Physics-Informed Neural Networks for Exterior Potential Flow Around a Circular Cylinder Without Far-Field Boundary Conditions

Physics-informed neural networks (PINNs) have emerged as a promising framework for solving partial differential equations by embedding physical laws directly into the learning process. While PINNs have shown strong performance for bounded-domain problems, their application to exterior flow problems typically relies on artificial far-field boundary conditions to truncate the computational domain. In this work, we investigate the capability of PINNs to solve the exterior potential flow around a circular cylinder using only the solid boundary condition, without imposing any far-field constraints. The governing Laplace equation for the stream function is enforced through the physics-informed loss, while the no-penetration condition on the cylinder surface is prescribed as the sole boundary condition. Numerical results demonstrate that the proposed PINN accurately recovers the stream function, velocity field, and pressure coefficient distribution throughout the exterior domain. Despite the absence of far-field boundary conditions, the learned solution exhibits physically consistent far-field behaviour within the sampled domain, strong agreement with analytical solutions, and low global and maximum errors. These results indicate that, for classical potential flow problems, PINNs can infer physically consistent far-field behaviour directly from the governing equations and solid boundary information alone. The findings provide new insight into the behaviour of PINNs in unbounded domains and highlight their potential for solving exterior flow problems without reliance on artificial boundary truncation.