Simulation of Dripping Faucet Chaos Based on Physics-Informed Neural Networks

Dripping faucets exhibit chaotic dynamics with order–chaos transitions and multi-field coupling. This study built a physics-informed neural network (PINN) model using high-speed camera and numerical simulation data. The model incorporates physical constraints and employs multi-dimensional verification to simulate chaos and ensure consistency with the real system. Strategies including yargeted preprocessing, feature extraction, and physics enhancement alleviate the scarcity and poor quality of chaotic data. The PINN with an adapted network structure significantly improves prediction accuracy and generalization, boosting computational efficiency by over 100 times. More precisely, the inference speedup relative to FEM reached ~3800× under comparable resolution; this refers to prediction (inference) time, not training time. Long short-term memory (LSTM) performed best in predicting chaotic regions, achieving a 0.92 correlation between predicted and actual maximum Lyapunov exponents. A multi-step prediction strategy, physics-constrained loss function, and comprehensive verification framework ensure long-term prediction accuracy and physical consistency. Out-of-distribution validation on unseen fluids (diethylene glycol, glycerol–diethylene glycol) and extrapolated flow rates confirmed that the PINN retained 87–91% accuracy under OOD conditions, versus 71–78% for the LSTM baseline. A systematic sensitivity analysis further demonstrated that the loss-function weighting coefficients occupied a robust near-optimal plateau. The model comparison is fully quantitative, with all metrics reported alongside 95% bootstrap confidence intervals and a small-data learning curve demonstrating the PINN’s advantage in data-scarce regimes. Deep learning-based chaos identification and Lyapunov exponent estimation accurately capture the system’s chaotic characteristics. Computational optimization, hybrid precision training, distributed strategies, and model compression enhanced the simulation efficiency and indicate the feasibility of deployment. This study demonstrates that machine learning can effectively reveal the nonlinear dynamic behavior of dripping faucet systems, offering a novel approach for complex fluid dynamics and related applications.