become more and more time-consuming. Thus accelerating Monte Carlo simulation is becoming an increasingly important issue in designing modern systems. Field-Programmable Gate Arrays (FPGAs) have advantages over CPUs and GPUs in terms of reconfigurable, bit-wise parallelization, hign performance and low power consumption. Thus the use of FPGAs is becoming a promising solution for accelerating Monte Carlo simulations. However, there are some challenges to overcome: the diversity of algorithms, parallel algorithm design and optimal hardware structure customization. Existing FPGA structures consume considerable resources, have limitations in the parallel structure, and most of them are customized for specific algorithms. .This project emphasizes accelerating Monte Carlo computations using FPGA-based techniques. We break through the following key techniques: an word-length determination tool which is capable of automatically transforming the system from Floating-Point model to Fixed-Point model and providing a series of word-length solutions that form a tradeoff balance between hardware complexity and signal quality, a framework for generating multivariate Gaussian random numbers in parallel. Based on these key techniques, we design a FPGA-based structure for accelerating coupled electron-photon transportation for Dose Calculation in Radiation Therapy Treatment Planning, as well as a parallel framework for accelerating a Monte-Carlo based CDS pricing model. The research results of this project will provide an important infrastructure for High Performance Computation system design.

蒙特卡罗模拟是一种广泛应用于分子物理学、金融工程学等领域求解科学计算问题的重要方法。随着科学技术的发展，运用蒙特卡罗方法解决实际问题的复杂性不断增大，导致对计算设备运算能力的需求也在不断地增强。开发新的计算模式以实现对蒙特卡罗模拟进行加速已成为现代科学计算急需解决的重要问题。近年来，FPGA芯片以其可重构、支持细粒度并行、高性能、低功耗等优势，已成为理想的计算加速平台。然而，FPGA加速蒙特卡罗计算还面临着算法特征多样性、算法并行结构设计困难、硬件结构优化复杂等挑战。.本项目以FPGA可重构体系结构为研究平台，在深入分析蒙特卡罗科学计算特点的基础上，对利用FPGA加速蒙特卡罗计算所需解决的浮点转定点、并行随机数生成等关键技术进行深入地研究。并在此基础上实现光子/电子联合输运方程以及金融工程领域CDS定价模型的FPGA加速系统。研究成果将为我国高性能科学计算的发展提供坚实的理论与技术支撑。

本项目对蒙特卡罗(MC)计算的多FPGA并行加速技术进行了深入地研究。集中解决了实现并行加速的几项关键技术，并在此基础上实现了对多维高斯随机数生成、粒子输运方程计算及金融衍生产品定价模型的计算加速。具体研究内容包括：..1) 提出了一种面向多FPGA的并行MC计算加速器的设计框架。并重点对以下几项关键技术进行了突破： 提出了自适应编码CORDIC算法ARC及改进自适应编码 CORDIC算法EARC。相对于传统CORDIC算法，ARC算法和EARC算法在等同角度分辨率条件下能够有效减少循环迭代次数，不但有效减少了资源开销和功耗开销，并且提高了计算精度；基于FJA技术，提出了一种面向多FPGA的MC并行加速框架。基于该框架可以产生任意路不相关的均匀分布随机数序列，为MC计算的并行化提供了技术支撑；提出了基于UVM的模拟验证平台。基于该平台可以对MC并行加速器进行完备的随机测试和定向测试；提出一种柔性可扩展高阶路由器微体系结构。该结构通过在单个瓦片内聚合多个物理端口，能有效降低了存储及总线开销。..2）提出了一种并行多维高斯随机数硬件加速结构。该结构采用了WELL19937算法作为均匀分布随机数发生器，能够产生任意路互不相关的多维高斯随机数向量，且具有高性能、低硬件消耗的特点。. 3) 提出了一种光子输运快速MC模拟的并行FPGA加速结构。该结构通过流水线并行、位级并行以及特殊的结构设计，能够高效的完成光子输运模拟，同时保持较低的硬件开销。 . 4）提出了一种金融衍生产品定价模型的并行FPGA加速框架。基于该框架，选择了期权定价和信用违约互换两种金融衍生产品定价模型进行了实现，实验结果表明，所设计的两种加速结构均具有很好的可扩展性。在性能上要优于通用处理器。在周期、随机数质量、性能/面积消耗比等指标上均要优于相关工作。并且在性能和面积消耗上均优于相应的浮点实现。..本项目相关研究成果在《IEEE Transactions on Parallel and Distributed Systems》、FPT、WCSE、ICCSN等国外期刊会议上发表论文7篇。其中SCI检索论文1篇，EI检索论文6篇。培养博士研究生2名。申请国家发明专利2项。

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