Related papers: A smooth basis for atomistic machine learning
Semi-supervised learning is highly useful in common scenarios where labeled data is scarce but unlabeled data is abundant. The graph (or nonlocal) Laplacian is a fundamental smoothing operator for solving various learning tasks. For…
In this work, we develop new optimization algorithms that use approximate second-order information combined with the gradient regularization technique to achieve fast global convergence rates for both convex and non-convex objectives. The…
In this article, we propose general criteria to construct optimal atomic centered basis sets in quantum chemistry. We focus in particular on two criteria, one based on the ground-state one-body density matrix of the system and the other…
Geometric deep learning has sparked a rising interest in computer graphics to perform shape understanding tasks, such as shape classification and semantic segmentation. When the input is a polygonal surface, one has to suffer from the…
We explore different ways to simplify the evaluation of the smooth overlap of atomic positions (SOAP) many-body atomic descriptor [Bart\'{o}k et al., Phys. Rev. B 87, 184115 (2013)]. Our aim is to improve the computational efficiency of…
The atomization energies of molecules from first-principles density functional approximations improve from the local spin-density approximation (LSDA) to the Perdew-Burke-Ernzerhof (PBE)) generalized gradient approximation (GGA) to the…
Manifold learning and dimensionality reduction techniques are ubiquitous in science and engineering, but can be computationally expensive procedures when applied to large data sets or when similarities are expensive to compute. To date,…
The second eigenvalue of the Laplacian matrix and its associated eigenvector are fundamental features of an undirected graph, and as such they have found widespread use in scientific computing, machine learning, and data analysis. In many…
Achieving high-fidelity control of quantum systems is essential for realization of a practical quantum computer. Composite pulse sequences which suppress different types of errors can be nested to suppress a wide variety of errors but the…
We introduce a statistical physics inspired supervised machine learning algorithm for classification and regression problems. The method is based on the invariances or stability of predicted results when known data is represented as…
We revisit the problem of spectral clustering in multimodal settings, where each data modality is encoded as a graph Laplacian. While classical approaches--including joint diagonalization, spectral co-regularization, and multiview…
Statistical learning methods show great promise in providing an accurate prediction of materials and molecular properties, while minimizing the need for computationally demanding electronic structure calculations. The accuracy and…
Let $M\subset S^{n+1}$ be the hypersurface generated by rotating a hypersurface $M_0$ contained in the interior of the unit ball of $\mathbb{R}^{n-k+1}$. More precisely, $M=\{(\sqrt{1-|m|^2}\, y, m):y\in S^k, m\in M_0\}$. We derive the…
The ability to learn good representations of states is essential for solving large reinforcement learning problems, where exploration, generalization, and transfer are particularly challenging. The Laplacian representation is a promising…
Spatial documentation is exponentially increasing given the availability of Big IoT Data, enabled by the devices miniaturization and data storage capacity. Bayesian spatial statistics is a useful statistical tool to determine the dependence…
The well-known spatial integration schemes in molecular electronic structure theory, immune to cusps and point singularities of some kind at atomic positions, use a set of weighting functions to split the integrand into a sum of…
A core problem in machine learning is to learn expressive latent variables for model prediction on complex data that involves multiple sub-components in a flexible and interpretable fashion. Here, we develop an approach that improves…
From understanding the sand on the beach to the foam on your beer, soft sphere simulations have been crucial to the study of the amorphous world around us. However, many of the materials we interact with on a daily basis aren't comprised of…
In this paper we use a deterministic multi-asperity model to investigate the elastic contact of rough spheres. Synthetic rough surfaces with controllable spectra were used to identify individual asperities, their locations and curvatures.…
Given a conformal action of a discrete group on a Riemann surface, we study the maximization of Laplace and Steklov eigenvalues within a conformal class, considering metrics invariant under the group action. We establish natural conditions…