>>12810076Not sure about better method, but more likely different ways of setting up NNs. For example, generative models have exploded recently- the ability to train RNNs (VAEs, GANs) to generate anything from text to new molecules to whatever.
Transfer learning/Reinforcement learning I think will become bigger and bigger- it's probably the "last frontier" of what we need/want AI to do. It will still probably use some sort of NN at its core.
One of the unexplored parts of NN is the backpropagation- we use the same technique in every single application of learning. There has been recent work (like this year) that is starting to explore other algorithms for backpropagation which looks promising.
Dynamic learning will be another area to explore: Progressive GANs (like style-GANs) are an example. Training on coarse datasets, then freezing weights, adding another set of layers, training on finer datasets, etc.