Advances in two-phase flow and heat transfer using physics-informed neural networks

Two-phase flow phenomena are ubiquitous in critical industrial sectors, including petroleum engineering, nuclear power generation, chemical processing, and environmental applications, where accurate prediction of interfacial dynamics, phase transitions, and heat transfer mechanisms is essential for system safety and operational efficiency. The inherent complexity of two-phase flow systems, characterized by sharp density gradients, moving interfaces, topological changes, and multi-scale coupling effects, presents formidable challenges for numerical modeling. Traditional computational fluid dynamics (CFD) approaches, despite their theoretical maturity, face significant limitations when addressing core two-phase flow problems such as interface tracking, phase-change heat transfer, and strong nonlinear coupling. Physics-informed neural networks (PINN) have emerged as a transformative computational paradigm that synergistically combines the universal approximation capabilities of deep neural networks with the fundamental principles of physics. By embedding governing partial differential equations, boundary conditions, and experimental observations directly into the neural network training process through carefully designed loss functions, PINN overcomes the limitations of both traditional numerical methods and purely data-driven approaches. The method offers distinct advantages, including mesh-free solutions, automatic differentiation for gradient computation, enhanced physical consistency, and superior performance on high-dimensional problems with complex geometries.This comprehensive review systematically examines the theoretical foundations, algorithmic innovations, and practical applications of PINNs in two-phase flow modeling. The analysis encompasses key technical developments specifically tailored for two-phase flow systems, including interface representation methods, multi-scale modeling strategies for bridging microscopic interfacial physics with macroscopic flow behavior, adaptive weighting algorithms for balancing multi-physics loss terms, and stability enhancement techniques for handling density jumps and discontinuous material properties. The review comprehensively covers PINN applications across five major categories of two-phase flow systems. Gas-liquid flows are examined through applications in bubble dynamics, interface instabilities, and boiling heat transfer. Liquid-liquid systems are analyzed focusing on phase separation dynamics, fingering instabilities, and porous media applications. Gas-solid flow modeling encompasses particle transport, collision dynamics, and fluidization characteristics. Liquid-solid suspensions are investigated through sedimentation studies and rheological modeling. Phase change heat transfer systems integrate phase transition with transport phenomena, enabling coupled flow-thermal predictions with enhanced physical consistency. Performance evaluations across these applications reveal significant advantages of PINN methods compared to conventional CFD approaches, including computational speedup, prediction accuracy, and superior capability for handling inverse problems and parameter identification. The mesh-free nature of PINN proves particularly beneficial for problems involving complex topological changes, moving boundaries, and extreme aspect ratios.Despite these advances, several critical challenges remain. Method universality is limited by the need for problem-specific network architectures and constraint formulations, restricting scalable deployment across diverse two-phase flow scenarios. Interface physics modeling requires further refinement to achieve higher interface sharpening, improved mass conservation, and enhanced long-term stability under extreme operating conditions. Current research primarily addresses traditional engineering two-phase flows with mature theoretical foundations, while exploration of frontier problems at micro scales and extreme conditions remains limited. Industrial deployment capabilities need strengthening through the development of real-time prediction systems, reliability assessment frameworks, and robust engineering implementation strategies. To address these challenges, future research directions emphasize the development of universal PINN frameworks capable of handling diverse two-phase flow configurations, integration of multi-source heterogeneous data for enhanced model robustness, breakthrough innovations in interface physics modeling, and systematic advancement of industrial deployment technologies. As artificial intelligence continues to deepen its integration with physical sciences, PINNs are positioned to play increasingly pivotal roles in two-phase flow research and engineering applications, providing powerful theoretical tools and technical support for innovation and industrial development.