Artificial neural networks (ANNs) were trained using simulated displacement fields to perform stiffness estimation from MRE data. These neural network-based inversions (NNIs) are evaluated in simulation and in vivo. In a test set of simulated data, NNI is shown to provide a more accurate estimate of stiffness compared to a standard direct inversion (DI) approach. In vivo, NNI-based stiffness strongly correlated with DI-based stiffness across a range of fibrosis stages in the liver and ages in the brain, indicating that NNI can detect relevant biology. Finally, test-retest error in the brain is reduced using NNI compared to DI.