Author(s): Muhammad Waqar; Moez Louati; Mohamed S. Ghidaoui
Linked Author(s): Muhammad Waqar, Moez LOUATI, Mohamed S. Ghidaoui
Keywords: Rtificial intelligence; Leak detection; Hydraulics; Machine learning; Water-hammer
Abstract: In computational fluid dynamics, application of machine learning (ML) has gained momentum ever since the introduction of physics-informed neural networks (PINNs) wherein physics is used as constraint. In this paper, a PINN algorithm is developed to predict the transient wave propagation in a simple reservoir-pipe-valve (RPV) system. The training data is generated by solving the water-hammer equations using the method of characteristics (MOC). Then, pressure-time signal at either end of the pipe and at one point inside the pipe as well as the initial state of the system are provided as input to the neural network (NN). The PINN model parameters (i.e., weights and biases) are optimized using (1) adaptive moment estimation (Adam), and (2) limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) algorithms. The loss function which determines the convergence of training process is the sum of (1) the mean-squared-error between the predicted and exact input data, and (2) the homogeneous one-dimensional wave equation. The latter loss function is based on wave physics which restricts the NN to must satisfy the wave equation inside the domain of interest. The results show that L-BFGS based solution is in good agreement with the exact MOC solution, whereas Adam optimizer fails to satisfy the physics-based constraint inside the domain of interest. Moreover, the results of PINN model are compared with the ordinary NN wherein the physics-based constraint is absent. It is found that the ordinary NN approach is unable to predict the wavefield, implying that physics-based constraint is essential. Through this paper, we hope to develop interest in PINNs in hydraulics as it is an integrated framework to develop physics constrained data-driven models.