Approximating elliptic PDE by perturbation of neural dynamics
L. F. Cheung, Leong Kwan Li · 2002
After finite difference discretization, solving elliptic partial differential equation (PDE) numerically would be equivalent to solving a positive definite linear system Ax=b. By rescaling the linear system so as to bound the solution x around the origin, we introduce the term Ax-b as a perturbation to an artificial neural network and show that the equilibrium state around the origin is an approximate solution.