Ultra-deep ocean drilling is expected to develop to deeper and deeper fields. Such drilling has some problems. One of them is that weight on bit (WOB) can not be measured in real time, that is important for drilling operation. Therefore, simulation models estimating WOB are needed. However, previous studies have shown insufficient accuracy of physics-based models. In this research, we introduced a black box model with recurrent neural networks for WOB estimation. We revealed such black box model has applicability to ultra-deep ocean drilling systems, but it has low adaptability to extrapolation. In order to compensate a black box model and a physics-based model, by combining both of them we created a new model called grey box model. This grey box model was revealed to have high accuracy. This research is expected to be a guideline of grey box model with neural networks.