Spectral Homogenization of the Radiative Transfer Equation via Low-Rank Tensor Train Decomposition
Radiative transfer in absorbing-scattering media requires solving a transport equation across a spectral domain with 10^5 - 10^6 molecular absorption lines. Line-by-line (LBL) computation is prohibitively expensive, while existing approximations sacrifice spectral fidelity. We show that the Young-measure homogenization framework produces solution tensors I that admit low-rank tensor-train (TT) decompositions whose bond dimensions remain bounded as the spectral resolution Ns increases. Using molecular line parameters from the HITRAN database for H2O and CO2, we demonstrate that: (i) the TT rank saturates at r = 8 (at tolerance e = 10^-6) from Ns = 16 to 4096, independent of single-scattering albedo, Henyey-Greenstein asymmetry, temperature, and pressure; (ii) quantized tensor-train (QTT) representations achieve sub-linear storage scaling; (iii) in a controlled comparison using identical opacity data and transport solver, the homogenized approach achieves over an order of magnitude lower L2 error than the correlated-k distribution at equal cost; and (iv) for atomic plasma opacity (aluminum at 60 eV, TOPS database), the TT rank saturates at r = 15 with fundamentally different spectral structure (bound-bound and bound-free transitions spanning 12 decades of dynamic range), confirming that rank boundedness is a property of the transport equation rather than any particular opacity source. These results establish that the spectral complexity of radiative transfer has a finite effective rank exploitable by tensor decomposition, complementing the spatial-angular compression achieved by existing TT and dynamical low-rank approaches.
Code (0)
등록된 구현이 없습니다.
Similar Papers 제목 키워드 기반
Physics Informed Neural Networks for Simulating Radiative Transfer
We propose a novel machine learning algorithm for simulating radiative transfer. Our algorithm is based on physics informed neural networks (PINNs), which are trained by minimizing the residual of the underlying radiativ…
BIG-bench Machine LearningDeepRTE: Pre-trained Attention-based Neural Network for Radiative Tranfer
In this study, we propose a novel neural network approach, termed DeepRTE, to address the steady-state Radiative Transfer Equation (RTE). The RTE is a differential-integral equation that governs the propagation of radiat…
Computational EfficiencyRTETowards a Foundation Model for Partial Differential Equations Across Physics Domains
We present PDE-FM, a modular foundation model for physics-informed machine learning that unifies spatial, spectral, and temporal reasoning across heterogeneous partial differential equation (PDE) systems. PDE-FM combines…
Macroscopic auxiliary asymptotic preserving neural networks for the linear radiative transfer equations
We develop a Macroscopic Auxiliary Asymptotic-Preserving Neural Network (MA-APNN) method to solve the time-dependent linear radiative transfer equations (LRTEs), which have a multi-scale nature and high dimensionality. T…
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 t…
Active LearningCPUTime SeriesTime Series Analysis+1