Training and testing dataset from different source Neural network

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I am currently building a neural network to classify handwritten characters. I have downloaded the EMNIST dataset to train my neural network. For testing, I also collected samples from students. Is the approach to use different sources for the training and testing dataset valid?

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Normally we would use a dataset that is available publicly. Separate it into training and testing sets. This allows for replication of your results and comparison to other approaches.

You could also try your trained neural net on another data set as you suggest, but I would suggest you start by replicating results on a public dataset to check your implementation is correct.