Path integral radiative transfer via polyline representation allowing GPU implementation

Abstract

Many research areas require simulating particle transport through scattering media. For instance, radiative transfer is useful for computer graphics and for neutron transport in nuclear physics. These transport simulations tend to be computationally expensive for problems involving large amounts of multiple scattering in generic geometries, requiring significant time to compute. Finding a fast solution for these types of problems remains an open area for research. Previous work shows that radiative transfer can be represented as a Feynman Path Integral over all paths between two points in a space. The path integral assigns a weight to each path based on the local curvature of the path, accumulating a transport kernel by summing the weights of all of the paths. Previous work demonstrated a Monte Carlo method for computing the radiative transfer Feynman path integral via repeatedly perturbing paths to generate new paths, using a discrete Frenet-Serret framework and an expensive root-solve calculation. The approach is highly parallelizable on the CPU, however computations require a supercomputer to complete in reasonable time. While a GPU implementation was considered for this previous approach, the root-solve and path representation mapped poorly to the GPU, hindering a reasonable implementation. In the present work, we propose a representation of paths as polylines, and a new curve perturbation method that guarantees production of a new unique path each execution while maintaining the boundary conditions of each path, but without the time-consuming root-solve. The new perturbation method’s structure maps well to the GPU, allowing implementation in CUDA which outperforms the CPU, and allows the utilization of GPU hardware.