Learning Green's Function Efficiently Using Low-Rank Approximations
Kishan Wimalawarne Taiji Suzuki Sophie Langer
Learning the Green's function using deep learning models enables to solve
different classes of partial differential equations. A practical limitation of
using deep learning for the Green's function is the repeated computationally
expensive Monte-Carlo integral approximations. We propose to learn the Green's
function by low-rank decomposition, which results in a novel architecture to
remove redundant computations by separate learning with domain data for
evaluation and Monte-Carlo samples for integral approximation. Using
experiments we show that the proposed method improves computational time
compared to MOD-Net while achieving comparable accuracy compared to both PINNs
and MOD-Net.