PHYSICS-INFORMED NEURAL NETWORKS FOR INVERSE PROBLEMS IN TURBULENT AND MULTI-PHASE FLOWS: A CRITICAL ASSESSMENT OF PERFORMANCE, UNCERTAINTY, AND SCALABILITY

Physics-Informed Neural Networks (PINNs) have emerged as a transformative paradigm for solving inverse problems in fluid mechanics, offering the ability to integrate sparse observational data with the governing physical laws encoded by the Navier-Stokes equations. This review critically evaluates the application of PINNs to inverse problems in turbulent and multi-phase flows—two of the most challenging regimes in computational fluid dynamics. We examine how embedding Navier-Stokes constraints into neural architectures enables the reconstruction of flow fields from limited measurements, a capability particularly valuable in oceanography, aerodynamics, and industrial process monitoring where dense experimental data are unavailable. The review systematically addresses three key sub-themes: uncertainty quantification in PINN predictions, the computational cost trade-offs between PINNs and traditional CFD solvers, and the development of hybrid PINN-CFD frameworks for industrial applications such as gas-liquid separators. Our analysis reveals that while PINNs demonstrate remarkable data efficiency and can outperform purely data-driven models in sparse-data scenarios, significant challenges persist in high-Reynolds-number turbulent flows, multi-phase systems with moving interfaces, and real-time industrial deployment. We identify critical research gaps, including the need for robust uncertainty estimation methods, scalable training algorithms for large-domain problems, and standardized benchmarking protocols. Finally, we offer perspectives on emerging trends, including self-adaptive PINNs, physics-informed operators, and the integration of digital twin frameworks for predictive industrial maintenance.