Related papers: A smooth basis for atomistic machine learning

Smoothing a signal based on local neighborhoods is a core operation in machine learning and geometry processing. On well-structured domains such as vector spaces and manifolds, the Laplace operator derived from differential geometry offers…

Approximation/interpolation from spaces of positive definite or conditionally positive definite kernels is an increasingly popular tool for the analysis and synthesis of scattered data, and is central to many meshless methods. For a set of…

We consider Bayesian inverse problems arising in data assimilation for dynamical systems governed by partial and stochastic partial differential equations. The space-time dependent field is inferred jointly with static parameters of the…

We present a machine learning-based approach for characterising the environment that affects the dynamics of an open quantum system. We focus on the case of an exactly solvable spin-boson model, where the system-environment interaction,…

We use molecular simulations to study the nonadhesive and adhesive atomic-scale contact of rough spheres with radii ranging from nanometers to micrometers over more than ten orders of magnitude in applied normal load. At the lowest loads,…

We introduce a novel framework that directly learns a spectral basis for shape and manifold analysis from unstructured data, eliminating the need for traditional operator selection, discretization, and eigensolvers. Grounded in…

In this paper we study the statistical properties of Laplacian smoothing, a graph-based approach to nonparametric regression. Under standard regularity conditions, we establish upper bounds on the error of the Laplacian smoothing estimator…

While many geological and geophysical processes such as the melting of icecaps, the magnetic expression of bodies emplaced in the Earth's crust, or the surface displacement remaining after large earthquakes are spatially localized, many of…

Physically-motivated and mathematically robust atom-centred representations of molecular structures are key to the success of modern atomistic machine learning (ML) methods. They lie at the foundation of a wide range of methods to predict…

Despite the fundamental progress in autonomous molecular and materials discovery, data scarcity throughout chemical compound space still severely hampers the use of modern ready-made machine learning models as they rely heavily on the…

Machine-learning of atomic-scale properties amounts to extracting correlations between structure, composition and the quantity that one wants to predict. Representing the input structure in a way that best reflects such correlations makes…

Smooth sensitivity is one of the most commonly used techniques for designing practical differentially private mechanisms. In this approach, one computes the smooth sensitivity of a given query $q$ on the given input $D$ and releases $q(D)$…

We consider the problem of learning soft assignments of $N$ items to $K$ categories given two sources of information: an item-category similarity matrix, which encourages items to be assigned to categories they are similar to (and to not be…

Many remarkably robust, rapid and spontaneous self-assembly phenomena in nature can be modeled geometrically starting from a collection of rigid bunches of spheres. This paper highlights the role of symmetry in sphere-based assembly…

The discrete Laplacian on Euclidean triangulated surfaces is a well-established notion. We introduce discrete Laplacians on spherical and hyperbolic triangulated surfaces. On the one hand, our definitions are close to the Euclidean one in…

The approximation properties of the finite element method can often be substantially improved by choosing smooth high-order basis functions. It is extremely difficult to devise such basis functions for partitions consisting of arbitrarily…

We investigate in this paper the existence of a metric which maximizes the first eigenvalue of the Laplacian on Riemannian surfaces. We first prove that, in a given conformal class, there always exists such a maximizing metric which is…

Manifold learning is a central task in modern statistics and data science. Many datasets (cells, documents, images, molecules) can be represented as point clouds embedded in a high dimensional ambient space, however the degrees of freedom…

In geometry processing, smoothness energies are commonly used to model scattered data interpolation, dense data denoising, and regularization during shape optimization. The squared Laplacian energy is a popular choice of energy and has a…

We study the problem of the basis of an open quantum system, under a quantum chaotic environment, which is preferred in view of its stationary reduced density matrix (RDM), that is, the basis in which the stationary RDM is diagonal. It is…