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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Machine Learning Moment Closure Models for the Radiative Transfer Equation III: Enforcing Hyperbolicity and Physical Characteristic Speeds

This is the third paper in a series in which we develop machine learning (ML) moment closure models for the radiative transfer equation. In our previous work (Huang et al. in J Comput Phys 453:110941, 2022), we proposed an approach to learn the gradient of the unclosed high order moment, which performs much better than learning the moment itself and the conventional $P_N$ closure. However, while the ML moment closure has better accuracy, it is not able to guarantee hyperbolicity and has issues with long time stability. In our second paper (Huang et al., in: Machine learning moment closure models for the radiative transfer equation II: enforcing global hyperbolicity in gradient based closures, 2021. arXiv:2105.14410), we identified a symmetrizer which leads to conditions that enforce that the gradient based ML closure is symmetrizable hyperbolic and stable over long time. The limitation of this approach is that in practice the highest moment can only be related to four, or fewer, lower moments. In this paper, we propose a new method to enforce the hyperbolicity of the ML closure model. Motivated by the observation that the coefficient matrix of the closure system is a lower Hessenberg matrix, we relate its eigenvalues to the roots of an associated polynomial. Here, we design two new neural network architectures based on this relation. The ML closure model resulting from the first neural network is weakly hyperbolic and guarantees the physical characteristic speeds, i.e., the eigenvalues are bounded by the speed of light. The second model is strictly hyperbolic and does not guarantee the boundedness of the eigenvalues. Several benchmark tests including the Gaussian source problem and the two-material problem show the good accuracy, stability and generalizability of our hyperbolic ML closure model.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Mahakala: A Python-based Modular Ray-tracing and Radiative Transfer Algorithm for Curved Spacetimes

We introduce Mahakala, a Python-based, modular, radiative ray-tracing code for curved spacetimes. We employ Google's JAX framework for accelerated automatic differentiation, which can efficiently compute Christoffel symbols directly from the metric, allowing the user to easily and quickly simulate photon trajectories through non-Kerr spacetimes. JAX also enables Mahakala to run in parallel on both CPUs and GPUs. Mahakala natively uses the Cartesian Kerr–Schild coordinate system, which avoids numerical issues caused by the pole in spherical coordinate systems. We demonstrate Mahakala's capabilities by simulating 1.3 mm wavelength images (the wavelength of Event Horizon Telescope observations) of general relativistic magnetohydrodynamic simulations of low-accretion rate supermassive black holes. The modular nature of Mahakala allows us to quantitatively explore how different regions of the flow influence different image features. We show that most of the emission seen in 1.3 mm images originates close to the black hole and peaks near the photon orbit. We also quantify the relative contribution of the disk, forward jet, and counterjet to 1.3 mm images.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

A Survey of Multimaterial Treatments for Thermal Radiative Transfer

Arbitrary Lagrangian-Eulerian methods are a popular choice for hydrodynamic modeling in radiation (rad-hydro) simulations. Because these methods involve a relaxation step that moves the mesh relative to material boundaries, multimaterial spatial zones are generally present. Accurate treatments of these zones are needed to resolve various physical phenomena of interest for inertial confinement fusion applications. However, these codes are often paired with single-material, deterministic thermal radiative transfer (TRT) codes that are oblivious to the material compositions of each zone. These single-material TRT codes can only accept homogenized material properties (opacities, specific heats, etc.) from the hydrodynamic code and output homogenized solutions. After each TRT time step, the multimaterial hydrodynamic code must dehomogenize the quantities computed by the TRT package in order to update subzonal material temperatures. The process by which hydrodynamic codes perform this dehomogenization has not been well documented in previous literature, and the methods can vary significantly from code to code. The purpose of this paper is to document, study, and compare existing techniques used for rad-hydro simulations as well as present a new method with potentially promising results. We summarize several methods and give comparisons on infinite-medium problems as well a finite-medium problem for two of the methods.

42 ENGINEERING↗
DOE OSTI2023

A Monte Carlo Thermal Radiative Transfer Solver with Nonlinear Elimination

Here in this paper, we present a new Monte Carlo method for solving the thermal radiative transfer (TRT) equations via the method of nonlinear elimination (NLEM). This method is inspired by the previous application of NLEM to thermal radiation diffusion. Our approach, called diffusion accelerated Implicit Monte Carlo (DAIMC), is a hybrid technique which combines a Monte Carlo method for solving a purely-absorbing transport equation and a diffusion solution that accounts for effective scattering, or absorption–reemission. The method aims to improve the implicitness of the traditional implicit Monte Carlo (IMC) method. We derive DAIMC generally for 3D Cartesian geometries, but in this paper, we present results and analysis in 1D slab geometry. These preliminary results indicate that DAIMC implementations may provide more accurate and robust TRT solutions than IMC in certain test problems.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

Radiative transfer in stars by feebly interacting bosons

Starting from first principles, we study radiative transfer by new feebly-interacting bosons (FIBs) such as axions, axion-like particles (ALPs), dark photons, and others. Our key simplification is to include only boson emission or absorption (including decay), but not scattering between different modes of the radiation field. Based on a given distribution of temperature and FIB absorption rate in a star, we derive explicit volume-integral expressions for the boson luminosity, reaching from the free-streaming to the strong-trapping limit. The latter is seen explicitly to correspond to quasi-thermal emission from a “FIB sphere” according to the Stefan-Boltzmann law. Our results supersede expressions and approximations found in the recent literature on FIB emission from a supernova core and, for radiatively unstable FIBs, provide explicit expressions for the nonlocal (“ballistic”) transfer of energy recently discussed in horizontal-branch stars.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

Machine Learning for Memory Reduction in the Implicit Monte Carlo Simulations of Thermal Radiative Transfer [Slides]

Project Goal: Use parametric Machine Learning methods in order to reduce memory requirements at checkpointing & restarting in the IMC simulations of Thermal Radiative Transfer using: Expectation Maximization and Weighted Gaussian Mixture Model-based approach for `particle-data compression', introduced in Plasma Physics to model Maxwellian particle distributions by Luis Chacon and Guangye Chen; Expectation Maximization with Weighted Hyper-Erlang Model in order to compress isotropic IMC particle data in the frequency domain; and Expectation Maximization and von Mises-Fisher Mixture Model for compression of anisotropic IMC particle data in the angular domain (work-in-progress).

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

Comparison of spherical harmonics method and discrete ordinates method for radiative transfer in a turbulent jet flame

Here, in this study, we systematically compared the accuracy and computational cost of two popular solution methods for the radiative transfer equation (RTE): the spherical harmonics method (P N ) and the discrete ordinates method (DOM). We first investigated convergence characteristics of different orders of P N and DOM in a series of 1D homogeneous configurations with varying optical thicknesses. Both solvers perform better for optically thicker cases. The accuracy of P N methods increases with its order, , but the gain in accuracy reduces with the increase in , i.e., improvement of P 7 over P 5 is less than that of P 3 over P 1 . This decreasing trend becomes more prominent as the optical thickness decreases. On the other hand, DOM’s accuracy increases almost linearly with the increase in the number of ordinates (or polar angles in this study) in all cases. While comparing the directional profile of radiative intensity, both solvers perform better when the radiative intensity is more isotropic. These solvers were then connected with a full spectrum k-distribution (FSK) spectral model and used to perform radiation-coupled simulations of a turbulent jet flame in an axi-symmetric cylindrical domain. Results obtained from P 1 to P 7 approximations for P N , and 2 x 4, 4 x 4, 4 x 8, 8 x 8 finite angles for DOM are compared with that from an optically thin model, and a reference solution from line-by-line (LBL) photon Monte Carlo (PMC) method. The choice of radiation solver shows a noticeable impact on the temperature distribution of the flame. The P N solvers lead to slightly higher radiant fractions and the DOM solvers lead to slightly lower radiant fractions than the PMC benchmark solution. Finally, the computational costs of each of these solvers are also reported and an intermittent evaluation / time blending scheme to improve the computational efficiency of radiation solvers in radiation-coupled simulations are also demonstrated.

42 ENGINEERING↗
DOE OSTI2026

Second Order Closures for the Radiative Transfer Equation: Some Are Unstable

The largest existing simulations of cosmic reionization model radiative transfer with moment methods that require a closure relation. The two most commonly used closure relations are M1 and OTVET; both close the moment hierarchy at the first moment. We explore the properties of a higher, second-order closure. We show that direct generalizations of M1 and OTVET to one higher order are physically unstable - i.e., the closure equations themselves result in unstable solutions, not just their numerical implementation. In fact, a generalization of OTVET to any order higher than the first one is unstable. We are also able to show that any local (i.e., depending only on the local moments of the radiation field, like M1) second-order closure that depends only on the radiation intensity and radiation flux, but does not explicitly depend on the radiation pressure, is physically unstable. This result restricts the choice of possible second-order closure relations.

Gnedin, Nickolay Y. [Fermilab; Chicago U., Astron.↗
DOE OSTI2022

Machine learning moment closure models for the radiative transfer equation I: Directly learning a gradient based closure

In this paper, we take a data-driven approach and apply machine learning to the moment closure problem for the radiative transfer equation in slab geometry. Instead of learning the unclosed high order moment, we propose to directly learn the gradient of the high order moment using neural networks. This new approach is consistent with the exact closure we derive for the free streaming limit and also provides a natural output normalization. Finally, a variety of benchmark tests, including the variable scattering problem, the Gaussian source problem with both periodic and reflecting boundaries, and the two-material problem, show both good accuracy and generalizability of our machine learning closure model.

Computer science↗
DOE OSTI2023

Enhanced Cloud Top Longwave Radiative Cooling Due To the Effect of Horizontal Radiative Transfer in the Stratocumulus to Trade Cumulus Transition Regime

Abstract Recent studies develop the SPeedy Algorithm for Radiative TrAnsfer through CloUd Sides (SPARTACUS) to handle the influence of horizontal RT on vertical radiative fluxes within an atmospheric column. The present study applies SPARTACUS to large eddy simulation (LES)‐generated cloud fields across the stratocumulus to trade cumulus transition (STCT) regime with coarse and fine vertical resolutions. The results show that, as the vertical resolution increases, radiation simulations show increasingly stronger cloud‐top longwave (LW) radiative cooling. Consequently, the sharp radiative heating gradient across the cloud layer in the LES‐like resolution simulations cannot be resolved with the coarse resolution simulations. Including the horizontal RT typically enhances cloud LW radiative cooling rate by less than 10% for all the cloud fields but more significantly in the cloud fields during the STCT. The enhanced cloud LW radiative cooling also occurs in the lower cloud layer in the decoupled cumulus cloud regime.

Geology↗
DOE OSTI2021

Axisymmetric Radiative Transfer Models of Kilonovae

The detailed observations of GW170817 proved for the first time directly that neutron star mergers are a major production site of heavy elements. The observations could be fit by a number of simulations that qualitatively agree, but can quantitatively differ (e.g., in total r-process mass) by an order of magnitude. We categorize kilonova ejecta into several typical morphologies motivated by numerical simulations, and apply a radiative transfer Monte Carlo code to study how the geometric distribution of the ejecta shapes the emitted radiation. We find major impacts on both spectra and light curves. The peak bolometric luminosity can vary by two orders of magnitude and the timing of its peak by a factor of five. These findings provide the crucial implication that the ejecta masses inferred from observations around the peak brightness are uncertain by at least an order of magnitude. Mixed two-component models with lanthanide-rich ejecta are particularly sensitive to geometric distribution. A subset of mixed models shows very strong viewing angle dependence due to lanthanide "curtaining," which persists even if the relative mass of lanthanide-rich component is small. The angular dependence is weak in the rest of our models, but different geometric combinations of the two components lead to a highly diverse set of light curves. We identify geometry-dependent P Cygni features in late spectra that directly map out strong lines in the simulated opacity of neodymium, which can help to constrain the ejecta geometry and to directly probe the r-process abundances.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

pySMARTS: SMARTS Python Wrapper (Simple Model of the Atmospheric Radiative Transfer of Sunshine)

The pySMARTS module contains functions for calling SMARTS: Simple Model of the Atmospheric Radiative Transfer of Sunshine, from NREL, developed by Dr. Christian Gueymard. SMARTS software can be obtained from: https://www.nrel.gov/grid/solar-resource/smarts.html Users will be responsible to obtain a copy of SMARTS from NREL, honor it's license, and download the SMART files into their PVLib folder. This wrapper is shared under a BSD-3-Clause License, and was originally coded in Matlab by Juan Russo (2001), updated and ported to python by Silvana Ayala (2019-2020).

Ayala Pelaez, Silvana↗
DOE OSTI2025

Outflowing photoionized plasma in Circinus X-1 using the high-resolution X-ray spectrometer Resolve onboard XRISM and the radiative transfer code cloudy

High-resolution X-ray spectroscopy is a key to understanding the mass inflow and outflow of compact objects. Spectral lines carry information about the ionization, density, and velocity structures through their intensity ratios and profiles. They are formed in non-local thermodynamic equilibrium conditions under the intense radiation field from the compact objects; thus radiative transfer (RT) calculation is a requisite for proper interpretations. We present such a study for a low-mass X-ray binary, Circinus X-1, from which the P Cygni profile was discovered using the X-ray grating spectrometer onboard Chandra. We observed the source using the X-ray microcalorimeter onboard XRISM at an orbital phase of 0.93–0.97 and revealed many spectral features unidentified before: the higher series transitions ($n{\rightarrow }1$; $n>2$) of highly ionized (H- and He-like) S, Ca, Ar, and Fe in emission and absorption, the Fe K$\alpha$ and K$\beta$ inner-shell excitation absorption of mildly ionized (O- to Li-like) Fe, and resolved fine-structure level transitions in the Fe Ly$\alpha$ and He$\alpha$ complexes. They blend with each other at different velocity shifts on top of apparently variable continuum emission that changed its flux by an order of magnitude within a 70 ks telescope time. Despite such complexity in the observed spectra, most of them can be explained by a simple model consisting of the photoionized plasma outflowing at $\sim$300 km s$^{-1}$ and the variable blocking material in the line of sight of the incident continuum emission from the accretion disk. We demonstrate this with the aid of the RT code cloudy for the line ratio diagnostics and spectral fitting. We further constrain the physical parameters of the outflow and argue that the outflow is launched close to the outer edge of the accretion disk and can be driven radiatively by being assisted by the line force calculated using the RT simulation.

X-rays: binaries↗
DOE OSTI2025

Monte Carlo Simulations of Polarized Radiative Transfer in Neutron Star Atmospheres

Soft X-ray emission from neutron stars affords powerful diagnostic tools for uncovering their surface and interior properties, as well as their geometric configurations. In the atmospheres of neutron stars, the presence of magnetic fields alters the photon-electron scattering cross sections, resulting in nontrivial angular dependence of intensity and polarization of the emergent signals. This paper presents recent developments of our Monte Carlo simulation, MAGTHOMSCATT, which tracks the complex electric field vector for each photon during its transport. Our analysis encompasses the anisotropy and polarization characteristics of X-ray emission for field strengths ranging from nonmagnetic to extremely magnetized regimes that are germane to magnetars. In the very low field domain, we reproduced the numerical solution to the radiative transfer equation for nonmagnetic Thomson scattering, and provided analytical fits for the angular dependence of the intensity and the polarization degree. These fits can be useful for studies of millisecond pulsars and magnetic white dwarfs. By implementing a refined injection protocol, we show that, in the magnetar regime, the simulated intensity and polarization pulse profiles of emission from extended surface regions becomes invariant with respect to the ratio of photon (ω) and electron cyclotron (ω B ) frequencies once ω/ω B ≲ 0.01. This circumvents the need for simulations pertinent to really high magnetic field strengths, which are inherently slower. Our approach will be employed elsewhere to model observational data to constrain neutron star geometric parameters and properties of emitting hot spots on their surfaces.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

Airborne hyperspectral imaging of nitrogen deficiency on crop traits and yield of maize by machine learning and radiative transfer modeling

Nitrogen is an essential nutrient that directly affects plant photosynthesis, crop yield, and biomass production for bioenergy crops, but excessive application of nitrogen fertilizers can cause environmental degradation. To achieve sustainable nitrogen fertilizer management for precision agriculture, there is an urgent need for nondestructive and high spatial resolution monitoring of crop nitrogen and its allocation to photosynthetic proteins as that changes over time. Here, we used visible to shortwave infrared (400–2400 nm) airborne hyperspectral imaging with high spatial (0.5 m) and spectral (3–5 nm) resolutions to accurately estimate critical crop traits, i.e., nitrogen, chlorophyll, and photosynthetic capacity (CO 2 -saturated photosynthesis rate, V max,27 ), at leaf and canopy scales, and to assess nitrogen deficiency on crop yield. We conducted three airborne campaigns over a maize (Zea mays L.) field during the growing season of 2019. Physically based soil-canopy Radiative Transfer Modeling (RTM) and data-driven approaches i.e. Partial-Least Squares Regression (PLSR) were used to retrieve crop traits from hyperspectral reflectance, with ground truth of leaf nitrogen, chlorophyll, V max,27 , Leaf Area Index (LAI), and harvested grain yield. To improve computational efficiency of RTMs, Random Forest (RF) was used to mimic RTM simulations to generate machine learning surrogate models RTM-RF. The results show that prior knowledge of soil background and leaf angle distribution can significantly reduce the ill-posed RTM retrieval. RTM-RF achieved a high accuracy to predict leaf chlorophyll content (R 2 = 0.73) and LAI (R 2 = 0.75). Meanwhile, PLSR exhibited better accuracy to predict leaf chlorophyll content (R 2 = 0.79), nitrogen concentration (R 2 = 0.83), nitrogen content (R 2 = 0.77), and V max,27 (R 2 = 0.69) but required measured traits for model training. We also found that canopy structure signals can enhance the use of spectral data to predict nitrogen related photosynthetic traits, as combining RTM-RF LAI and PLSR leaf traits well predicted canopy-level traits (leaf traits × LAI) including canopy chlorophyll (R 2 = 0.80), nitrogen (R 2 = 0.85) and V max,27 (R 2 = 0.82). Compared to leaf traits, we further found that canopy-level photosynthetic traits, particularly canopy V max,27 , have higher correlation with maize grain yield. This study highlights the potential for synergistic use of process-based and data-driven approaches of hyperspectral imaging to quantify crop traits that facilitate precision agricultural management to secure food and bioenergy production.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2024

A reduced-order model for nonlinear radiative transfer problems based on moment equations and POD-Petrov-Galerkin projection of the normalized Boltzmann transport equation

A data-driven projection-based reduced-order model (ROM) for nonlinear thermal radiative transfer (TRT) problems is presented. The TRT ROM is formulated by (i) a hierarchy of low-order quasidiffusion (aka variable Eddington factor) equations for moments of the radiation intensity and (ii) the normalized Boltzmann transport equation (BTE). The multilevel system of moment equations is derived by projection of the BTE onto a sequence of subspaces which represent elements of the phase space of the problem. Exact closure for the moment equations is provided by the Eddington tensor. A Petrov-Galerkin (PG) projection of the normalized BTE is formulated using a proper orthogonal decomposition (POD) basis representing the normalized radiation intensity over the whole phase space and time. The Eddington tensor linearly depends on the solution of the normalized BTE. By linear superposition of the POD basis functions, a low-rank expansion of the Eddington tensor is constructed with coefficients defined by the PG projected normalized BTE. The material energy balance (MEB) equation is coupled with the effective gray low-order equations which exist on the same dimensional scale as the MEB equation. The resulting TRT ROM is structure and asymptotic preserving. A detailed analysis of the ROM is performed on the classical Fleck-Cummings (F-C) TRT multigroup test problem in 2D geometry. Numerical results are presented to demonstrate the ROM's effectiveness in the simulation of radiation wave phenomena. Importantly, the ROM is shown to produce solutions with sufficiently high accuracy while using low-rank approximation of the normalized BTE solution. Essential physical characteristics of supersonic radiation wave are preserved in the ROM solutions.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗