A Post-Hoc Physics-Guided Neural Network for Parameter Estimation in an Equation of State of Cavitation Bubbles

This study utilizes experimental cavitation bubble radius data, captured through high-speed photography, to create a physics-guided neural network (PGNN) that models pressure evolution based on the Rayleigh-Plesset equation, a nonlinear ordinary differential equation for a spherical bubble in an infinite body of incompressible fluid. The primary objective is to estimate the parameters of an equation of state (EOS) for cavitation bubbles. The approach incorporates the Mie-Grüneisen form of the Jones-Wilkins-Lee (JWL) EOS through coefficient comparison, introducing a new method for calculating dynamic pressure contributions from the velocity and acceleration of a bubble. A key distinction in this model is the use of the maximum expanded volume, rather than the initial volume, as a reference point. This modification allows JWL EOS parameters to be derived directly from the maximum bubble radius, which is more readily and accurately measurable than the initial radius. This shift not only simplifies parameter estimation for underwater explosions but also has the potential to reduce the need for extensive experimental studies in parameter calculation. Moreover, the JWL form of the EOS expresses pressure as a function of other state variables, such as internal energy and density of gaseous medium within the bubble. The method is validated with experimental data from both underwater explosions and laser-induced cavitation bubbles available in the literature. The results reveal similar pressure-radius profiles across both cases, supporting the JWL EOS’s broad applicability to different bubble generation techniques, including electrical spark and laser generated bubbles. These findings suggest the possibility of using laser or spark-induced bubbles as effective substitutes in explosion studies, with the added advantage of evaluating crucial parameters such as maximum radius, peak overpressure, temperature, and shockwave velocity. This approach could significantly extend the scalability and practical applicability of cavitation bubble studies, aiding in controlled underwater explosion experimentation and providing a versatile tool for future research on EOS parameters in similar dynamic systems.