Potential energy surfaces from high fidelity fitting of ab initio points: the permutation invariant polynomial - neural network approach

With advances in ab initio theory, it is now possible to calculate electronic energies within chemical (<1 kcal/mol) accuracy. However, it is still challenging to represent faithfully a large number of ab initio points with a multidimensional analytical function over a large configuration space, which is needed for accurate dynamical studies. In this Review, we discuss our recent work on a new potential-fitting approach based on artificial neural networks, which are ultra-flexible in representing any multidimensional real functions. A unique feature of our neural network approach is how the symmetries, particularly those associated with the exchange of identical atoms in the system, are enforced. To this end, symmetry functions in the form of symmetrised monomials that satisfy a particular type of symmetry possessed by the system are used in the input layer of the neural network. This approach is rigorous, accurate, and efficient. It is also simple to implement, requiring no modification of the neural network routines. Its applications to the construction of multi-dimensional potential energy surfaces in many gas phase and gas-surface systems as surveyed here.