Utilizing Physics Informed Neural Networks for Disrupted Signal Dynamics

Physics-informed neural networks (PINNs) have been used in many applications including engineering and physical sciences. PINNs allow the incorporation of a priori understanding of a process’ structure into the modeling. We attempt to leverage the PINN structure toward the evaluation of disruptions to classical dynamical models by combining elements of ordinary differential equations into our loss function with sigmoidal gating to balance the penalties for deviations from the data with those for structural deviations. This enables the identification of the signal structure and the limits of disruption influence. As a use case, we consider stock value from 2019-2021, which expresses approximately exponential growth interrupted by the 2020 COVID-19 market crash. We train a PINN on this data and identify the underlying exponential trend and disruption bounds. We aim for this architecture to be an alternative to other PINN variations, combining signal identification with the identification of disruption bounds and steepness.