A Recurrent Neural-network-based Ultra-Fast, Robust and Scalable Solver of Linear Equation Systems with Potential Integration in a Speeding-up of FEM Solver Architectures

摘要

Various algorithms exist to solve linear algebraic equations. Most of them are very good algorithms, however which could be implemented only on single processor computers. This makes these algorithms becoming inefficient when trying to implement them on multi-processor platforms. The main root of the problem lies in the nature of the algorithms as they are essentially designed to be used on single processors. Hence, the search for new algorithms that fits better for implementation on parallel systems is necessary. Using parallel computing frameworks like neural networks can provide a good basis to support algorithms or concepts highly compatible with parallel platforms and thereby ensuring a low implementation cost. In this paper, we do suggest and demonstrate a new way of solving linear algebraic equations using a Cellular Neural Network (CNN) Processor. Although similar works have been performed by using different types of Neural Networks such as Recurrent Neural Networks (RNN) and Artificial Neural Networks (ANN) the fact of involving the CNN nonlinearity does increase convergence speed and provide feasible solutions for an implementation on analog processors.