SKIRT: the design of a suite of input models for Monte Carlo radiative transfer simulations

The Monte Carlo method is the most popular technique to perform radiative transfer simulations in a general 3D geometry. The algorithms behind and acceleration techniques for Monte Carlo radiative transfer are discussed extensively in the literature, and many different Monte Carlo codes are publicly available. On the contrary, the design of a suite of components that can be used for the distribution of sources and sinks in radiative transfer codes has received very little attention. The availability of such models, with different degrees of complexity, has many benefits. For example, they can serve as toy models to test new physical ingredients, or as parameterised models for inverse radiative transfer fitting. For 3D Monte Carlo codes, this requires algorithms to efficiently generate random positions from 3D density distributions. We describe the design of a flexible suite of components for the Monte Carlo radiative transfer code SKIRT. The design is based on a combination of basic building blocks (which can be either analytical toy models or numerical models defined on grids or a set of particles) and the extensive use of decorators that combine and alter these building blocks to more complex structures. For a number of decorators, e.g. those that add spiral structure or clumpiness, we provide a detailed description of the algorithms that can be used to generate random positions. Advantages of this decorator-based design include code transparency, the avoidance of code duplication, and an increase in code maintainability. Moreover, since decorators can be chained without problems, very complex models can easily be constructed out of simple building blocks. Finally, based on a number of test simulations, we demonstrate that our design using customised random position generators is superior to a simpler design based on a generic black-box random position generator.Comment: 15 pages, 4 figures, accepted for publication in Astronomy and Computin

Diffusive optical tomography in the Bayesian framework

Many naturally-occuring models in the sciences are well-approximated by simplified models, using multiscale techniques. In such settings it is natural to ask about the relationship between inverse problems defined by the original problem and by the multiscale approximation. We develop an approach to this problem and exemplify it in the context of optical tomographic imaging. Optical tomographic imaging is a technique for infering the properties of biological tissue via measurements of the incoming and outgoing light intensity; it may be used as a medical imaging methodology. Mathematically, light propagation is modeled by the radiative transfer equation (RTE), and optical tomography amounts to reconstructing the scattering and the absorption coefficients in the RTE from boundary measurements. We study this problem in the Bayesian framework, focussing on the strong scattering regime. In this regime the forward RTE is close to the diffusion equation (DE). We study the RTE in the asymptotic regime where the forward problem approaches the DE, and prove convergence of the inverse RTE to the inverse DE in both nonlinear and linear settings. Convergence is proved by studying the distance between the two posterior distributions using the Hellinger metric, and using Kullback-Leibler divergence

Probabilistic Dalek -- Emulator framework with probabilistic prediction for supernova tomography

Supernova spectral time series can be used to reconstruct a spatially resolved explosion model known as supernova tomography. In addition to an observed spectral time series, a supernova tomography requires a radiative transfer model to perform the inverse problem with uncertainty quantification for a reconstruction. The smallest parametrizations of supernova tomography models are roughly a dozen parameters with a realistic one requiring more than 100. Realistic radiative transfer models require tens of CPU minutes for a single evaluation making the problem computationally intractable with traditional means requiring millions of MCMC samples for such a problem. A new method for accelerating simulations known as surrogate models or emulators using machine learning techniques offers a solution for such problems and a way to understand progenitors/explosions from spectral time series. There exist emulators for the TARDIS supernova radiative transfer code but they only perform well on simplistic low-dimensional models (roughly a dozen parameters) with a small number of applications for knowledge gain in the supernova field. In this work, we present a new emulator for the radiative transfer code TARDIS that not only outperforms existing emulators but also provides uncertainties in its prediction. It offers the foundation for a future active-learning-based machinery that will be able to emulate very high dimensional spaces of hundreds of parameters crucial for unraveling urgent questions in supernovae and related fields.Comment: 7 pages, accepted at ICML 2022 Workshop on Machine Learning for Astrophysic

Deep learning for the modeling and inverse design of radiative heat transfer

Deep learning is having a tremendous impact in many areas of computer science and engineering. Motivated by this success, deep neural networks are attracting increasing attention in many other disciplines, including the physical sciences. In this work, we show that artificial neural networks can be successfully used in the theoretical modeling and analysis of a variety of radiative-heat-transfer phenomena and devices. By using a set of custom-designed numerical methods able to efficiently generate the required training data sets, we demonstrate this approach in the context of three very different problems, namely (i) near-field radiative heat transfer between multilayer systems that form hyperbolic metamaterials, (ii) passive radiate cooling in photonic crystal slab structures, and (iii) thermal emission of subwavelength objects. Despite their fundamental differences in nature, in all three cases we show that simple neural-network architectures trained with data sets of moderate size can be used as fast and accurate surrogates for doing numerical simulations, as well as engines for solving inverse design and optimization in the context of radiative heat transfer. Overall, our work shows that deep learning and artificial neural networks provide a valuable and versatile toolkit for advancing the field of thermal radiatio

Ray-tracing for complex astrophysical high-opacity structures

We present a ray-tracing technique for radiative transfer modeling of complex three-dimensional (3D) structures which include dense regions of high optical depth like in dense molecular clouds, circumstellar disks, envelopes of evolved stars, and dust tori around active galactic nuclei. The corresponding continuum radiative transfer problem is described and the numerical requirements for inverse 3D density and temperature modeling are defined. We introduce a relative intensity and transform the radiative transfer equation along the rays to solve machine precision problems and to relax strong gradients in the source term. For the optically thick regions where common ray-tracers are forced to perform small trace steps, we give two criteria for making use of a simple approximative solver crossing the optically thick region quickly. Using an example of a density structure with optical depth changes of 6 orders of magnitude and sharp temperature variations, we demonstrate the accuracy of the proposed scheme using a common 5th-order Runge-Kutta ray-tracer with adaptive step size control. In our test case, the gain in computational speed is about a factor of 870. The method is applied to calculate the temperature distribution within a massive molecular cloud core for different boundary conditions for the radiation field.Comment: 21 pages, 5 figures to appear in Astrophysical Journa