Recent studies have explored the delay propagation network among airports by inferring Granger causality among time series using linear methods. Granger causality indicates whether delays at one airport can help predict delays at itself or other airports and thus help to understand the interconnection among airports. This paper makes inferences about the Granger causality relation among airports by applying a nonlinear multilayer perceptron method to the arrival delay time series in Europe and China. We find that the propagation results can be overestimated with data input containing early arrival flights, besides delayed flights. Europe presents a smaller magnitude of delay propagation than China, considering only delayed flights, indicated by the link densities of the networks with the same penalty parameter. Unlike some recent research findings, our results suggest that large airports have more out-degree and more impact in the delay propagation network. These results can help predict and understand delay propagation in daily operations or simulation environments.