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This work addresses the development of a physics-informed neural network(PINN) with a loss term derived from a discretized time-dependent reduced-ordersystem. In this work, first, the governing equations are discretized using afinite difference scheme (whereas, any other discretization technique can beadopted), then projected on a reduced or latent space using the ProperOrthogonal Decomposition (POD)-Galerkin approach and next, the residual arisingfrom discretized reduced order equation is considered as an additional losspenalty term alongside the data-driven loss term using different variants ofdeep learning method such as Artificial neural network (ANN), Long Short-TermMemory based neural network (LSTM). The LSTM neural network has been proven tobe very effective for time-dependent problems in a purely data-drivenenvironment. The current work demonstrates the LSTM network's potential overANN networks in physics-informed neural networks (PINN) as well. The potentialof using discretized governing equations instead of continuous form lies in theflexibility of input to the PINN. Different sizes of data ranging from small,medium to big datasets are used to assess the potential ofdiscretized-physics-informed neural networks when there is very sparse or nodata available. The proposed methods are applied to a pitch-plunge airfoilmotion governed by rigid-body dynamics and a one-dimensional viscous Burgers'equation. The current work also demonstrates the prediction capability ofvarious discretized-physics-informed neural networks outside the domain wherethe data is available or governing equation-based residuals are minimized.

Physics Informed Neural Network Framework for Unsteady Discretized Reduced Order System