Sensitivity-Guided Parameter Estimation of Bubbly Liquid via a Nonlinear Wave Equation and Physics-InformedNeuralNetworks

Abstract

Interactions between ultrasound and microbubbles underlie a range of biomedical and industrial applications, yet predicting how the physical parameters of the medium and bubbles govern nonlinear wave propagation remains difficult. This study proposes a parameter estimation framework that combines a Korteweg-de Vries-Burgers (KdVB) equation, describing weakly nonlinear wave propagation in a bubbly liquid, with a physics-informed neural network (PINN). The contributions are threefold. First, the PINN reproduces the reference solution of the governing equation in the forward problem, with a near-zero prediction error at the initial time that confirms the initial condition is enforced exactly as intended. Second, prior to inverse estimation, a sensitivity analysis is introduced that quantifies, at both the coefficient and solution levels, how each of eight physical parameters influences the KdVB equation, allowing the expected difficulty of estimating each parameter to be assessed in advance. Third, based on this assessment, single-parameter inverse estimation is performed for seven of the eight parameters using the PINN. Liquid viscosity, bubble initial radius, liquid density, sound speed, and liquid pressure are estimated with errors of 0.8-2.1%, the polytropic exponent converges only partially, and the surface tension coefficient cannot be estimated at all, consistent with the sensitivity analysis. These results establish a general framework for identifying and estimating the physical parameters governing nonlinear wave propagation in bubbly liquids from observed waveform data.