Title :
Approximating elliptic PDE by perturbation of neural dynamics
Author :
Cheung, Leung Fu ; Li, Leong Kwan
Author_Institution :
Dept. of Appl. Math., Hong Kong Polytech., Hong Kong
Abstract :
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
Keywords :
approximation theory; finite difference methods; linear systems; mathematics computing; partial differential equations; perturbation techniques; recurrent neural nets; approximate solution; elliptic partial differential equation; equilibrium state; finite difference discretization; linear system; neural dynamics; perturbation; recurrent neural network; Artificial neural networks; Boundary conditions; Differential equations; Finite difference methods; Finite element methods; Linear systems; Neural networks; Neurons; Partial differential equations; Recurrent neural networks;
Conference_Titel :
Neural Networks, 1995. Proceedings., IEEE International Conference on
Conference_Location :
Perth, WA
Print_ISBN :
0-7803-2768-3
DOI :
10.1109/ICNN.1995.488882
