Physics-Informed Machine Learning for Turbulence and Fluid–Structure Interaction in Flapping Wing Systems

Turbulent flows with fluid–structure interactions (FSI) are prevalent in both natural and engineered systems—ranging from insect flight and fish locomotion to flapping wing micro air vehicles and soft robotics. These systems involve unsteady, multiscale flow phenomena coupled with moving or deforming boundaries, which introduces additional computational complexity to classical turbulence modelling. Traditional approaches such as Reynolds-Averaged Navier–Stokes (RANS) and Large Eddy Simulation (LES) offer limited practicality in this context: RANS models fail to capture all transient features of the interaction, and LES becomes computationally intractable for long-duration or parameter-sweep simulations involving moving geometries.;;Physics-informed machine learning (ML) methods offer a promising alternative by embedding governing fluid dynamics equations directly into neural network training. Such models—especially Physics-Informed Neural Networks (PINNs), convolutional neural networks (CNNs), and generative adversarial networks (GANs)—have shown success in approximating turbulent fields and enhancing coarse-resolution simulations. However, their application to coupled FSI systems with complex kinematics such as flapping wings remains an open challenge.;;Research Gap;;Despite recent progress, current ML approaches struggle with three major issues in turbulent FSI modelling:;1. Long-Term Unsteady Dynamics: Standard PINNs are sensitive to temporal sparsity and exhibit degradation over long simulation horizons, particularly in the presence of moving boundaries.;2. Immersed Boundary Complexity: Most ML-based solvers are designed for static or fixed-domain problems. Modelling unsteady flows around flapping wings often requires body-attached reference frames or remeshing, introducing further error and instability.;3. Small-Scale Turbulence Recovery: While CNN-based super-resolution models have achieved success on canonical flows, they typically lack the ability to infer subfilter-scale dynamics in highly unsteady, geometry-coupled problems without large training datasets.;;Aims and Objectives;;This project aims to develop physics-informed machine learning frameworks capable of resolving the coupled dynamics of turbulence and FSI in flapping wing configurations. It builds on recent developments in immersed boundary-aware PINNs, multi-resolution CNNs, and turbulence super-resolution networks.;;The specific objectives are:;1. Sequential PINNs for FSI Systems: Extend PINNs to handle unsteady FSI problems with flapping wings using sequential learning. Two strategies will be implemented and tested: (i) progressive time-domain growth and (ii) time-domain decomposition with transfer learning. The latter is expected to mitigate error accumulation over long simulations.;2. Immersed Boundary Learning Framework: Integrate immersed boundary-aware PINNs that avoid body-fitted coordinate transformations. This enables modelling of complex flapping kinematics without grid deformation or remeshing.;3. Super-Resolution of Turbulent FSI Fields: Develop physics-constrained super-resolution models using U-Net variants to reconstruct fine-scale turbulence around moving boundaries. Subfilter-scale closure will be addressed through embedded conservation constraints and dynamic refinement.;4. Validation and Benchmarking: Apply the models to flapping airfoil configurations under varying Reynolds numbers and kinematic parameters. Compare against LES/Immersed Boundary Methods and experimental results for flow field reconstruction and force recovery.;;By combining turbulence modelling, FSI, and deep learning, this project will generate new tools for simulating complex bio-inspired and engineering systems with high fidelity at reduced computational cost.