  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.
