The melt pool in Directed Energy Deposition (DED) exhibits inherent uncertainties due to complex thermal-fluid interactions, rapid phase changes, and dynamic process variations. These factors make precise modeling and control challenging, resulting in inhomogeneous thermal and geometric characteristics. Accurately predicting and managing these variations ensures optimal material properties and geometric precision. This research presents a robust surrogate model employing advanced Recurrent Neural Network architectures, including Long Short-Term Memory (LSTM), Bidirectional LSTM (Bi-LSTM), and Gated Recurrent Units (GRU), to predict melt pool thermal histories and geometries. Leveraging a time-series dataset generated from multi-physics simulations and a factorial design of experiments, the model achieves R-squared values of 0.980 for peak temperature and 0.885 for melt pool depth prediction. Among the evaluated algorithms, the GRU model offers the best balance of accuracy and efficiency, reducing computation time by 45.3% compared to Bi-LSTM while maintaining robust predictive performance. Uncertainty quantification and residual analysis are applied in this research to demonstrate the model reliability, enabling early anomaly detection in DED.