Embedded Atom Neural Network Potentials: Efficient and Accurate Machine Learning with a Physically Inspired Representation

Abstract

We propose a simple, but efficient and accurate machine learning (ML) model for developing high-dimensional potential energy surface. This so-called embedded atom neural network (EANN) approach is inspired by the well-known empirical embedded atom method (EAM) model used in condensed phase. It simply replaces the scalar embedded atom density in EAM with a Gaussian-type orbital based density vector, and represents the complex relationship between the embedded density vector and atomic energy by neural networks. We demonstrate that the EANN approach is equally accurate as several established ML models in representing both big molecular and extended periodic systems, yet with much fewer parameters and configurations. It is highly efficient as it implicitly contains the three-body information without an explicit sum of the conventional costly angular descriptors. With high accuracy and efficiency, EANN potentials can vastly accelerate molecular dynamics and spectroscopic simulations in complex systems at ab initio level. TOC graphic3 Accurate and efficient interaction potential energy surfaces (PESs) are crucial for spectroscopic, molecular dynamics, and thermodynamics simulations 1 . Traditional empirical or semi-empirical force field models such as the embedded atom method (EAM) 2-3 , while physically meaningful and highly efficient, are severely limited by their accuracy. More recently, tremendous efforts have been devoted to developing machine learning (ML) based PESs 4 , which are capable of representing a large set of ab initio data more accurately on chemical properties 5 , molecules 6-13 , gas phase and surface reactions 14-18 , and materialsError! Bookmark not defined. 10,[19][20][21][22] .Since known ML techniques in computer science themselves do not recognize the intrinsic symmetry of a chemical system, it is essential to design a ML representation for a PES that preserves rotational, translational, and permutational symmetry in an accurate and efficient way 23 . In this regard, permutation invariant polynomials (PIPs) in terms of internuclear distances 24 were used as the input of neural networks (NNs) 14 and Gaussian process regression (GPR) 25 in low-dimensional systems. For highdimensional problems, Behler and Parrinello 26 first handcrafted a set of atom centered symmetry functions (ACSFs) 23 as the input of atomistic neural networks (AtNN), which were later improved in various ways 9, 27 . More recently, the deep learning molecular dynamics (DPMD) model 10 and its symmetrized edition (DeepPot-SE) 28 map the coordinate matrix to a multi-output NN making descriptors themselves self-adapted in training. Deep tensor NN (DTNN) model 11 utilizes a vector of nuclear charges and an inter-atomic distance matrix as descriptors and its variant SchNet model 12 further introduces a continuous-filter convolutional layer to extract features from these

Complex reaction processes in combustion unraveled by neural network-based molecular dynamics simulation

“…Both networks use the ResNet architecture 75 . The size of the embedding network was set to (25,50,100) and the size of the embedding matrix was set to 12. The size of the fitting network is set to (240, 240, 240).…”

“…Neural networks constitute a very flexible and unbiased class of mathematical functions, which in principle is able to approximate any real-valued function to arbitrary accuracy. Since Behler and Parrinello proposed the high-dimensional neural network approach 19,20 , several methods have been developed to implement this approach and many different kind of NN PESs have been proposed for water, small organic molecules, and metalloid materials [21][22][23][24][25] . For example, the sGDML [26][27][28] , SchNet 29 , PhysNet 30 , and FCHL 31 methods.…”

Global optimization of chemical cluster structures: Methods, applications, and challenges

“…Their PESs are fitted to different forms of MLPs (like the Gaussian process or deep neural networks), enabling fast GO of up to 100 atoms with an accuracy close to that of first‐principles methods. There are several forms of MLPs in this field, like Behler–Parrinello symmetry functions [277], deep potentials [278], and embedded atom neural network potetial [279]. There is no consensus regarding which is the most suitable approach for GO of cluster structures.…”

Machine Learning Transition Temperatures from 2D Structure

“…[48,49] For quantum molecular properties, geometry (and atom type) are typically chosen as input because even the slightest changes in geometry can affect the wavefunction and its observables. [50][51][52][53] On the other hand, macroscopic properties are more robust to higher-level or coarse-gained descriptors. [54][55][56][57][58] In the case of melting, for example, a molecular crystal may be identified by descriptors or a molecular fingerprint [59][60][61][62] derived from its repeating structural unit.…”