Intelligent modeling of nonlinear dynamical systems by machine learning

An intelligent data-driven method of modeling nonlinear dynamical systems named as LSTM network with output recurrence (OR-LSTM) is proposed, which can learn the inherent characteristics of the dynamical systems from data and predict the states of the systems given external excitation and initial conditions. For the proposed OR-LSTM architecture, the most important key point is output recurrence connections. In order to evaluate it, a teacher-forcing LSTM network without output recurrence connections (TF-LSTM) is designed for comparison. The differences between OR-LSTM and TF-LSTM from the perspective of gradient propagation and parameter updating are analyzed firstly. To verify the capability of the LSTM networks in dynamical systems modeling, the oscillation of a 42-story reinforced concrete frame-core tube building under severe and extreme seismic excitations are modeled. The results show that the OR-LSTM network performs well and maintains the long-term robustness in earthquake responses prediction, even only known displacements of 9 stories. However, the TF-LSTM network fails. In order to evaluate the extensive practicability of the OR-LSTM network, the famous Van der Pol dynamic system and Lorenz dynamic system with strong nonlinearity are also modeled by the proposed method. The results show that OR-LSTM network is competent in modeling most of nonlinear dynamic systems, while has limited in fully chaotic systems, but the predictable length of time sequence and prediction accuracy are improved.