Three approaches on estimating geometric sensitivities in radiative transfer with Monte Carlo

Abstract

The Monte Carlo method, renowned for its ability to handle the spectral and geometric complexities of 3D radiative transfer, is extensively utilized across various fields, including concentrated solar power design, atmospheric science, and computer graphics. The success of this method also extends to the estimation of sensitivity—the derivative of an observable with respect to a given system parameter, which is, however, particularly challenging when these parameters involve geometric deformation. Bridging statistical physics and computer graphics, distinct methodologies have emerged within these fields for estimating geometric sensitivity, each employing unique terminologies and mathematical frameworks, leading to seemingly disparate approaches. In this paper, we review the three main approaches to sensitivity estimation: (1) Expectation Differentiation, which employs a vectorized Monte Carlo algorithm to simultaneously estimate the intensity and its sensitivity; (2) Differentiable Rendering, predominantly used in computer graphics and applied in numerous contexts; (3) Transport Model for Sensitivity, which conceptualizes sensitivity as a physical quantity with its own transport equations and boundary conditions, thereby facilitating engineering and physics analyses. We aim to enhance readers’ ability to tackle sensitivity-related challenges by providing a comparative understanding of these three perspectives. We achieve this through a simplified one-dimensional radiative transfer case study, offering an accessible platform for comparing and classifying these approaches based on their theoretical underpinnings and practical application in Monte Carlo algorithms.