Predicting Output Responses of Nonlinear Dynamical Systems With Parametrized Inputs Using LSTM

Long Short-Term Memory (LSTM) has been more and more used to predict time evolution of dynamics for many problems, especially the fluid dynamics. Usually, it is applied to the latent space after dimension reduction of the full dynamical system by proper orthogonal decomposition (POD), autoencoder (AE) or convolutional autoencoder (CAE). In this work, we propose to directly apply LSTM to the data of the output without dimension reduction for output response prediction. The dimension of the output is usually small, and no dimension reduction is necessary, thus no accuracy loss is caused by dimension reduction. Based on the standard LSTM structure, we propose an LSTM network with modified activation functions which is shown to be much more robust for predicting periodic waveforms. We are especially interested in showing the efficiency of LSTM for predicting the output responses corresponding to time-vary input signals, which is rarely considered in the literature. However, such systems are of great interests in electrical engineering, mechanical engineering, and control engineering, etc. Numerical results for models from circuit simulation, neuron science and a electrochemical reaction have shown the efficiency of LSTM in predicting the dynamics of output responses.