Multigroup Thermal Radiation Transport with Tensor Trains

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. We consistently achieve compression factors $>$100$\times$ and speedups $>$2$\times$. The solver is evaluated across a range of test problems with varying levels of complexity. In addition, we further analyze the low-rank structure of the merged spatio-spectral core to evaluate the potential for additional compression via more advanced TT decompositions.