Laser powder-bed fusion is an additive manufacturing (AM) process that offers exciting advantages for the fabrication of metallic parts compared to traditional techniques, such as the ability to create complex geometries with less material waste. However, the intricacy of the additive process and extreme cyclic heating and cooling leads to material defects and variations in mechanical properties; this often results in unpredictable and even inferior performance of additively manufactured materials. Key indicators for the potential performance of a fabricated part are the geometry and temperature of the melt pool during the building process, due to its impact upon the underlining microstructure. Computational models, such as those based on the finite element method, of the AM process can be used to elucidate and predict the effects of various process parameters on the melt pool, according to physical principles. However, these physics-based models tend to be too computationally expensive for real-time process control. Hence, in this work, a hybrid model utilizing neural networks is proposed and demonstrated to be an accurate and efficient alternative for predicting melt pool geometries in AM, which provides a unified description of the melting conditions. The results of both a physics-based finite element model and the hybrid model are compared to real-time experimental measurements of the melt pool during single-layer AM builds using various scanning strategies.