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The TROPOspheric Monitoring Instrument (TROPOMI) on board the Sentinel 5-Precursor satellite provides daily global observations of atmospheric methane, enabling the detection of super-emitters that are often missing or highly underestimated in bottom-up inventories. The emission rates of these super-emitters are typically quantified using mass balance-based approaches which have large associated uncertainties. Here, we train a convolutional neural network using simulated TROPOMI methane observations and meteorological reanalysis data in order to create ML-SPERE, a machine learning (ML)-based methodology for estimating the emission rates of super-emitter methane plumes observed by TROPOMI. We show that ML-SPERE outperforms the Integrated Mass Enhancement (IME) method on simulated TROPOMI methane plumes and under ideal observation conditions (where the plume head is visible) can achieve a reduction in median absolute percentage error from 42% to 24%. Additionally, our ML-SPERE quantifications for synthetic plumes are unbiased across wind speeds, whereas the IME estimates are systematically biased low at low wind speeds (a regime in which most TROPOMI methane super-emitting plumes are detected). Moving beyond synthetic data to real world application (where ground truth emission rates are not known), we apply ML-SPERE to TROPOMI methane observations of a 200-day well blowout in Kazakhstan and find agreement with TROPOMI-based IME estimates within uncertainties, a smaller offset relative to inverse modeling results than exhibited by TROPOMI IME estimates, and improved consistency with IME estimates derived from high-resolution point-source imagers. We additionally quantify a year's worth of TROPOMI detections of methane super-emitters around the globe, and find generally good agreement with IME quantifications. Global trends in estimated methane emissions via ML-SPERE and the IME method for this dataset are largely consistent, with exceptions in northern Russia, the Congo basin, and southwestern Australia. We also find evidence to suggest that IME emission rate estimates for this dataset are negatively biased at low wind speeds, and that ML-SPERE estimates may be unbiased, as seen in our simulation studies. While our experiments with simulated plumes demonstrate that ML-SPERE more accurately recovers emission rates than the IME method, agreement between the methods for real-world plumes (where no ground truth exists) provides confidence in the robustness of both approaches. Although quantifications remain largely constrained by uncertainties in wind fields (as with the IME method), ML-SPERE provides a valuable addition to the suite of quantification methods available for TROPOMI methane plume observations, owing to its computational efficiency, improved accuracy over the IME method, and reduced sensitivity to wind-related biases.