  We present our ongoing work aimed at accelerating a particle-resolved direct
numerical simulation model designed to study aerosol-cloud-turbulence
interactions. The dynamical model consists of two main components - a set of
fluid dynamics equations for air velocity, temperature, and humidity, coupled
with a set of equations for particle (i.e., cloud droplet) tracing. Rather than
attempting to replace the original numerical solution method in its entirety
with a machine learning (ML) method, we consider developing a hybrid approach.
We exploit the potential of neural operator learning to yield fast and accurate
surrogate models and, in this study, develop such surrogates for the velocity
and vorticity fields. We discuss results from numerical experiments designed to
assess the performance of ML architectures under consideration as well as their
suitability for capturing the behavior of relevant dynamical systems.
