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Due to computational constraints, running global climate models (GCMs) for many years requires a lower spatial grid resolution (${\gtrsim}50$ km) than is optimal for accurately resolving important physical processes. Such processes are approximated in GCMs via subgrid parameterizations, which contribute significantly to the uncertainty in GCM predictions. One approach to improving the accuracy of a coarse-grid global climate model is to add machine-learned state-dependent corrections at each simulation timestep, such that the climate model evolves more like a high-resolution global storm-resolving model (GSRM). We train neural networks to learn the state-dependent temperature, humidity, and radiative flux corrections needed to nudge a 200 km coarse-grid climate model to the evolution of a 3~km fine-grid GSRM. When these corrective ML models are coupled to a year-long coarse-grid climate simulation, the time-mean spatial pattern errors are reduced by 6-25% for land surface temperature and 9-25% for land surface precipitation with respect to a no-ML baseline simulation. The ML-corrected simulations develop other biases in climate and circulation that differ from, but have comparable amplitude to, the baseline simulation.