Accurate Reduced Floating-Point Precision Implicit Monte Carlo

TL;DR

This work addresses implementing an accurate IMC scheme for thermal radiative transfer in reduced-precision arithmetic by combining scaling strategies, floating-point arithmetic manipulations, and batching. The authors validate their approach by comparing half-precision ($16$-bit) IMC results against a double-precision baseline on the Su & Olson benchmark, using Julia and providing open-source code. They demonstrate that, with careful techniques (relative positioning, cross-section scaling, stable summation, and robust random-number generation), half-precision results achieve close agreement to the double-precision solutions, evidenced by $L^2$ relative errors on the order of a few percent to a few tenths across key quantities. The study highlights the potential for memory- and compute-efficient radiative-transfer simulations on modern hardware, while outlining limitations and avenues for further improvement, such as dynamic re-scaling and extending to other IMC variants.

Abstract

This work describes methodologies to successfully implement the Implicit Monte Carlo (IMC) scheme for thermal radiative transfer in reduced-precision floating-point arithmetic. The methods used can be broadly categorized into scaling approaches and floating-point arithmetic manipulations. Scaling approaches entail re-scaling values to ensure computations stay within a representable range. Floating-point arithmetic manipulations involve changes to order of operations and alternative summation algorithms to minimize errors in calculations. The Implicit Monte Carlo method has nonlinear dependencies, quantities spanning many orders of magnitude, and a sensitive coupling between radiation and material energy that provide significant difficulties to accurate reduced-precision implementations. Results from reduced and higher-precision implementations of IMC solving the Su & Olson volume source benchmark problem are compared to demonstrate the accuracy of a correctly implemented reduced-precision IMC code. We show that the scaling approaches and floating-point manipulations used in this work can produce solutions with similar accuracy using half-precision data types as compared to a standard double-precision implementation.

Figures (2)

• Figure 1: Half-Precision Radiation Energy Density Scatter Case
• Figure 3: Half-Precision Material Energy Density Scatter Case