Operator learning for predicting multiscale bubble growth dynamics

TL;DR

This paper demonstrates that deep operator networks can effectively unify multiscale bubble growth models at macro and micro levels, simplifying complex multiscale simulations by learning the underlying dynamics directly.

Contribution

It introduces a novel application of DeepONet to learn and predict coupled multiscale bubble dynamics, bridging deterministic macroscale and stochastic microscale models.

Findings

DeepONet accurately predicts multirate bubble growth dynamics.

The framework unifies macroscale and microscale models effectively.

Results suggest potential for simplifying multiscale modeling workflows.

Abstract

Simulating and predicting multiscale problems that couple multiple physics and dynamics across many orders of spatiotemporal scales is a great challenge that has not been investigated systematically by deep neural networks (DNNs). Herein, we develop a framework based on operator regression, the so-called deep operator network (DeepONet), with the long term objective to simplify multiscale modeling by avoiding the fragile and time-consuming "hand-shaking" interface algorithms for stitching together heterogeneous descriptions of multiscale phenomena. To this end, as a first step, we investigate if a DeepONet can learn the dynamics of different scale regimes, one at the deterministic macroscale and the other at the stochastic microscale regime with inherent thermal fluctuations. Specifically, we test the effectiveness and accuracy of DeepONet in predicting multirate bubble growth dynamics, which is described by a Rayleigh-Plesset (R-P) equation at the macroscale and modeled as a stochastic nucleation and cavitation process at the microscale by dissipative particle dynamics (DPD). Taken together, our findings demonstrate that DeepONets can be employed to unify the macroscale and microscale models of the multirate bubble growth problem, hence providing new insight into the role of operator regression via DNNs in tackling realistic multiscale problems and in simplifying modeling with heterogeneous descriptions.