Atmospheric General Circulation Models (GCMs) continue to increase in complexity which is especially true for their computationally-demanding physical parameterizations. This work explores whether, and how, computationally-efficient machine learning (ML) techniques can become an option for replacing physical parameterization schemes in GCMs. We test this idea in a model hierarchy with NCAR’s Community Atmosphere Model version 6 (CAM6) which is part of NCAR’s Community Earth System Model (CESM 2.1). In particular, dry and idealized-moist CAM6 model configurations are considered which employ simplified physical forcing mechanisms for radiation, boundary layer mixing, surface fluxes, and precipitation (in the moist setup). Several ML models are developed, trained, and tested offline using CAM6 output data. The assessed ML techniques include linear regression, random forests, and neural networks with and without convolutional layers. Using a variety of ML hyperparameter choices, all of the ML methods are able to capture the general structure of the CAM6 physical forcing. However, in order to capture the details in the physical forcing patterns, the ML hyperparameters must be tuned. Once tuned, we compare different ML techniques against one another in order to assess their strengths and weaknesses. Future work will explore the online coupling of the ML-generated physical tendencies to the CAM6 atmospheric dynamical core.