High-dimensional neural network potential-energy surfaces

High-dimensional neural network potential-energy surfaces 5.1 Definition of the problem 

Unfortunately, NN potentials for high-dimensional systems are currently very rare. This has two reasons First, most groups working on the development of NN potentials are mainly interested in molecular systems. Second, dealing with high-dimensional NN PESs is technically much more involved. Only two main approaches have been reported in the literature so far, which will be discussed below. 

There are several conceptual problems, which have to be solved when constructing NN potentials for high-dimensional systems. First, the number of atoms determining the NN input must be variable. It is not acceptable to fit an individual NN potential for each system size. On the other hand, a fitted NN is only valid for a fixed number of input nodes, because only then the numerical values of all connecting weights are available. Therefore, the effective number of degrees of freedom for the NN needs to be fixed somehow even for systems with a variable total number of atoms. Second, 

Recently, two approaches have been published independently for the construction of high-dimensional NN potentials overcoming these problems. They are based on a decomposition of the total energy into local contributions depending on the local atomic environments. These approaches will be discussed in the following sections. 

2 High-dimensional neural network potentials based on a sum of bond energies 

---

S. Lorenz, A. Gross, M. Scheffler, Representing high-dimensional potential-energy surfaces for reactions at surfaces by neural networks, Chem. Phys. Lett. 395 (4-6) (2004) 210-215. 

---