Deep Generalized Green's Functions

Understand

In this study, we address the challenge of obtaining a Green's function operator for linear partial differential equations (PDEs).

• The Green's function is well-sought after due to its ability to directly map inputs to solutions, bypassing the need for common numerical methods such as finite difference and finite elements methods.
• However, obtaining an explicit form of the Green's function kernel for most PDEs has been a challenge due to the Dirac delta function singularity present.
• To address this issue, we propose the Deep Generalized Green's Function (DGGF) as an alternative, which can be solved for in an efficient and accurate manner using neural network models.