Related papers: A smooth basis for atomistic machine learning

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…

Atomic-level modeling performed at large scales enables the investigation of mesoscale materials properties with atom-by-atom resolution. The spatial complexity of such cross-scale simulations renders them unsuitable for simple human visual…

In the past few years, following the differentiable programming paradigm, there has been a growing interest in computing the gradient information of physical processes (e.g., physical simulation, image rendering). However, such processes…

To understand the dynamics of optimization in deep neural networks, we develop a tool to study the evolution of the entire Hessian spectrum throughout the optimization process. Using this, we study a number of hypotheses concerning…

We present a detailed study of the use of localized spherical-wave basis sets, first introduced in the context of linear-scaling, in first-principles density-functional calculations. Several parameters that control the completeness of this…

In this paper, the problem of decentralized eigenvalue decomposition of a general symmetric matrix that is important, e.g., in Principal Component Analysis, is studied, and a decentralized online learning algorithm is proposed. Instead of…

Learning representations that can disentangle explanatory attributes underlying the data improves interpretabilty as well as provides control on data generation. Various learning frameworks such as VAEs, GANs and auto-encoders have been…

The quantum phase estimation algorithm stands as the primary method for determining the ground state energy of a molecular electronic Hamiltonian on a quantum computer. In this context, the ability to initialize a classically tractable…

We study the problem of learning local metrics for nearest neighbor classification. Most previous works on local metric learning learn a number of local unrelated metrics. While this "independence" approach delivers an increased flexibility…

Machine learning over-fitting caused by data scarcity greatly limits the application of machine learning for molecules. Due to manufacturing processes difference, big data is not always rendered available through computational chemistry…

We present a scheme to controllably improve the accuracy of tight-binding Hamiltonian matrices derived by projecting the solutions of plane-wave ab initio calculations on atomic orbital basis sets. By systematically increasing the…

Stratified models depend in an arbitrary way on a selected categorical feature that takes $K$ values, and depend linearly on the other $n$ features. Laplacian regularization with respect to a graph on the feature values can greatly improve…

Molecule-optimized basis sets, based on approximate natural orbitals, are developed for accelerating the convergence of quantum calculations with strongly correlated (multi-referenced) electrons. We use a low-cost approximate solution of…

The combination of modern scientific computing with electronic structure theory can lead to an unprecedented amount of data amenable to intelligent data analysis for the identification of meaningful, novel, and predictive structure-property…

Gausslets are one of the few basis constructions for electronic structure that combine locality, orthonormality, variable resolution, and an accurate diagonal approximation for the electron-electron interaction, but the original…

We consider the quasi-static problem governing the localized surface plasmon modes and permittivity eigenvalues $\epsilon$ of smooth, arbitrarily shaped, axisymmetric inclusions. We develop an asymptotic theory for the dense part of the…

The representation of atomic configurations for machine learning models has led to the development of numerous descriptors, often to describe the local environment of atoms. However, many of these representations are incomplete and/or…

This thesis consolidates, improves and extends the smooth entropy framework for non-asymptotic information theory and cryptography. We investigate the conditional min- and max-entropy for quantum states, generalizations of classical R\'enyi…

The friction of a nanosized sphere in commensurate contact with a flat substrate is investigated by performing molecular dynamics simulations. Particular focus is on the distribution of shear stress within the contact region. It is noticed…

Trustworthy machine learning necessitates meticulous regulation of model reliance on non-robust features. We propose a framework to delineate and regulate such features by attributing model predictions to the input. Within our approach,…