Predicting of the function values
Before trying out deep learning I suggest you to try out Random Forests as the nature of your data seems non-linear to me and RFs are good at fitting non-linear data. If it doesn't work out well try doing a simple feed forward neural network with non-linear activation function as it also fits non linear functions really well. Also, machine learning is more about trying and testing as every dataset is different and you can never know in advance which model will work out well.