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[2602.17708] Spectral Homogenization of the Radiative Transfer Equation via Low-Rank Tensor Train Decomposition
Summary
This paper presents a novel approach to solving the radiative transfer equation using low-rank tensor train decomposition, enhancing computational efficiency while maintaining spectral fidelity.
Why It Matters
The findings address a significant challenge in radiative transfer calculations, where traditional methods are computationally expensive. By demonstrating that spectral complexity can be effectively managed through tensor decomposition, this research has implications for various fields including atmospheric science, astrophysics, and computational physics, potentially leading to more efficient simulations and analyses.
Key Takeaways
- Low-rank tensor train decomposition can significantly reduce computational costs in radiative transfer calculations.
- The proposed method maintains spectral fidelity while achieving lower error rates compared to traditional approaches.
- The effective rank of the transport equation is finite, allowing for efficient tensor decomposition.
- Quantized tensor-train representations offer sub-linear storage scaling, enhancing data management.
- Results are validated using real molecular line parameters, ensuring practical applicability.
Physics > Chemical Physics arXiv:2602.17708 (physics) [Submitted on 12 Feb 2026] Title:Spectral Homogenization of the Radiative Transfer Equation via Low-Rank Tensor Train Decomposition Authors:Y. Sungtaek Ju View a PDF of the paper titled Spectral Homogenization of the Radiative Transfer Equation via Low-Rank Tensor Train Decomposition, by Y. Sungtaek Ju View PDF Abstract: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 d...
