Representations of molecules and materials for interpolation of quantum-mechanical simulations via machine learning

Langer, M.; Goeßmann, Alex; Rupp, Matthias

doi:10.1038/s41524-022-00721-x

Cited by 98 publications

(111 citation statements)

References 140 publications

(186 reference statements)

Supporting

Mentioning

109

Contrasting

Order By: Relevance

“…The development of descriptors for highdimensional systems considering all symmetries and in-variances exactly, which in the initial years has been a formidable challenge, can now be considered as solved, and there are two alternative approaches based on predefined or learnable descriptors. Both are equally suited for high-quality potentials, but since the first messagepassing networks have been introduced only a few years ago, most applications published to date rely on predefined descriptors like ACSFs 67 , SOAP 110 and many others 63 . Still, a yet unsolved problem is the combinatorial growth in the number of predefined descriptors with increasing number of elements in the system.…”

Section: Discussion and Outlookmentioning

confidence: 99%

See 1 more Smart Citation

Neural Network Potentials: A Concise Overview of Methods

Kocer¹,

Ko²,

Behler³

2021

Preprint

View full text Add to dashboard Cite

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 longrange 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.

show abstract

Section: Discussion and Outlookmentioning

confidence: 99%

“…This problem has now been solved, and from today's perspective it is hard to imagine the difficult situation of early MLP developers, because a huge variety of different descriptors for high-dimensional systems is now readily available 63,64 . The resulting very powerful second generation of MLPs based on Eq.…”

Section: Bim-nn [78]mentioning

confidence: 99%

Neural Network Potentials: A Concise Overview of Methods

Kocer¹,

Ko²,

Behler³

2021

Preprint

View full text Add to dashboard Cite

show abstract

“…In recognition of this challenge, the development and application of machine learning techniques to produce accurate and computationally efficient surrogate models of ab initio calculations has become a very active area of research [1][2][3][4][5][6][7][8][9][10][11][12]. Broadly speaking, the success of these techniques depends on the identification of a sufficiently descriptive feature space which captures the variance of the data one wishes to model.…”

Section: Introductionmentioning

confidence: 99%

Entangling Solid Solutions: Machine Learning of Tensor Networks for Materials Property Prediction

Sommer¹,

Dunham²

2022

Preprint

View full text Add to dashboard Cite

Progress in the application of machine learning techniques to the prediction of solid-state and molecular materials properties has been greatly facilitated by the development state-of-the-art feature representations and novel deep learning architectures. A large class of atomic structure representations based on expansions of smoothed atomic densities have been shown to correspond to specific choices of basis sets in an abstract many-body Hilbert space. Concurrently, tensor network structures, conventionally the purview of quantum many-body physics and quantum information, have been successfully applied in supervised and unsupervised learning tasks in computer vision and natural language processing. In this work, we argue that architectures based on tensor networks are well-suited to machine learning on Hilbert-space representations of atomic structures. This is demonstrated on supervised learning tasks involving widely available datasets of density functional theory calculations of metal and semiconductor alloys. In particular, we show that certain standard tensor network topologies exhibit strong generalizability even on small training datasets while being parametrically efficient. We further relate this generalizability to the presence of complex entanglement in the trained tensor networks. We also discuss connections to learning with generalized structural kernels and related strategies for compressing large input feature spaces.

show abstract

“…Machine-learning potentials (MLPs) [1][2][3][4] are flexible functions fitted to reference energy and force data from, e.g., electronic structure methods. Their computational advantage does not arise from simplified physical models but from avoiding redundant calculations through interpolation.…”

Section: Introductionmentioning

confidence: 99%

“…While traditional empirical potentials have seen success in applications across decades of research, their rigid functional forms limit their accuracy. More recently, MLPs with flexible functional forms and built-in physics domain knowledge in the form of engineered features or deep neural network architectures have emerged as an alternative [2,12,13]. State-of-the-art MLPs can simulate the dynamics of large ("high-dimensional") atomistic systems with an accuracy close to the underlying electronic-structure reference method but orders of magnitude faster.…”

Section: Introductionmentioning

confidence: 99%

Ultra-fast interpretable machine-learning potentials

Xie¹,

Rupp²,

Hennig³

2021

Preprint

Self Cite

View full text Add to dashboard Cite

All-atom dynamics simulations are an indispensable quantitative tool in physics, chemistry, and materials science, but large systems and long simulation times remain challenging due to the trade-off between computational efficiency and predictive accuracy. To address this challenge, we combine effective two-and three-body potentials in a cubic B-spline basis with regularized linear regression to obtain machine-learning potentials that are physically interpretable, sufficiently accurate for applications, as fast as the fastest traditional empirical potentials, and two to four orders of magnitude faster than state-of-the-art machine-learning potentials. For data from empirical potentials, we demonstrate exact retrieval of the potential. For data from density functional theory, the predicted energies, forces, and derived properties, including phonon spectra, elastic constants, and melting points, closely match those of the reference method. The introduced potentials might contribute towards accurate all-atom dynamics simulations of large atomistic systems over long time scales.

show abstract

Representations of molecules and materials for interpolation of quantum-mechanical simulations via machine learning

Cited by 98 publications

References 140 publications

Neural Network Potentials: A Concise Overview of Methods

Neural Network Potentials: A Concise Overview of Methods

Entangling Solid Solutions: Machine Learning of Tensor Networks for Materials Property Prediction

Ultra-fast interpretable machine-learning potentials

Contact Info

Product

Resources

About