For RF, the number of trees was searched from 10 to 1000. For KRR, the regularization strength ω was searched from 0.001 to 100. For Graph Neural Networks (GNNs), CGCNN was trained with the following hyperparameters: 32 batch size, 100 epochs, 5 message passing layers, 1 hidden layer after pooling, 64 hidden atom features in message passing layers. ALIGNN was trained with the following hyperparameters: 32 batch size, 100 epochs, 4 message passing layers, 1 hidden layer after pooling, 256 hidden atom features in message passing layers, in line with the original paper . For the crystal twins pre-trained model (CT), the same fine-tuning hyperparameters as the original paper were used (128 batch size, 200 epochs, 3 message passing layers) .