<p>A machine learning-based surrogate model for bubble dynamics and cavitation behavior under sinusoidal waves has broad applications in science and engineering. In biomedical ultrasound, it can predict the nonlinear oscillations of microbubbles for targeted drug delivery, suboperation, and high-intensity focused ultrasound (HIFU) therapy, thereby enhancing treatment safety and efficiency. In underwater acoustics and naval engineering, such models help analyze cavitation around ship propellers and sonar devices, reducing noise, vibration, and material erosion. Similarly, in energy systems like hydropower turbines, compressors, and pumps, surrogate models accelerate the prediction of cavitation-related performance losses and blade damage, supporting more reliable design and operation. In order to find anomalies, cancers, and other medical issues, it is also used to evaluate organs like the liver, kidneys, heart, and blood arteries. Fluid dynamics difficulties have been greatly impacted by the development of contemporary simulation tools such as Artificial Intelligence (AI) and Machine Learning (ML). This study employs an Artificial Neural Network (ANN)-based machine learning technique to analyze the behavior of spherical gas bubbles in Carreau fluids when exposed to an ambient sonic field. The developed dynamical system is trained using an ANN application, specifically the Levenberg–Marquardt Scheme (LMS), a highly nonlinear and complex network. ANN approximation utilizes the Adam optimizer function to evaluate the numerical solution of the problem. The effectiveness of the proposed scheme is tested through the computation of MSE and the comparison of the optimal curve function against the iterative approach.</p>