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An overview of computational methods to describe high-dimensional potentialenergy surfaces suitable for atomistic simulations is given. Particularemphasis is put on accuracy, computability, transferability and extensibilityof the methods discussed. They include empirical force fields, representationsbased on reproducing kernels, using permutationally invariant polynomials, andneural network-learned representations and combinations thereof. Futuredirections and potential improvements are discussed primarily from a practical,application-oriented perspective.

High-Dimensional Potential Energy Surfaces for Molecular Simulations