DOE OSTI · 2575583
Thermal Radiation Transport with Tensor Trains
Abstract
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.
Explore related subjects
Keep this discovery
Explore connections, maps & timelines
Gorodetsky, Alex A. [Univ. of Michigan, Ann Arbor, MI (United States); Los Alamos National Laboratory (LANL), Ann Arbor, MI (United States)] (ORCID:0000000331528206), Mullen, Patrick Dean [Los Alamos National Laboratory (LANL), Ann Arbor, MI (United States)] (ORCID:0000000321314634), Deshpande, Aditya [Univ. of Michigan, Ann Arbor, MI (United States); Los Alamos National Laboratory (LANL), Ann Arbor, MI (United States)] (ORCID:000900098285861X), Dolence, Joshua C. [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)] (ORCID:0000000343538751), Meyer, Chad D. [Los Alamos National Laboratory (LANL), Ann Arbor, MI (United States); Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)] (ORCID:0000000275306173), Miller, Jonah Maxwell [Los Alamos National Laboratory (LANL), Ann Arbor, MI (United States); Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)] (ORCID:0000000164327860), Roberts, Luke Forrest [Los Alamos National Laboratory (LANL), Ann Arbor, MI (United States); Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)] (ORCID:0000000173647946). 2025-07-14. Thermal Radiation Transport with Tensor Trains. https://doi.org/10.3847/1538-4357%2Fadda3f
Cite the original work for its findings. Save a collection to share your selection of sources.