Trajectory Prediction of a Water Rocket Using Physics-Informed Neural Networks (PINNs) Compared with Deep Learning Models

Abstract

Water rockets provide an effective platform for exploring fundamental physics concepts such as Newton’s laws of motion and projectile trajectories. This study presents a comparative analysis between a data-driven Deep Learning (DL) model and a Physics-Informed Neural Network (PINN) for predicting two-dimensional trajectories of water rockets. The experimental data, collected from launches with varying internal pressures of 1.5, 2.2, 2.7, and 3.2 bar and water volumes (100 - 300 mL), were extracted from video recordings and converted into time-position datasets. Both models were trained on the same dataset using identical training parameters. The results indicate that the PINN model demonstrated superior accuracy, achieving a Root Mean Square Error (RMSE) of 0.2949 m, whereas the MLP yielded a much higher RMSE of 0.3158 m. This result highlights that embedding the governing physical equations of motion into the PINN’s learning process enhances its robustness against the imperfections and noise inherent in real-world data, leading to more reliable and accurate predictions than a purely data-driven approach.