Hydrodynamic cloak design aiming to suppress water flow disturbance by objects has become a popular research topic, with promising applications in drag reduction and stealth technology for marine engineering, bioengineering, and chemical engineering. Existing methods primarily utilize transformation optics theory (TOT) to derive analytical solutions for anisotropic viscosity tensors, which then inform the design process. However, they are limited to the Stokes equations, i.e., a simplified form derived from the full Navier-Stokes (NS) equations at Reynolds number (i.e., $\mathrm{Re}$) $\ll 1$, which neglects the important nonlinear flow convection term. In this study, we propose a framework based on the physics-informed neural network (PINN) to guide the design of hydrodynamic cloaks under the full NS equations, thereby enabling the characterization of effects across a wide range of Reynolds numbers. Within this framework, the PINN is employed to learn the anisotropic viscosity tensor necessary to achieve the design objective of enhancing upstream and downstream velocity field similarity, effectively weakening wake disturbance. Based on the learned anisotropic viscosity tensor, multiple candidate cloaks can be designed and evaluated. The optimal cloaks are then determined by implementing computational fluid dynamics (CFD) validation. Additionally, CFD results for the optimal cloaks demonstrate that the proposed method is effective for both two-dimensional (2D) and three-dimensional (3D) flows at $\mathrm{Re}=1$, 100, and 400, achieving up to a 64.46% reduction in the relative root mean square error of the downstream velocity profile compared to the upstream one. Furthermore, the analysis of the cloak mechanism using the $Q$-criterion reveals that the cloaked object generates an expanded zero-$Q$-criterion region, where the deformation of the fluid parcel compensates for its rigid-body rotation. As a result, flow disturbances around the object are effectively minimized.

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• Cloaking
• Hydrodynamic waves
• Wave-structure interactions
• Artificial neural networks
• Devices
• Metamaterials
• Machine learning
• Navier-Stokes equation