Physics-informed neural networks modelling for systems with moving immersed boundaries: Application to an unsteady flow past a plunging foil

Physics informed neural networks (PINNs) have been explored extensively in the recent past for solving various forward and inverse problems for facilitating querying applications in fluid mechanics. However, investigations on PINNs for unsteady flows past moving bodies, such as flapping wings are scarce. Earlier studies mostly relied on transferring the problems to a body-attached frame of reference, which could be restrictive towards handling multiple moving bodies/deforming structures. The present study attempts to couple the benefits of PINNs with a fixed Eulerian frame of reference, and proposes an immersed boundary aware framework for developing surrogate models for unsteady flows past moving bodies. Specifically, high-resolution velocity reconstruction and pressure recovery as a hidden variable are the main goals. The framework has been developed by using downsampled velocity data obtained from prior simulations to train the PINNs model. The efficacy of the velocity reconstruction has been tested against high resolution IBM simulation data, whereas the efficacy of the pressure recovery has been tested against high resolution simulation data from an arbitrary Lagrange Eulerian (ALE) solver. Under the present framework, two PINN variants, (i) a moving-boundary-enabled standard Navier–Stokes based PINN (MB-PINN), and, (ii) a moving-boundary-enabled IBM based PINN (MB-IBM-PINN) have been formulated.

Relaxation of physics constraints in PINNs models has been identified to be a useful strategy in improving the predictions. A fluid-solid partitioning of the physics losses in MB-IBM-PINN has been allowed, in order to investigate the effects of solid body points while training. This strategy enables MB-IBM-PINN to match with the performance of MB-PINN under certain loss-weighting conditions. Interestingly, MB-PINN is found to be superior to MB-IBM-PINN when a priori knowledge of the solid body position and velocity is available. To improve the data efficiency of MB-PINN, a physics based data sampling technique has also been investigated. It is observed that a suitable combination of physics constraint relaxation and physics based sampling can achieve a model performance comparable to the case of using all the data points, under a fixed training budget.