Comparison of Physics-Informed Neural Networks (PINNs) and Experimental Reality in Fluid Viscosity Dynamics

Determining fluid viscosity using the conventional falling-sphere method is frequently confronted with challenges related to experimental variability and measurement instrument limitations. As an alternative, Physics-Informed Neural Networks (PINNs) offer a computational approach capable of integrating physical laws into the neural network architecture. This study aims to evaluate the predictive accuracy of the PINNs model regarding the velocity of a falling sphere, as well as to compare it with the analytical solution of Stokes flow and experimental data. Data collection was conducted using a viscometer equipped with five infrared sensors, while the PINNs model was trained by balancing the experimental data loss and the physics loss derived from the equation of motion. The comparative results demonstrate that PINNs generally succeed in modeling the dynamics of the sphere's motion, convergently reaching terminal velocity. Nevertheless, two primary modeling limitations were identified. First, the model experiences an overshoot during the initial phase of motion due to the network's spectral bias effect when responding to drastic velocity changes. Second, the experimental data reveal a persistent velocity deceleration in the final phase that both the analytical and PINNs predictions failed to capture. This empirical anomaly indicates the occurrence of a shift in boundary-layer separation alongside the thixotropic effects of the fluid. In conclusion, PINNs prove to be a promising approach for bridging the gap between computational modeling and experimentation; however, this architecture still requires the inclusion of dynamic parameters to fully accommodate the complexity of fluids under real-world conditions.