In this paper, we propose a deep learning (DL)-based approach for efficiently computing the inverse of Hermitian matrices using truncated polynomial expansion (TPE). Our model-driven approach involves optimizing the coefficients of the TPE during an offline training procedure for a given number of TPE terms. We apply this method to signal detection in uplink massive multiple-input multiple-output (MIMO) systems, where the matrix inverse operation required by linear detectors, such as zero-forcing (ZF) and minimum mean square error (MMSE), is approximated using TPE. Our simulation results demonstrate that the proposed learned TPE-based method outperforms the conventional TPE method with optimal coefficients in terms of asymptotic convergence speed and reduces the computational complexity of the online detection stage, albeit at the expense of the offline training stage. However, the limited number of trainable parameters leads to a swift offline training process.