Reconstruction of Damped Vibration System Equations Based on Artificial Intelligence Technology

Data science has always been the driving force behind the dawn of the Fourth Industrial Revolution. Over the past decade, the sharp decline in the cost of sensors, data storage, and computing resources has made data-driven discovery methods possible, which has had a transformative impact on science and promoted various innovations in characterizing high-dimensional data generated by experimental observations. The field of AI4 Science aims to apply AI to physical domains. However, mainstream deep learning methods are criticized as a “black box,” with their internal workings being difficult to understand. Therefore, interpretable machine learning aims to break through the “black box” mechanism, allowing us to understand the internal workings of machine learning in a human-readable manner. This makes AI-assisted scientific discovery possible. This paper takes the damped oscillator as the research object. A YOLOv8 visual model trained on a custom dataset is used to obtain spatiotemporal data. On one hand, symbolic regression with the introduction of information criteria is employed to automatically discover explicit expressions between data. On the other hand, we conceptualize the problem of dynamical discovery from the perspective of sparse regression, constructing a candidate function library through numerical differentiation with total variation regularization, and ultimately accurately reconstructing the differential equation and nonlinear laws of damped vibration. We have verified the strong scientific interpretability and universality of the results obtained by this method using both experimental and simulation data.