Related papers: A smooth basis for atomistic machine learning

Amorphous silicon (a-Si) is a widely studied non-crystalline material, and yet the subtle details of its atomistic structure are still unclear. Here, we show that accurate structural models of a-Si can be obtained by harnessing the power of…

We explore the impact of optimizations of the single-particle basis on the convergence behavior and robustness of ab initio no-core shell model calculations. Our focus is on novel basis sets defined by the natural orbitals of a correlated…

In the last several years, the intimate connection between convex optimization and learning problems, in both statistical and sequential frameworks, has shifted the focus of algorithmic machine learning to examine this interplay. In…

For compact domains with smooth boundaries, we present an approximation scheme for surface spline approximation that delivers precise $L_p$ approximation orders on well known smoothness spaces. This scheme overcomes the boundary effects…

While spherical data arises in many contexts, including in directional statistics, the current tools for density estimation and population comparison on spheres are quite limited. Popular approaches for comparing populations (on Euclidean…

Neural simulation-based inference is a powerful class of machine-learning-based methods for statistical inference that naturally handles high-dimensional parameter estimation without the need to bin data into low-dimensional summary…

Spherically-symmetric atom-centered descriptors of atomic environments have been widely used for constructing potential or free energy surfaces of atomistic and colloidal systems and to characterize local structures using machine learning…

Function approximation based on data drawn randomly from an unknown distribution is an important problem in machine learning. The manifold hypothesis assumes that the data is sampled from an unknown submanifold of a high dimensional…

Given an optimization problem, the Hessian matrix and its eigenspectrum can be used in many ways, ranging from designing more efficient second-order algorithms to performing model analysis and regression diagnostics. When nonlinear models…

Machine learning (ML) models for molecules and materials commonly rely on a decomposition of the global target quantity into local, atom-centered contributions. This approach is convenient from a computational perspective, enabling…

Symmetries are known to dictate important physical properties and can be used as a design principle in particular in wave physics, including wave structures and the resulting propagation dynamics. Local symmetries, in the sense of a…

The growing prevalence of nonsmooth optimization problems in machine learning has spurred significant interest in generalized smoothness assumptions. Among these, the (L0, L1)-smoothness assumption has emerged as one of the most prominent.…

The density of states for an extended MIT bag model is studied numerically by using a parameterized smooth representation which provides the best fit to the numerical data. It is found that the mass dependence of the surface term in the…

The Laplace operator encodes the behavior of physical systems at vastly different scales, describing heat flow, fluids, as well as electric, gravitational, and quantum fields. A key input for the Laplace equation is the curvature of space.…

We present a method to discretize the Kohn-Sham Hamiltonian matrix in the pseudopotential framework by a small set of basis functions automatically contracted from a uniform basis set such as planewaves. Each basis function is localized…

Normalization Layers (NLs) are widely used in modern deep-learning architectures. Despite their apparent simplicity, their effect on optimization is not yet fully understood. This paper introduces a spherical framework to study the…

In this work we explore the fidelity of numerical approximations to the analytic spectra of hyperbolic partial differential equation systems with variable coefficients. We are particularly interested in the ability of discrete methods to…

Metasurfaces have shown promising potentials in shaping optical wavefronts while remaining compact compared to bulky geometric optics devices. Design of meta-atoms, the fundamental building blocks of metasurfaces, relies on trial-and-error…

Probabilistic smoothing is a standard tool for global optimization, but existing methods rely on Gaussian kernels and specific transforms, often resulting in strong hyperparameter sensitivity and limited robustness. We propose a general…

We unify $\textit{kernel density estimation}$ and $\textit{empirical Bayes}$ and address a set of problems in unsupervised learning with a geometric interpretation of those methods, rooted in the $\textit{concentration of measure}$…