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

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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.