Physics-informed neural network for vortex-induced vibration: Flow reconstruction and load prediction from sparse data in multi-cylinder systems

Accurate and efficient prediction of vortex-induced vibration (VIV) remains a long-standing challenge in engineering and fluid dynamics because experimental measurements are often noise sensitive, while high-fidelity simulations incur substantial computational cost. This paper presents a physics-informed neural network (PINN) framework for fluid-structure interaction (FSI) problems that embeds the incompressible Navier-Stokes equations as a soft constraint in the loss function. The framework employs a sinusoidal representation network (SIREN)-based architecture and a progressive training strategy, in which the weight assigned to the physics-equation loss is increased linearly during optimisation. This strategy gradually shifts the learning emphasis from data fitting to physics enforcement, thereby improving convergence and enhancing robustness to noisy observations. Meanwhile, the SIREN-based formulation retains its capability to resolve high-frequency flow features. The method reconstructs complete spatio-temporal flow fields and infers latent pressure distributions and fluid forces on vibrating cylinders from sparse velocity observations and measured structural displacement, without using pressure or force measurements. Validation is performed for VIV of a single cylinder and of three rigidly connected cylinders in an equilateral triangular arrangement at Reynolds number R e = 150 and reduced velocity U r = 5 , with mass ratio m * = 2 in both cases and spacing ratio s / D = 2 for the three-cylinder configuration. For the single-cylinder case, the velocity and pressure fields are accurately reconstructed, with time-averaged relative L 2 errors below 1% for both quantities. For the three-cylinder case, complex wake interactions are resolved. When trained with contaminated velocity and displacement observations, integrated force predictions remain essentially unchanged, while velocity and pressure errors increase only modestly, reflecting the regularising effect of the embedded physics constraints.