Graph neural network architectures, which take graphs representing the crystal structures as inputs, were used for the machine learning models. The graph representations contain atoms as nodes and interatomic distances as edges. Here, the atoms are represented with a one-hot encoding of the element with a vector length of 100 within the node attributes. The edge attributes contain interatomic distances within a cutoff of 8 Å and up to 12 neighbors per node, where the distances were then expanded by a Gaussian basis to a length of 50. In this work, an additional state attribute is included, representing the level of theory used, or "fidelity," as an integer. The graph neural network itself adopts the MatErials Graph Network (MEGNet) architecture where the node, edge, and state attributes are propagated sequentially in the stated order during the graph convolutional steps. The overall model contains one pre-processing layer, four graph convolutional layers, one pooling layer using the Set2Set function, and finally two post-processing layers. The pre-processing, post-processing, and graph convolutional update functions are all fully-connected layers with Rectified Linear Unit (ReLU) activation functions and with dimensions of 128, 128 and (128, 128), respectively. The models were trained with the AdamW optimizer using an initial learning rate of 0.0005 and a batch size of 128 for a total of 250 epochs. The model state with the lowest validation mean absolute error (MAE) is saved and used for testing. The training:validation:testing ratio used is 80:5:15, and the samples were randomly split across the training, validation, and testing sets. For all cases in this work, the same hyperparameters were used in the models. For the individual models, the models were trained separately. In multi-task learning, the output dimension was expanded to four, and the predictions were performed simultaneously with a single model for all fidelities (i.e., levels of theory). For multifidelity learning, we adopt the approach used by Chen et al. where each fidelity is considered a unique data sample and structures with different fidelities can appear in both training and testing data splits. The model training and testing was set up and performed using the MatDeepLearn framework, which is implemented using the PyTorch and PyTorch geometric libraries. The training and evaluation were conducted on four NVIDIA Tesla V100 ('Volta') graphics processing units (GPUs).