The correlation between manufacturing parameters and the resulting surface topography is most often described with standardized profile surface texture parameters (R-parameters). However, in many cases, they represent a strong simplification as the most common parameters are often neither function-oriented nor unambiguously correlated with the manufacturing parameters. Therefore, we investigate whether a neural network is a suitable alternative to establish a more comprehensive correlation between the surface topography and the manufacturing parameters. The learned correlation provides possibilities to be used for subsequent monitoring of the manufacturing process. Our approach is to predict the manufacturing parameters from a measured topography dataset with a convolutional neural network as a regression model. As the training of neural networks requires large amounts of data, stochastic surface models are applied to generate artificial profiles and thus increase the available amount of data. The prediction accuracy and consequently its correlation with the manufacturing parameters are evaluated for a case study of an abrasive process. In this case study, it is first determined whether artificial or measured profiles and which of their representations (frequency or time dependent) provide the best information to train the network. The network featuring the most reliable prediction of the manufacturing parameters is then used for further analysis. By comparing this network with a linear regression model between manufacturing parameters and R-parameters, its performance is benchmarked and can be suggested as a suitable alternative to predict and monitor manufacturing parameters based on the measured surface topography.