Constructing high‐dimensional neural network potentials: A tutorial review

By J. Behler. 2015

750 citations recorded by the source corpus.

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 first-principles 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 high-dimensional 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. © 2015 Wiley Periodicals, Inc.

Subfields: Materials Chemistry, Physical and Theoretical Chemistry

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Materials Chemistry

In Physical and Theoretical Chemistry

Citations in the corpus

N-body Networks: a Covariant Hierarchical Neural Network Architecture for Learning Atomic Potentials (2018, positive): “…amount of activity in machine learned atomic potentials (MLAP), and molecular dynamics simulations based on this approach are starting to yield results that outperform other methods (Bart´ok et al., 2010; Behler, 2015; Shapeev, 2015; Chmiela et al., 2016; Zhang et al., 2017; Sch¨utt et al., 2017).”
Towards universal neural network potential for material discovery applicable to arbitrary combination of 45 elements (2021, background): “Architecture Invariance NN type Scalar sph Vector Tensor BPNN [5] E(3) Invariant MLP X ANI-1 [2] E(3) Invariant MLP X ANI-2x [6] E(3) Invariant MLP X Schrodinger-ANI [7] E(3) Invariant MLP X TensorMol-0.”
Machine Learning for High-entropy Alloys: Progress, Challenges and Opportunities (2022, methodology): “Since the neural networks are applied to every atom, NNP is also referred to as high-dimensional NNP (HDNNP) [146].”
Physically informed artificial neural networks for atomistic modeling of materials (2018, methodology): “The currently existing, mathematical NN potentials [14–18, 32–37] partition the total energy E into a sum of atomic energies, E = ∑ iEi.”