Recently, many advancements have been made in accelerated MRI reconstruction with the use of neural networks. Such deep learning methods learn a suitable MRI prior distribution from large sets of training data. For MRI images acquired with an uncommon scanning sequence, large datasets required for training are not available. Additionally, deep learning methods do not generalize well to unseen data. Therefore, in this research, a framework is proposed for accelerated MRI reconstruction trained with simulated data. The framework uses a Recurrent Inference Machine (RIM). The RIM is a deep learning framework that learns an iterative inference process. The RIM framework has been chosen as it is designed to learn the inversion process itself rather than the image statistics. Therefore, RIMs have a low tendency to overfit, and a high capacity to generalize to unseen data. The framework is evaluated by reconstructing undersampled data of in-vivo brain MRI images and comparing them with zero-filled reconstructions, reconstructions of an identical framework trained with in-vivo data and ESPIRiT reconstructions. The comparison shows that the framework does partly learn the inference process; however, the reconstructions still contain artefacts and the reconstruction of the framework trained with in-vivo data and the ESPIRiT method are of higher quality. For simulated data to replace in-vivo data for the training of the RIM, the simulated data has to be more similar to the in-vivo data.