Modeling and Simulation of Nonlinear Dynamics Using Physics-Informed Deep Neural Networks

Development of Physics-Informed Neural Networks (PINNs) as nonlinear dynamics surrogates is investigated. PINNs are unsupervised neural networks in which the input-output relationship is established via a specific dynamic relationship (differential equation). In this regard, the derivatives are determined by utilizing Automatic Differentiation over the network’s graph. Hence, PINNs can be utilized to build complex surrogates for nonlinear dynamical systems which can later be used in real-time control applications. In this study, it is shown that PINNs can adequately capture the dynamics investigated. Even in regions of the state space where there are no training sample points, a PINN surrogate provides an acceptable approximation of the dynamical system. To investigate the hypothesis, three categories of nonlinear dynamics are examined: (1) self-sustained, (2) excitatory, and (3) chaotic systems. As implied by the results, PINNs can estimate self-sustaining and chaotic systems with sufficient accuracy. However, the concept is not as successful with excitatory dynamics that mandates further detailed studies on these surrogates.