Inferring multiscale bubble growth dynamics by deep neural operator learning*

Simulating and predicting multiscale problems that couple multiple physics and dynamics across many orders of spatiotemporal scales is a great challenge in complex fluids. In this talk, we will present a composite deep neural network (a branch and a trunk network) for regressing nonlinear operators to predict multiscale bubble growth dynamics. We consider tiny bubbles of initial size from 100 nm to 10 μm modelled by the Rayleigh–Plesset equation in the deterministic continuum regime above 1 μm and the many-body dissipative particle dynamics method for bubbles below 1 μm in the stochastic microscale regime. We simulate the multirate bubble growth dynamics caused by randomly time-varying liquid pressures drawn from Gaussian random fields, and collect simulation data of bubble growth for both deterministic continuum regime and stochastic microscale regime. Subsequently, we train the composite deep neural network based on mixed data to learn the governing operator of multiscale bubble growth dynamics. Results show that the trained neural operator can capture correct physics and make accurate predictions of bubble growth on-the-fly (within a fraction of a second) across four orders of magnitude difference in spatial scales and two orders of magnitude in temporal scales. We will demonstrate that the deep neural operator framework is general for learning nonlinear operators for diverse physical problems, including learning transient mechanical response of composites subject to a dynamic loading.