Efficient and accurate analysis of oscillation dynamics for dissipative cavity solitons based on the artificial neural network

As a conventional means to analyze the system mechanism based on partial differential equations (PDE) or nonlinear dynamics, iterative algorithms are computationally intensive. In this framework, the details of oscillating dynamics of cavity solitons are beyond the reach of traditional mathematical analysis. In this work, we demonstrate that this long-standing challenge could be tackled down with the Long Short-Term Memory (LSTM) neural network. We propose the incorporating parameter-fed ports, which are capable of recognizing period-doubling bifurcations of respiratory solitons and quickly predicting nonlinear dynamics of solitons with arbitrary parameter combinations and arbitrary time series lengths. The model predictions capture oscillatory features with a small Root Mean Square Errors (RMSE) = 0.01676 and an absolute error that barely grows with the length of the prediction time. Lugiato-Lefever equation (LLE) based parameter space boundaries for typical oscillatory patterns are plotted at about 120 times the speed relative to the split-step Fourier method (SSFM) and higher resolution.