The growing frequency of weather anomalies driven by climate change necessitates energy-efficient heating solutions to reduce carbon emissions. Geothermal heat pumps offer an ecological alternative, but their installation requires precise planning to avoid negative impacts on groundwater. Pelzer and Schulte [PS24] proposed a Convolutional Neural Network (CNN) to predict steady-state heat plumes from these heat pumps, but their model isn’t built to generalize across varying input orientations. To address this limitation, we introduce three approaches: (1) the Oriented Boxes approach, which rotates input data during inference to match a fixed training orientation; (2) the Data Augmentation approach, which extends the training dataset with rotated data samples; and (3) the Equivariant Convolutional Neural Network (ECNN) approach, which directly incorporates rotational equivariance into the network architecture. Evaluated on metrics such as the Mean Absolute Error (MAE) and the Root Mean Square Error (RMSE), the ECNN approach shows the most significant improvement, enhancing performance by up to 50% compared to the baseline CNN. The other approaches achieve gains of 30%-40%. These results demonstrate that introducing approximate rotational equivariance, especially through ECNNs, is highly effective for improving the generalization of CNNs to data with varying orientations. The code of this thesis can be found under: https://github.com/pLm-k/1HP_NN_equivariance/ tree/release_24