Recent developments in computer processing power lead to new paradigms of how problems in many-body physics and especially polymer physics can be addressed. Parallel processors can be exploited to generate millions of molecular configurations in complex environments at a second, and concomitant free-energy landscapes can be estimated. Databases that are complete in terms of polymer sequences and architecture form a powerful training basis for cross-checking and verifying machine learning-based models. We employ an exhaustive enumeration of polymer sequence space to benchmark the prediction made by a neural network. In our example, we consider the translocation time of a copolymer through a lipid membrane as a function of its sequence of hydrophilic and hydrophobic units. First, we demonstrate that massively parallel Rosenbluth sampling for all possible sequences of a polymer allows for meaningful dynamic interpretation in terms of the mean first escape times through the membrane. Second, we train a multi-layer neural network on logarithmic translocation times and show by the reduction of the training set to a narrow window of translocation times that the neural network develops an internal representation of the physical rules for sequence-controlled diffusion barriers. Based on the narrow training set, the network result approximates the order of magnitude of translocation times in a window that is several orders of magnitude wider than the training window. We investigate how prediction accuracy depends on the distance of unexplored sequences from the training window.