Constructing high‐dimensional neural network potentials: A tutorial review

Abstract

A lot of progress has been made in recent years in the development of atomistic potentials using machine learning (ML) techniques. In contrast to most conventional potentials, which are based on physical approximations and simplifications to derive an analytic functional relation between the atomic configuration and the potential-energy, ML potentials rely on simple but very flexible mathematical terms without a direct physical meaning. Instead, in case of ML potentials the topology of the potential-energy surface is "learned" by adjusting a number of parameters with the aim to reproduce a set of reference electronic structure data as accurately as possible. Due to this bias-free construction, they are applicable to a wide range of systems without changes in their functional form, and a very high accuracy close to the underlying firstprinciples data can be obtained. Neural network potentials (NNPs), which have first been proposed about two decades ago, are an important class of ML potentials. Although the first NNPs have been restricted to small molecules with only a few degrees of freedom, they are now applicable to highdimensional systems containing thousands of atoms, which enables addressing a variety of problems in chemistry, physics, and materials science. In this tutorial review, the basic ideas of NNPs are presented with a special focus on developing NNPs for high-dimensional condensed systems. A recipe for the construction of these potentials is given and remaining limitations of the method are discussed.

A fingerprint based metric for measuring similarities of crystalline structures

“…Furthermore, the fingerprint distance can be used as a simple measure of the similarity between two structures with a higher likelihood that they are identical if the fingerprint distance is small. In this context, machine learning methods (such as Bayesian techniques, 57 support vector machines, 58 and neural network [59][60][61][62] ) could be trained with attributes derived from our fingerprint to better quantify crystal structure similarities. The new fingerprint can also accurately explore local environments to create atomic and structural attributes for machine learning techniques trained to predict material properties.…”

Ensemble-Average Representation of Pt Clusters in Conditions of Catalysis Accessed through GPU Accelerated Deep Neural Network Fitting Global Optimization

“…19 Therefore, two transformations are performed on the input sample data in Cartesian coordinates {r j }. The original coordinates {r j } (after k-body selection procedure) are first transformed to interatomic distances {a m }, where m = 1, 2, ..., C(k, 2) are the indices of all interatomic distances in the k-body fragment.…”

Vibrational energy transfer near a dissociative adsorption transition state: State-to-state study of HCl collisions at Au(111)

“…6,7 In addition, there is copious evidence that electron-hole pairs (EHPs) can couple to the vibrational degrees of freedom of molecules colliding with a metal surface-a scenario that cannot be described within the BOA. 8 While methods for constructing full dimensional PESs for surface chemistry are rapidly advancing, [9][10][11][12] the inclusion of electronically nonadiabatic effects still is a major challenge. Understanding the structure and energetics of the transition state is essential for a proper description of a chemical reaction.…”