Comparison Of Single and Double Physics-Informed Neural Networks for Modelling Air Injection into a Tank Filled with Liquid

Multiphase flows (MF) are ubiquitous in natural and engineered systems, with applications spanning petroleum transportation, chemical processing, nuclear reactor cooling, environmental engineering, and biomedical devices. Air injection into water- filled vessels represents a fundamental configuration for investigating gas-liquid interactions, bubble behaviour, and interfacial transport mechanisms. Understanding these phenomena is critical for optimizing aeration efficiency, mixing performance, and mass transfer operations. Traditional computational fluid dynamics (CFD) methods for simulating such systems are computationally intensive and often rely on empirical closures for interfacial dynamics. Machine learning (ML), particularly physics-informed neural networks (PINNs), has emerged as a promising alternative or complement to CFD for modelling complex MF systems with improved efficiency. This study develops and compares two PINN implementations—single-network (PINN-1) and double-network (PINN-2)—for modeling air injection into a 2D tank filled with liquid through a nozzle located at bottom of the tank. Results demonstrate that PINN-2 consistently outperforms PINN-1, delivering lower relative errors and enhanced accuracy in reconstructing velocity, pressure, and volume fraction fields across the temporal domain. The decomposed architecture proves more effective at disentangling complex couplings among flow variables. Both frameworks successfully capture dominant flow features including interfacial deformation and vortical structures, with localized discrepancies near steep gradients. According to our literature review, no previous research comparing single and double PINNs addressing air-injection scenarios has been documented, emphasizing the innovative nature of this research.