Multigroup Thermal Radiation Transport with Tensor Trains

TL;DR

This paper applies tensor-train algorithms to multigroup thermal radiation transport, enabling efficient simulations of extremely large discretized problems by exploiting low-rank structures.

Contribution

It demonstrates the effectiveness of TT representations in solving large-scale multigroup radiation transport problems with significant compression and speedup.

Findings

Achieved over 100x compression factors in test problems.

Realized more than 2x speedup in computations.

Identified potential for up to 7x additional compression through alternative TT topologies.

Abstract

We investigate the application of tensor-train (TT) algorithms to multigroup thermal radiation transport (i.e., photon radiation transport). The TT framework enables simulations at discretizations that might otherwise be computationally infeasible on conventional hardware. We show that solutions to certain multigroup problems possess an intrinsic low-rank structure, which the TT representation leverages effectively. This enables us to solve problems where the discretized solution size exceeds a trillion parameters on a single node. The solver is evaluated on a range of test problems with varying levels of complexity, consistently achieving compression factors greater than $100 \times$ and speedups exceeding $2 \times$. We also investigate alternative TT topologies by analyzing the low-rank structure of the merged spatio-spectral core to assess the potential for greater compression. This analysis suggests that compression gains could increase by factors as large as $7$. Our results indicate that the low-rank structure of the merged spatio-spectral core captures the spatio-spectral complexity of the solution, largely driven by the opacity structure of the medium. Beyond identifying opportunities for improved compression, this analysis highlights the types of errors that may arise in angle-integrated quantities when exploiting this low-rank structure.