Simultaneously detecting hidden solid boundaries and reconstructing flow fields from sparse observations poses a significant inverse challenge in fluid mechanics. This study presents a physics-informed neural network (PINN) framework designed to infer the presence, shape, and motion of static or moving solid boundaries within a flow field. By integrating a body fraction parameter into the governing equations, the model enforces no-slip/no-penetration boundary conditions in solid regions while preserving conservation laws of fluid dynamics. Using partial flow field data, the method simultaneously reconstructs the unknown flow field and infers the body fraction distribution, thereby revealing solid boundaries. The framework is validated across diverse scenarios, including incompressible Navier-Stokes and compressible Euler flows, such as steady flow past a fixed cylinder, an inline oscillating cylinder, and subsonic flow over an airfoil. The results demonstrate accurate detection of hidden boundaries, reconstruction of missing flow data, and estimation of trajectories and velocities of a moving body. Further analysis examines the effects of data sparsity, velocity-only measurements, and noise on inference accuracy. The proposed method exhibits robustness and versatility, highlighting its potential for applications when only limited experimental or numerical data are available.

翻译：从稀疏观测数据中同时检测隐式固体边界并重构流场，是流体力学领域一项重要的反问题挑战。本研究提出一种物理信息神经网络（PINN）框架，旨在推断流场中静态或运动固体边界的存在、形态及运动状态。通过将体积分数参数嵌入控制方程，该模型在固体区域强制实施无滑移/无穿透边界条件，同时保持流体动力学守恒定律。利用部分流场数据，该方法能够同步重构未知流场并推断体积分数分布，从而揭示固体边界。该框架在多种场景下得到验证，涵盖不可压缩Navier-Stokes流动与可压缩Euler流动，包括固定圆柱绕流、同轴振荡圆柱绕流以及翼型亚音速绕流等案例。结果表明，该方法能准确检测隐式边界、重构缺失流场数据，并有效估计运动物体的轨迹与速度。进一步研究分析了数据稀疏性、纯速度测量以及噪声对推断精度的影响。所提方法展现出良好的鲁棒性与泛用性，凸显了其在仅能获取有限实验或数值数据场景中的应用潜力。