AMC-SS Self-Optimized Monte Carlo Methods for Radiative Transport

蒙特卡罗(MC)方法是在六十多年前发展起来的，目的是研究中子通过可裂变核材料组件的输运。在其间的几年里，它们的使用急剧增长，现在它们为许多其他重要的科学和工程问题提供了计算支持的黄金标准，这些问题是使用辐射传输方程建模的。仅在生物医学中的例子就包括对不同组织系统中的光-组织相互作用进行建模，以及基于准确的剂量测量为癌症患者建立可靠的放射治疗计划。由于MC模拟在这些和许多其他应用中的重要性，MC模拟在全世界使用的计算机时间中占了相当大的比例，仅在美国就占了超级计算机费用的50%以上。多年来，人们已经提出并采用了许多关于MC方法的重大改进，但取得的根本进展很少。这个项目通过开发新的MC算法来提出这样的改进，通过在算法中引入学习机制来加速MC方法的收敛。如果执行得当，这种自适应学习机制会在计算效率(从技术上讲，是指数级增长的收敛速度)方面产生“滚雪球”式的增长，使使用新算法的计算能够在几秒钟内完成，而这将需要在同一计算机平台上进行数年甚至数百年的常规MC模拟。这项工作所涉及的理论原则已经被理解了至少十年，在“简单”问题上的实施已经产生了惊人的效率提升。然而，当尝试解决更复杂的问题时，由于计算复杂性的增加，计算优势就会消失。这个项目中将要开发的方法通过将计算范围缩小到它们最重要的部分，从而绕过了这些困难。在这样做的过程中，新的算法牺牲了在整个系统中表示RTE解决方案的无限精度，以非常小的数量的非常高的精度仅表示系统的“可测量的”。这些新方法背后的基本理论以及它们在“模型”交通问题上的应用将在今年的最初一年进行研究。

Monte Carlo (MC) methods were developed more than sixty years ago in order to investigate the transport of neutrons through fissionable assemblies of nuclear material. In the intervening years, their use has grown dramatically and they now provide a 'gold standard' of computational support for many other important problems of science and engineering that are modeled using the radiative transport equation. Examples in biomedicine alone include modeling light-tissue interactions in heterogeneous tissue systems and establishing reliable radiation therapy plans for cancer patients based on accurate dosimetry. Because of their importance in these and many other applications, MC simulations account for a significant fraction of all computer time used worldwide and for well over 50% of supercomputer expenses in the United States alone.Over the years many significant improvements in the MC method have been suggested and adopted but few fundamental advances have been made. This project proposes such an advance by developing novel MC algorithms that accelerate the convergence of the MC method through the introduction of a learning mechanism into the algorithm. When executed correctly, this adaptive learning mechanism causes a 'snowballing' increase in computational efficiency (technically, an exponentially increased convergence rate) that enables computations with the new algorithms to be completed in seconds that would require years and even centuries of conventional MC simulation on the same computer platform. The theoretical principles involved in this work have been understood for at least a decade and implementations on 'simple' problems have produced astonishing efficiency gains. However, when attempted on more complex problems, the computational advantage breaks down because of increases in computational complexity. The methods to be developed in this project circumvent these difficulties by narrowing the computations to only their most essential components. In doing this, the new algorithms sacrifice unlimited accuracy in representing the RTE solution throughout the system for very high precision in a much smaller number of quantities that represent just the system 'measurables'. The basic theory underlying these new methods and their application on 'model' transport problems will be investigated in this initial year of funding.