Thermal Radiation Transport with Tensor Trains

Journal Article · Mon Jul 14 00:00:00 EDT 2025 · The Astrophysical Journal

DOI:https://doi.org/10.3847/1538-4357/adda3f· OSTI ID:2575583

Gorodetsky, Alex A. ^[1]; Mullen, Patrick Dean ^[2]; Deshpande, Aditya ^[1]; Dolence, Joshua C. ^[3]; Meyer, Chad D. ^[4]; Miller, Jonah Maxwell ^[4]; Roberts, Luke Forrest ^[4]

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1. Univ. of Michigan, Ann Arbor, MI (United States); Los Alamos National Laboratory (LANL), Ann Arbor, MI (United States)
2. Los Alamos National Laboratory (LANL), Ann Arbor, MI (United States)
3. Univ. of Michigan, Ann Arbor, MI (United States); Los Alamos National Laboratory (LANL), Ann Arbor, MI (United States); Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
4. Los Alamos National Laboratory (LANL), Ann Arbor, MI (United States); Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)

We present a novel tensor network algorithm to solve the time-dependent, gray thermal radiation transport equation. The method invokes a tensor train (TT) decomposition for the specific intensity. The efficiency of this approach is dictated by the rank of the decomposition. When the solution is “low rank,” the memory footprint of the specific intensity solution vector may be significantly compressed. The algorithm, following a step-then-truncate approach of a traditional discrete ordinates method, operates directly on the compressed state vector, thereby enabling large speedups for low-rank solutions. To achieve these speedups, we rely on a recently developed rounding approach based on the Gram-SVD. We detail how familiar S_N algorithms for (gray) thermal transport can be mapped to this TT framework and present several numerical examples testing both the optically thick and thin regimes. The TT framework finds low-rank structure and supplies up to ≃60× speedups and ≃1000× compressions for problems demanding large angle counts, thereby enabling previously intractable SN calculations and supplying a promising avenue to mitigate ray effects.

• Research Organization: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
• Sponsoring Organization: US Air Force Office of Scientific Research (AFOSR); USDOE National Nuclear Security Administration (NNSA), Office of Defense Programs (DP)
• Grant/Contract Number: 89233218CNA000001
• OSTI ID: 2575583
• Report Number(s): LA-UR--25-22716; 10.3847/1538-4357/adda3f; 1538-4357
• Journal Information: The Astrophysical Journal, Journal Name: The Astrophysical Journal Journal Issue: 1 Vol. 988; ISSN 0004-637X; ISSN 1538-4357
• Publisher: IOP Publishing
• Country of Publication: United States
• Language: English

Related Subjects

79 ASTRONOMY AND ASTROPHYSICS