Novel design of Morlet wavelet neural network for solving second order LaneEmden equation Abstract   In this study, a novel computational paradigm based on Morlet wavelet neural network (MWNN) optimized with integrated strength of genetic algorithm (GAs) and Interiorpoint algorithm (IPA) is presented for solving second order LaneEmden equation (LEE). The solution of the LEE is performed by using modeling of the system with MWNNs aided with a hybrid combination of global search of GAs and an efficient local search of IPA. Three variants of the LEE have been numerically evaluated and their comparison with exact solutions demonstrate the correctness of the presented methodology. The statistical analyses are performed to establish the accuracy and convergence via the Theilxe2x80x99s inequality coefficient, mean absolute deviation, and Nash Sutcliffe efficiency based metrics.

Sparse Wavelet Networks A wavelet network (WN) is a feedforward neural network that uses wavelets as activation functions for the neurons in its hidden layer. By predetermining the wavelet positions and dilations, the WN can turn into a linear regression model. The common approach for the construction of these WN families is to use leastsquares type algorithms. In this letter, we propose a novel approach by formulating a WN as a sparse linear regression problem, which we call a sparse wavelet network (SWN). In this WN, the problem of calculating the unknown inner parameters of the network becomes that of finding the sparse solution of an underdetermined system of linear equations. Our sparse solution algorithm is a nonconvex sparse relaxation approach inspired by smoothed L0 (SL0), a distinguished sparse recovery algorithm. The proposed SWN can be applied as a tool for the prediction and identification of dynamical systems.