Symbolic Monte Carlo method applied to the identification of radiative properties of a heterogeneous material

Abstract

A Symbolic Monte Carlo method (SMC) is applied to the identification of radiative properties of a heterogeneous semitransparent insulating material from measurements of directional-hemispherical transmittance and reflectance at room temperature. The polynomials obtained with SMC allow the development of a complete inverse analysis which determines if the inverse problem solution exists, is unique and stable. Moreover, the numerical efficiency of the absorption and scattering coefficients identification is improved since the radiative transfer equation is only solved once in the overall inverse iterative procedure.

A Functionalized Monte Carlo 3D Radiative Transfer Model: Radiative Effects of Clouds Over Reflecting Surfaces

“…It was our intention to emphasize this aspect rather than the perhaps more obvious benefits of the FMC methods: the fact that they greatly accelerate MC methods, as only one simulation is needed to recover the amount of information that would normally be output from an arbitrary large number of standard simulations. This property has been useful in particular in the context of parameter identification or inversion (Dunn, 1981;Floyd et al, 1986;Maanane et al, 2020;Sans, Blanco, et al, 2021) and more generally has a great potential for global nonlinear parametric sensitivity analyses. In other words, FMC methods can be thought of as a physically-informed machine learning technique.…”

5-ALA induced PpIX fluorescence spectroscopy in neurosurgery: a review

“…The use of an approximate RTE solution under experimental conditions is often due to experimental constraints, e.g., it is not possible to perform an in vivo transmittance measurement during neurosurgery. As computer performance improves, inverse approaches using Monte-Carlo ( Jacques, 1998 , 2003 ) and symbolic Monte-Carlo methods ( Galtier et al, 2017 ; Maanane et al, 2020 ) are also being developed. Whatever the model used to solve the RTE, measured fluorescence signal is then corrected using the estimated local optical properties of the tissue.…”

The Past and Future of the Monte Carlo Method in Thermal Radiation Transfer

“…The null-collision approach provides a convenient foundation for the "symbolic MC" technique [180][181][182][183]. As shown in Eq.…”

“…Symbolic MC is particularly useful if the radiative properties of the medium can be parameterized as a polynomial, in which case far fewer trials are needed to obtain an estimate for the intensity compared to the conventional approach. It is also well-suited to problems in which the objective is to infer unknown absorption and scattering coefficients from measured intensity values [180][181][182][183].…”