DNN-based method to solve absolute value equations derived from signal processing

Deep neural networks(DNN) have gained widespread application in the numerical approximation of various partial differential equations, however the investigations to non-linear matrix system are quite rare. In this paper, we construct an architecture of DNN to approximate the solution of absolute value equation (AVE) originated from the signal processing. The framework is quite simple and approximates well the solution of AVE with stochastic gradient descent technique used in deep learning. Some numerical experiments are carried out and showed our model not only can handle the case of unique solution for AVE, but also can obtain a good approximated solution when the AVE is not uniquely solvable.