Nonlinear modeling of sparkling drink bubbles using a physics informed long short term memory network

Bubble dynamics exist in many physical phenomena from the interaction between atmosphere and ocean, to food science of champagne bubbles. Bubble sound has recently been found to be a new way to understand bubbles and bubble dynamics. In this paper, we collect bubble sounds of different types of sparkling drinks, namely, sparkling water, beer, and champagne, and use the experimental data to construct a data driven model for sparkling bubbles. We apply dynamical reconstruction theory to the measured data and use false nearest neighbor, correlation dimension, and largest Lyapunov exponent to verify that the sparkling drink bubble dynamic is nonlinear and chaotic. Based on the derived physical principle on bubble pressure, we propose a novel physics informed long short term memory (PI-LSTM) neural network as a time series predictor to form a data driven with physics guidance model for bubble dynamics. It is shown here that the proposed PI-LSTM is effective in modeling the bubble sound data with improved accuracy compared to standard predictors including LSTM, multi-layer neural network and decision tree. The predictive analysis supports the nonlinear behavior of the bubble sound signals and demonstrates results consistent with the chaotic analysis.