Physics-Informed Neural Networks for One- Step-Ahead Prediction of Dynamical Systems

Abstract

During online implementation of vibration-based structural health monitoring (SHM) strategies, forward prediction of the system state may allow for improved detection speed. With adequately fast forward prediction, feedback systems can also be improved to provide in-time control plants. When using solely physics-driven models, small discrepancies between the physical system and digital model can result in significant deviation between the estimated and true output. On the opposite end, a solely data-driven model can only reasonably be applied in an identical, or sufficiently similar, scenario to that for which the data was collected. Using machine learning to combine data with known physics is a well-proved approach to overcoming this issue. One such method for this approach is the use of physics-informed neural networks (PINNs), which can be implemented as either a forward modeller, or a constrained learner, for equation solution discovery, or equation discovery. The former of these aims to provide the desired output from the governing physical equations, whereas the latter estimates the parameters in these equations. A significant advantage of PINNs is, given a suitable network architecture, the high speed and low computational-cost of their prediction step, which positions them as a useful approach for real-time estimation, given adequate training. A common assumption for PINNs is that the embedded physics is exhaustive with respect to the ‘true’ model. In this paper, a novel PINN-based architecture is presented to rapidly forward-predict the state of a dynamic system given an initial state. For the state estimation, the PINN acts as an equation solution discovery approach, and the novelty of the architecture here is to provide a more generalised predictor which can be applied to a wider range of instances. The PINN is intended to deliver its prediction within a prescribed time frame, which equals the sampling time of the acquisition/control system, and is here assessed against this goal.