So the background is that I want to use a deep neural network to model a system. In a traditional way to observe the system character, we will use the Gaussian noise as the inputs of the system, and then we could obtain the outputs of the system. Now I want to use the Gaussian noise (inputs) and the obtained outputs to train a deep neural network, an end-to-end model, to model this system.
If the data are structured, we can pre-train the networks layer by layer with auto-encoder to obtain a well-enough initial value of the weights. However, the inputs now are totally unstructured (Gaussian noise). How should I efficiently train the deep neural network I want? Are there some prior works on this issue?