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

by   Yuankai Teng, et al.

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



There are no comments yet.


page 1

page 2

page 3

page 4


FCNN: Five-point stencil CNN for solving reaction-diffusion equations

In this paper, we propose Five-point stencil CNN (FCNN) containing a fiv...

Stiff-PINN: Physics-Informed Neural Network for Stiff Chemical Kinetics

Recently developed physics-informed neural network (PINN) has achieved s...

Schwarz Waveform Relaxation Physics-Informed Neural Networks for Solving Advection-Diffusion-Reaction Equations

This paper develops a physics-informed neural network (PINN) based on th...

Informed Equation Learning

Distilling data into compact and interpretable analytic equations is one...

Diffusion Equations on Graphs

In brain imaging, the image acquisition and processing processes themsel...

Deep Learning for Physical Processes: Incorporating Prior Scientific Knowledge

We consider the use of Deep Learning methods for modeling complex phenom...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.