Related papers: A smooth basis for atomistic machine learning
We show that the driving force behind the regularizing effect of Laplacian smoothing on surface elements is the popular mean ratio quality measure. We use these insights to provide natural generalizations to polygons and polyhedra. The…
We consider the following eigenvalue optimization in the composite membrane problem with fractional Laplacian: given a bounded domain $\Omega\subset \mathbb{R}^n$, $\alpha>0$ and $0<A<|\Omega|$, find a subset $D\subset \Omega$ of area $A$…
Machine learning interatomic potentials are revolutionizing large-scale, accurate atomistic modelling in material science and chemistry. Many potentials use atomic cluster expansion or equivariant message passing frameworks. Such frameworks…
Atomic basis sets are widely employed within quantum mechanics based simulations of matter. We introduce a machine learning model that adapts the basis set to the local chemical environment of each atom, prior to the start of self…
The eigenfunctions of the Laplacian are a natural basis of functions for many tasks in computational mathematics. On the circle and sphere, the eigenfunctions are given by complex periodic exponentials and spherical harmonics, respectively,…
In this article, we consider the problem of approximating a finite set of data (usually huge in applications) by invariant subspaces generated through a small set of smooth functions. The invariance is either by translations under a…
Leveraging ab initio data at scale has enabled the development of machine learning models capable of extremely accurate and fast molecular property prediction. A central paradigm of many previous works focuses on generating predictions for…
Hard spheres are ubiquitous in condensed matter: they have been used as models for liquids, crystals, colloidal systems, granular systems, and powders. Packings of hard spheres are of even wider interest, as they are related to important…
In this paper, we consider a certain convolutional Laplacian for metric measure spaces and investigate its potential for the statistical analysis of complex objects. The spectrum of that Laplacian serves as a signature of the space under…
In this paper we consider two sources of enhancement for the meshfree Lagrangian particle method smoothed particle hydrodynamics (SPH) by improving the accuracy of the particle approximation. Namely, we will consider shape functions…
Particle-based shape modeling (PSM) is a popular approach to automatically quantify shape variability in populations of anatomies. The PSM family of methods employs optimization to automatically populate a dense set of corresponding…
We study the estimation of quadratic Sobolev-type integral functionals of an unknown density on the unit sphere. The functional is defined through fractional powers of the Laplace--Beltrami operator and provides a global measure of…
Electronic nearsightedness is one of the fundamental principles governing the behavior of condensed matter and supporting its description in terms of local entities such as chemical bonds. Locality also underlies the tremendous success of…
We reexamine the recently introduced basis-set correction theory based on density-functional theory consisting in correcting the basis-set incompleteness error of wave-function methods using a density functional. We use a one-dimensional…
The projection of the eigenfunctions obtained in standard plane-wave first-principle calculations is used for analyzing atomic-orbital basis sets. The "spilling" defining the error in such a projection allows the evaluation of the quality…
In this paper, we investigate the buckling problem of the drifting Laplacian of arbitrary order on a bounded connected domain in complete smooth metric measure spaces (SMMSs) supporting a special function, and successfully get a general…
In this paper, we study the problem of optimizing a two-layer artificial neural network that best fits a training dataset. We look at this problem in the setting where the number of parameters is greater than the number of sampled points.…
We propose a new smoothing method for obtaining surface densities from discrete particle positions from numerical simulations. This is an essential step for many applications in gravitational lensing. This method is based on the ``scatter''…
We prove estimates for eigenfunctions on a manifold equipped with a smooth metric. We use these estimates in order estimate the size of their nodal sets.
The Laplace eigenvalue problem on circular sectors has eigenfunctions with corner singularities. Standard methods may produce suboptimal approximation results. To address this issue, a novel numerical algorithm that enhances standard…