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SUMMARY The ability to accurately and reliably obtain images of shallow subsurface anomalies within the Earth is important for hazard monitoring and a fundamental understanding of many geologic structures, such as volcanic edifices. In recent years, machine learning (ML) has gained increasing attention as a novel approach for addressing complex problems in the geosciences. Here we present an ML-based inversion method to integrate cosmic-ray muon and gravity data sets for shallow subsurface density imaging at a volcano. Starting with an ensemble of random density anomalies, we use physics-based forward calculations to find the corresponding set of expected gravity and muon attenuation observations. Given a large enough ensemble of synthetic density patterns and observations, the ML algorithm is trained to recognize the expected spatial relations within the synthetic input–output pairs, learning the inherent physical relationships between them. Once trained, the ML algorithm can then interpolate the best-fitting anomalous pattern given data that were not used in training, such as those obtained from field measurements. We test the validity of our ML algorithm using field data from the Showa-Shinzan lava dome (Mt Usu, Japan) and show that our model produces results consistent with those obtained using a more traditional Bayesian joint inversion. Our results are similar to the previously published inversion, and suggest that the Showa-Shinzan lava dome consists of a relatively high-density (2200–2400 km m–3) cylindrical anomaly, about 300 m in diameter. Adding noise to synthetic training and testing data sets shows that, as expected, the ML algorithm is most robust in areas of high sensitivity, as determined by the forward kernels. Overall, we discover that ML offers a viable alternate method to a Bayesian joint inversion when used with gravity and muon data sets for subsurface density imaging.