Last year I read something about Neuron-Network Potential Energy Surface (NNPES) and I think it is worth learning. Here are my notes.
One recommended paper one should read is PCCP, 13, 17930 (2011) by Joerg Behler.
Here I do not want to introduce the detail of the idea, because paper above give a nice definition. NNPES do be a clever ider for it ignore the difficult physics in the problem. Instead, it use a pure mathematical way to fit the pointwise energies (here we call it 'training').
Some guys argue that this methods just give a NNPES without a deeply conprehension of the model. That is true. However, this method give an effective way to let scientific guys to run MD or MC. Somehow it is like ab initio way if one take the electronic methods as black box.
It should be kept in mind that in all NNPES is not that suitable for the high accuracy. One can read Dong H Zhang and his co-workers' work to see how they got an accurate result with the help of spline. I once tried one PES fitting using NN of the system of tri-boron (thanks to D.-Z. Yang), you can find that the NN works, but does not work accurately.