The Low Earth Orbit (LEO) region has been attractive to many space agencies and organisations because of its ease of access and the ideal opportunity for remote sensing. Due to the low altitudes, a satellite's orbital state is highly affected by the atmospheric drag force acting on the satellite's body. The largest variation in this drag force is caused by the changes in thermospheric density due to the complex interactions of the Sun with the Earth's thermosphere. In order to properly forecast the orbital state of a LEO satellite, the thermospheric densities need to be predicted as accurately as possible. The thermospheric density values can be estimated by using for example empirical atmospheric density models, such as the DTM2013 (Drag Temperature Model). During this thesis study it has been investigated whether the highly researched field of machine learning models could be used to develop a predictor for the along-track density values for the Swarm satellite constellation. This constellation has an abundant amount of trajectory-based time series of thermospheric density values from Precise Orbit Determination (POD) data. This research has focused on the development of Multi-layer Perceptron (MLP) models which are a type of Feed-Forward Neural Network. These MLP models have been trained and tested on past acceleration and solar activity data sets provided by the Swarm satellite mission and space weather observatories, respectively. The performance of these MLP models was then compared to two baseline models, namely a Calibrated Persistence Model (CPM) and the density values modelled by DTM2013. The results in this research led to the conclusion that a three-layer MLP model performed best when it was trained on data of the same spacecraft like the one it was supposed to perform along-track density forecasts for. The forecasting accuracy increased the most when the model was trained on long periods of training data characterised by high solar and low geomagnetic activity. When trained on these data sets, the MLP model has shown to outperform the baseline models when making predictions up until two days into the future during periods of high solar activity. The DTM2013 seems the best option to forecast density values during low solar activity. As an alternative to the DTM2013, the CPM seems a suitable model when one needs to quickly implement a forecasting model with decent performance irrespective from the presence of geomagnetic storms.