Neural Network Potentials: A Concise Overview of Methods

In the past two decades, machine learning potentials (MLP) have reached a level of maturity that now enables applications to large-scale atomistic simulations of a wide range of systems in chemistry, physics and materials science. Different machine learning algorithms have been used with great success in the construction of these MLPs. In this review, we discuss an important group of MLPs relying on artificial neural networks to establish a mapping from the atomic structure to the potential energy. In spite of this common feature, there are important conceptual differences, which concern the dimensionality of the systems, the inclusion of long-range electrostatic interactions, global phenomena like non-local charge transfer, and the type of descriptor used to represent the atomic structure, which can either be predefined or learnable. A concise overview is given along with a discussion of the open challenges in the field

A Fourth-Generation High-Dimensional Neural Network Potential with Accurate Electrostatics Including Non-local Charge Transfer

Machine learning potentials have become an important tool for atomistic simulations in many fields, from chemistry via molecular biology to materials science. Most of the established methods, however, rely on local properties and are thus unable to take global changes in the electronic structure into account, which result from long-range charge transfer or different charge states. In this work we overcome this limitation by introducing a fourth-generation high-dimensional neural network potential that combines a charge equilibration scheme employing environment-dependent atomic electronegativities with accurate atomic energies. The method, which is able to correctly describe global charge distributions in arbitrary systems, yields much improved energies and substantially extends the applicability of modern machine learning potentials. This is demonstrated for a series of systems representing typical scenarios in chemistry and materials science that are incorrectly described by current methods, while the fourth-generation neural network potential is in excellent agreement with electronic structure calculations.Comment: 13 pages, 11 figure

Robust estimation of bacterial cell count from optical density

Optical density (OD) is widely used to estimate the density of cells in liquid culture, but cannot be compared between instruments without a standardized calibration protocol and is challenging to relate to actual cell count. We address this with an interlaboratory study comparing three simple, low-cost, and highly accessible OD calibration protocols across 244 laboratories, applied to eight strains of constitutive GFP-expressing E. coli. Based on our results, we recommend calibrating OD to estimated cell count using serial dilution of silica microspheres, which produces highly precise calibration (95.5% of residuals <1.2-fold), is easily assessed for quality control, also assesses instrument effective linear range, and can be combined with fluorescence calibration to obtain units of Molecules of Equivalent Fluorescein (MEFL) per cell, allowing direct comparison and data fusion with flow cytometry measurements: in our study, fluorescence per cell measurements showed only a 1.07-fold mean difference between plate reader and flow cytometry data

Development of a Generally Applicable Machine Learning Potential with Accurate Long-Range Electrostatic Interactions

Machine learning potentials (MLPs) have become an indispensable tool for large-scale atomistic simulations, due to their accuracy comparable with ab-initio methods at considerably reduced computational cost. The development of MLPs has attracted increasing attention and numerous relevant applications in materials science, physics and chemistry have been reported. Most MLPs up to date are based on the approximation of locality, meaning that only short-range atomic interactions are considered. The total energy of the system can be decomposed into a sum of environment-dependent atomic energies. This approximation works well for the majority of systems and allows the MLPs to describe systems containing thousands of atoms with very high accuracy by just training on configurations of small systems. Moreover, they can incorporate long-range electrostatic interactions by employing fixed charges or more flexible environment-dependent charges. Despite countless encouraging developments of MLPs, they are unable to describe non-local effects arising from long-range charge transfer and multiple charge states. This shortcoming prevents the study of many interesting phenomena such as chemical interactions involving protonation/deprotonation and biological processes. A new generation of MLPs such as charge equilibration via neural network technique (CENT) and Becke population neural network (BpopNN) is now beginning to emerge in an effort to address these long standing challenges. In this thesis, the limitations of conventional MLPs are overcome by introducing a fourth-generation high-dimensional neural network potential (4G-HDNNP), which combines accurate atomic energies with a charge equilibration scheme relying on environment dependent atomic electronegativities. 4G-HDNNP describes the correct global charge distribution of the system, resulting in a markedly improved potential energy surface. The capabilities of the method have been demonstrated for a set of benchmark systems that involves non-local charge transfer, where existing methods fail even at the qualitative level. Finally, an extension of the 4G-HDNNP, namely the electrostatically embedded 4G-HDNNP (ee4G-HDNNP), is proposed to further enhance the description of non-local effects, and the general transferability to different configurations that are not covered in the reference data set. The promising improvements of ee4G-HDNNP compared to the 4G-HDNNP have been shown on a large data set of both neutral and charged sodium chloride clusters with large structural diversity. This novel method is anticipated to become a reliable tool for the study of many complex biological and electrochemical problems, while existing ab-initio methods combined with modern computer technology are still computationally demanding for large-scale atomistic simulations.2023-06-2

A fourth-generation high-dimensional neural network potential with accurate electrostatics including non-local charge transfer

Abstract Machine learning potentials have become an important tool for atomistic simulations in many fields, from chemistry via molecular biology to materials science. Most of the established methods, however, rely on local properties and are thus unable to take global changes in the electronic structure into account, which result from long-range charge transfer or different charge states. In this work we overcome this limitation by introducing a fourth-generation high-dimensional neural network potential that combines a charge equilibration scheme employing environment-dependent atomic electronegativities with accurate atomic energies. The method, which is able to correctly describe global charge distributions in arbitrary systems, yields much improved energies and substantially extends the applicability of modern machine learning potentials. This is demonstrated for a series of systems representing typical scenarios in chemistry and materials science that are incorrectly described by current methods, while the fourth-generation neural network potential is in excellent agreement with electronic structure calculations.Deutsche Forschungsgemeinschaft (German Research Foundation) https://doi.org/10.13039/50110000165

General-Purpose Machine Learning Potentials Capturing Nonlocal Charge Transfer

The development of first-principles-quality machine learning potentials (MLP) has seen tremendous progress, now enabling computer simulations of complex systems for which sufficiently accurate interatomic potentials have not been available. These advances and the increasing use of MLPs for more and more diverse systems gave rise to new questions regarding their applicability and limitations, which has constantly driven new developments. The resulting MLPs can be classified into several generations depending on the types of systems they are able to describe. First-generation MLPs, as introduced 25 years ago, have been applicable to low-dimensional systems such as small molecules. MLPs became a practical tool for complex systems in chemistry and materials science with the introduction of high-dimensional neural network potentials (HDNNP) in 2007, which represented the first MLP of the second generation. Second-generation MLPs are based on the concept of locality and express the total energy as a sum of environment-dependent atomic energies, which allows applications to very large systems containing thousands of atoms with linearly scaling computational costs. Since second-generation MLPs do not consider interactions beyond the local chemical environments, a natural extension has been the inclusion of long-range interactions without truncation, mainly electrostatics, employing environment-dependent charges establishing the third MLP generation. A variety of second- and, to some extent, also third-generation MLPs are currently the standard methods in ML-based atomistic simulations. In spite of countless successful applications, in recent years it has been recognized that the accuracy of MLPs relying on local atomic energies and charges is still insufficient for systems with long-ranged dependencies in the electronic structure. These can, for instance, result from nonlocal charge transfer or ionization and are omnipresent in many important types of systems and chemical processes such as the protonation and deprotonation of organic and biomolecules, redox reactions, and defects and doping in materials. In all of these situations, small local modifications can change the system globally, resulting in different equilibrium structures, charge distributions, and reactivity. These phenomena cannot be captured by second- and third-generation MLPs. Consequently, the inclusion of nonlocal phenomena has been identified as a next key step in the development of a new fourth generation of MLPs. While a first fourth-generation MLP, the charge equilibration neural network technique (CENT), was introduced in 2015, only very recently have a range of new general-purpose methods applicable to a broad range of physical scenarios emerged. In this Account, we show how fourth-generation HDNNPs can be obtained by combining the concepts of CENT and second-generation HDNNPs. These new MLPs allow for a highly accurate description of systems where nonlocal charge transfer is important

Robust training of machine learning interatomic potentials with dimensionality reduction and stratified sampling

Abstract Machine learning interatomic potentials (MLIPs) enable accurate simulations of materials at scales beyond that accessible by ab initio methods and play an increasingly important role in the study and design of materials. However, MLIPs are only as accurate and robust as the data on which they are trained. Here, we present DImensionality-Reduced Encoded Clusters with sTratified (DIRECT) sampling as an approach to select a robust training set of structures from a large and complex configuration space. By applying DIRECT sampling on the Materials Project relaxation trajectories dataset with over one million structures and 89 elements, we develop an improved materials 3-body graph network (M3GNet) universal potential that extrapolates more reliably to unseen structures. We further show that molecular dynamics (MD) simulations with the M3GNet universal potential can be used instead of expensive ab initio MD to rapidly create a large configuration space for target systems. We combined this scheme with DIRECT sampling to develop a reliable moment tensor potential for titanium hydrides without the need for iterative augmentation of training structures. This work paves the way for robust high-throughput development of MLIPs across any compositional complexity