A Novel Non-Inertial Frame of Physics-Informed Neural Networks for Reconstructing Flapping Wing Rotor Flows

This study tackles the challenge of extending Physics-Informed Neural Networks (PINNs)—a method that has demonstrated remarkable success in fixed-boundary fluid mechanics problems—to the more complex regime of flows with moving boundaries. A general framework called NIF-PINNs, based on a non-inertial reference system, is introduced to convert moving-boundary problems into fixed computational domains. The main contributions include: (i) reformulating the Navier-Stokes (NS) equations to maintain physical consistency in a non-inertial frame; (ii) enabling the handling of complex 2D and 3D motions solely through Euler-angle parameterization; and (iii) imposing the no-slip boundary condition as a hard constraint on the fixed domain, thus avoiding the complexity of dynamic mesh processing. The framework is applied to a three-dimensional flapping wing rotor (FWR). A dataset under multiple Reynolds number conditions is constructed using experimentally validated CFD data. Results demonstrate that NIF-PINNs accurately capture unsteady flow structures, with velocity and pressure predictions in close agreement with CFD benchmarks, while maintaining low prediction errors. This work establishes a practical PINNs-based framework for moving-boundary flow problems and provides a methodological foundation for simulating non-inertial and highly time-varying systems.