Physics-Informed Kolmogorov-Arnold Networks: A Superior Approach to Fluid Simulation

The lid-driven cavity flow serves as a fundamental benchmark in computational fluid dynamics (CFD), valued for its simple geometry and complex flow patterns, making it an ideal testbed for validating numerical methods. Traditional numerical approaches, such as finite difference and finite element methods, often require substantial computational resources, particularly for high-dimensional or turbulent flows. Physics-Informed Neural Networks (PINNs) have emerged as a promising alternative, integrating physical laws into the neural network training process to solve partial differential equations (PDEs) with limited data. However, PINNs face challenges in resolving high-gradient regions and ensuring convergence with sparse data. In this study, we introduce Physics-Informed Kolmogorov-Arnold Networks (PI-KAN), which leverage the Kolmogorov-Arnold representation theorem to replace fixed activation functions with learnable univariate spline functions on network edges. We compare PI-KAN with traditional PINNs in simulating the lid-driven cavity flow at a Reynolds number of 100. Our results demonstrate that PI-KAN achieves significantly lower training loss (from 0.24 to 0.18) compared to PINNs (from 100 to 1–10) and captures more accurate flow field details, including velocity magnitudes up to approximately 1.32 and flow patterns consistent with benchmark data from [1]. In contrast, PINNs exhibit lower velocities (up to 0.52) and incorrect flow directions. These findings highlight PI-KAN’s potential as a superior alternative for complex fluid dynamics simulations, offering enhanced accuracy and interpretability, with applications in engineering and scientific computing.