With the aim to enhance prediction accuracy for nonlinear time series, this paper put forward an improved deep Echo State Network based on reservoir states reconstruction driven by a Self-Normalizing Activation (SNA) function as the replacement for the traditional Hyperbolic tangent activation function to reduce the model’s sensitivity to hyper-parameters. The Strategy was implemented in a two-state reconstruction process by first inputting the time series data to the model separately. Once, the time data passes through the reservoirs and is activated by the SNA activation function, the new state for the reservoirs is created. The state is input to the next layer, and the concatenate states module saves. Pairs of states are selected from the activated multi-layer reservoirs and input into the state reconstruction module. Multiple input states are transformed through the state reconstruction module and finally saved to the concatenate state module. Two evaluation metrics were used to benchmark against three other ESNs with SNA activation functions to achieve better prediction accuracy.

Collective behaviors in nature and human societies have been intensively studied in recent decades. The Vicsek model is one of the typical models that explain self-ordered particle systems well. In the original Vicsek model, the neighbor strategy takes all its neighbors’ mean directions into account when updating particles’ directions, which leads to a longer convergence time and higher computation cost due to the excess number of neighbors. In this paper, we introduce a new neighbor strategy to the Vicsek model. It defines that each particle will only select a certain number of particles with the farthest distance that fall into its vision sector as its neighbors. In addition, we classify the Vicsek model as the static model and the dynamic model according to whether the features of particles in the model are constant or not. Moreover, we design a new rule to apply the new neighbor strategy to dynamic Vicsek models. The simulation results indicate that our new neighbor strategy can significantly decrease the average number of particles’ neighbors but still be able to further enhance the Vicsek model’s convergence performance. The comparative results found that the static and dynamic model applied with the new neighbor strategy outperforms the models that only apply view restriction or remote neighbor strategy in noiseless and noisy conditions.