Operator learning for predicting multiscale bubble growth dynamics

Journal Article · Wed Mar 10 00:00:00 EST 2021 · Journal of Chemical Physics

DOI:https://doi.org/10.1063/5.0041203· OSTI ID:1853305

Lin, Chensen ^[1]; Li, Zhen ^[2]; Lu, Lu ^[3]; Cai, Shengze ^[4]; Maxey, Martin ^[4]; Karniadakis, George Em ^[4]

---

1. Brown University, Providence, RI (United States); Brown Univ., Providence, RI (United States)
2. Clemson University, SC (United States)
3. Massachusetts Institute of Technology (MIT), Cambridge, MA (United States)
4. Brown University, Providence, RI (United States)

We report 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 the 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). First, we generate data using the R–P equation for multirate bubble growth dynamics caused by randomly time-varying liquid pressures drawn from Gaussian random fields (GRFs). Our results show that properly trained DeepONets can accurately predict the macroscale bubble growth dynamics and can outperform long short-term memory networks. We also demonstrate that the DeepONet can extrapolate accurately outside the input distribution using only very few new measurements. Subsequently, we train the DeepONet with DPD data corresponding to stochastic bubble growth dynamics. Although the DPD data are noisy and we only collect sparse data points on the trajectories, the trained DeepONet model is able to predict accurately the mean bubble dynamics for time-varying GRF pressures. 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.

• Research Organization: Brown Univ., Providence, RI (United States)
• Sponsoring Organization: US Army Research Laboratory (USARL); USDOE; USDOE Office of Science (SC)
• Grant/Contract Number: SC0019453
• OSTI ID: 1853305
• Alternate ID(s): OSTI ID: 1770228; OSTI ID: 2282000
• Journal Information: Journal of Chemical Physics, Journal Name: Journal of Chemical Physics Journal Issue: 10 Vol. 154; ISSN 0021-9606
• Publisher: American Institute of Physics (AIP)
• Country of Publication: United States
• Language: English

Related Subjects

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
Computational physics
artificial neural networks
bubble dynamics
coarse-grained simulations
computational fluid dynamics
machine learning
multiphase flows
multiscale methods
stochastic processes