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Partial differential equations are often used to model various physicalphenomena, such as heat diffusion, wave propagation, fluid dynamics,elasticity, electrodynamics and image processing, and many analytic approachesor traditional numerical methods have been developed and widely used for theirsolutions. Inspired by rapidly growing impact of deep learning on scientificand engineering research, in this paper we propose a novel neural network,GF-Net, for learning the Green's functions of linear reaction-diffusionequations in an unsupervised fashion. The proposed method overcomes thechallenges for finding the Green's functions of the equations on arbitrarydomains by utilizing physics-informed approach and the symmetry of the Green'sfunction. As a consequence, it particularly leads to an efficient way forsolving the target equations under different boundary conditions and sources.We also demonstrate the effectiveness of the proposed approach by experimentsin square, annular and L-shape domains.

Learning Green's Functions of Linear Reaction-Diffusion Equations with Application to Fast Numerical Solver