Nonparallel, Nonlocall Flow Stability Analysis Through a Physics-Informed Data-Driven Approach

Physics-informed data-driven modeling for flow stability analysis represents an inexpensive and easy-to-automate technique to simulate complex flow phenomena. The resulting models are easy to operate and couple to other flow solvers. While standard neural networks are largely used as surrogates to computational fluid dynamics (CFD) simulations, the volume of data to train such models is large, and the associated errors are not necessarily acceptable for a number of investigations. Physics-informed neural networks (PINNs) use the underlying flow physics, represented by partial differential equations, to enhance the modeling accuracy. PINNS also make it possible to successfully train a model based on sparse data. In this paper, we present numerical results that indicate the suitability of PINNs to recover disturbance fields for nonlocal, nonparallel flow stability analysis for a flat plate incompressible boundary layer flow. The data is generated by running a Parabolized Stability Equations (PSE) solver. The PINN is then employed to recover relevant metrics for stability analysis in flat plates, including an accurate reconstruction of the associated eigenfunctions. Our results indicate that the PINN predictions accurately capture the disturbance’s amplitude spatial behavior even when only sparse training data is available.