Chemical Reaction Informatics Team Seminar(Talk by Kishan Wimalawarne, Kyushu University).

【Team】Chemical Reaction Informatics Team
【Date】2026/July/3(Friday) 15:00-16:00(JST)
【Speaker】Talk by Kishan Wimalawarne, Kyushu University

Title: Learning Green’s function efficiently using low-rank approximations

Abstract:Physics-informed neural networks are gaining popularity in solving partial differential equations. Recently,
parameterization of the Green’s function using deep learning has shown to be efficient in solving partial
differential equations. However, a practical limitation of this approach is the repeated computation of Monte
Carlo integral approximations, which makes the learning process computationally expensive. To address this,
we propose DecGreenNet, a novel algorithm that uses low-rank decomposition to learn the Green’s function
efficiently. This novel architecture predicts the solution of PDE at a grid element using the product of two
networks; one taking each grid element as input and the other taking the Monte Carlo samples as input. This
novel architecture predicts the solution of PDE at a grid element using the product of two networks; one
taking each grid element as input and the other taking the Monte Carlo samples as input.
Experimental results show that the proposed method achieves faster training times compared to MOD-Net
while maintaining comparable or lower prediction error relative to both PINNs and MOD-Net. We also provide
a theoretical analysis for Green’s function based PINNs, including both DecGreenNet and MOD-Net, using a
clipped Green’s function. Our analysis shows that both MOD-Net and DecGreenNet obtains similar
convergence rates. Additionally, we demonstrate that tensor methods can be used for the decomposition of
the Green's function to learn high-dimensional PDEs. Finally, we discuss future research directions for both
algorithmic developments and theoretical analysis for Green's function based PINNs.