Related papers: Completeness of Atomic Structure Representations

Atom probe tomography (APT) is a burgeoning characterization technique that provides compositional mapping of materials in three-dimensions at near-atomic scale. Since its significant expansion in the past 30 years, we estimate that one…

Atomic electron tomography (AET) enables the determination of 3D atomic structures by acquiring a sequence of 2D tomographic projection measurements of a particle and then computationally solving for its underlying 3D representation.…

A relation algebra is called measurable when its identity is the sum of measurable atoms, and an atom is called measurable if its square is the sum of functional elements. In this paper we show that atomic measurable relation algebras have…

This paper proposes a machine learning (ML) method to predict stable molecular geometries from their chemical composition. The method is useful for generating molecular conformations which may serve as initial geometries for saving time…

The Atomic Cluster Expansion (Drautz, Phys. Rev. B 99, 2019) provides a framework to systematically derive polynomial basis functions for approximating isometry and permutation invariant functions, particularly with an eye to modelling…

Coordination geometries describe how the neighbours of a central particle are arranged around it. Such geometries can be thought to lie in an abstract topological space; a model of this space could provide a mathematical basis for…

Three-dimensional reconstruction of atomic structure, known as atomic electron tomography (AET), has found increasing applications in materials science. The AET has been limited to very small nanoparticles due to the challenges of obtaining…

When modeling physical properties of molecules with machine learning, it is desirable to incorporate $SO(3)$-covariance. While such models based on low body order features are not complete, we formulate and prove general completeness…

In these lectures, I discuss the role of symmetries in particle physics. I begin by discussing global symmetries and show that they can be realized differently in nature, depending on whether or not the vacuum state is left invariant by the…

The latest research of the proportionality of atomic weights of chemical elements made it possible to obtain 3 x 3 matrices for the calculation of information coefficients of proportionality Ip that can be used for 3D modeling of the…

In recent years, significant progress has been made in the development of machine learning potentials (MLPs) for atomistic simulations with applications in many fields from chemistry to materials science. While most current MLPs are based…

Atomic packing is an important metric for characterizing protein structures, as it significantly influences various features including the stability, the rate of evolution and the functional roles of proteins. Packing in protein structures…

Recently, machine learning potentials have been advanced as candidates to combine the high-accuracy of quantum mechanical simulations with the speed of classical interatomic potentials. A crucial component of a machine learning potential is…

Obtaining microscopic structure-property relationships for grain boundaries are challenging because of the complex atomic structures that underlie their behavior. This has led to recent efforts to obtain these relationships with machine…

As they carry great potential for modeling complex interactions, graph neural network (GNN)-based methods have been widely used to predict quantum mechanical properties of molecules. Most of the existing methods treat molecules as molecular…

Chemical space which encompasses all stable compounds is unfathomably large and its dimension scales linearly with the number of atoms considered. The success of machine learning methods suggests that many physical quantities exhibit…

Global machine learning force fields (MLFFs), that have the capacity to capture collective many-atom interactions in molecular systems, currently only scale up to a few dozen atoms due a considerable growth of the model complexity with…

One of the great challenges of modern science is to faithfully model, and understand, matter at a wide range of scales. Starting with atoms, the vastness of the space of possible configurations poses a formidable challenge to any simulation…

Density Functional Theory (DFT) has been a cornerstone in computational science, providing powerful insights into structure-property relationships for molecules and materials through first-principles quantum-mechanical (QM) calculations.…

Shape completion, the problem of estimating the complete geometry of objects from partial observations, lies at the core of many vision and robotics applications. In this work, we propose Point Completion Network (PCN), a novel…