Large-scale dynamical and thermodynamical processes are common environmental drivers of extreme weather events. However, such large-scale environmental conditions often display systematic biases in climate simulations, posing challenges to evaluating extreme weather events and associated risks in current and future climate. In this paper, a machine learning (ML) approach was employed to bias correct the large-scale wind, temperature, and humidity simulated by the E3SM atmosphere model at $\sim 1^\circ$ resolution. The usefulness of the proposed ML approach for extreme weather analysis was demonstrated with a focus on three extreme weather events, including tropical cyclones (TCs), extratropical cyclones (ETCs), and atmospheric rivers (ARs). We show that the ML model can effectively reduce climate bias in large-scale wind, temperature, and humidity while preserving their responses to imposed climate change perturbations. The bias correction is found to directly improve the water vapor transport associated with ARs, and the representations of thermodynamical flows associated with ETCs. When the bias-corrected large-scale winds are used to drive a synthetic TC track forecast model over the Atlantic basin, the resulting TC track density agrees better with that of the TC track model driven by observed winds. In addition, the ML model insignificantly interferes with the mean climate change signals of large-scale storm environments as well as the occurrence and intensity of three extreme events. This study suggests that the proposed ML approach can be used to improve the downscaling of extreme weather events by providing more realistic large-scale storm environments simulated by low-resolution climate models.