Solutions of linear equations and a class of nonlinear equations using recurrent neural networks

摘要

Artificial neural networks are computational paradigms which are inspired by biological neural networks (the human brain). Recurrent neural networks (RNNs) are characterized by neuron connections which include feedback paths. This dissertation uses the dynamics of RNN architectures for solving linear and certain nonlinear equations. Neural network with linear dynamics (variants of the well-known Hopfield network) are used to solve systems of linear equations, where the network structure is adapted to match properties of the linear system in question. Nonlinear equations inturn are solved using the dynamics of nonlinear RNNs, which are based on feedforward multilayer perceptrons. Neural networks are well-suited for implementation on special parallel hardware, due to their intrinsic parallelism. The RNNs developed here are implemented on a neural network processor (NNP) designed specifically for fast neural type processing, and are applied to the inverse kinematics problem in robotics, demonstrating their superior performance over alternative approaches.