Related papers: Numerical linked cluster expansions for inhomogene…
The Atomic Cluster Expansion (ACE) (Drautz, Phys. Rev. B 99, 2019) has been widely applied in high energy physics, quantum mechanics and atomistic modeling to construct many-body interaction models respecting physical symmetries.…
This paper presents Constrained Centroid Clustering (CCC), a method that extends classical centroid-based clustering by enforcing a constraint on the maximum distance between the cluster center and the farthest point in the cluster. Using a…
The development of physical simulators, called Ising machines, that sample from low energy states of the Ising Hamiltonian has the potential to drastically transform our ability to understand and control complex systems. However, most of…
AI-enabled precision medicine promises a transformational improvement in healthcare outcomes by enabling data-driven personalized diagnosis, prognosis, and treatment. However, the well-known "curse of dimensionality" and the clustered…
Cluster expansions are commonly employed as surrogate models to link the electronic structure of an alloy to its finite-temperature properties. Using cluster expansions to model materials with several alloying elements is challenging due to…
The extended Hubbard Hamiltonian is a widely accepted model for uncovering the effects of strong correlations on the phase diagram of low-dimensional systems, and a variety of theoretical techniques have been applied to it. In this paper…
We propose to improve the convergence properties of the single-reference coupled cluster (CC) method through an augmented Lagrangian formalism. The conventional CC method changes a linear high-dimensional eigenvalue problem with exponential…
A review of the coupled cluster method (CCM) applied to lattice quantum spin systems is presented here. The CCM formalism is explained and an application to the spin-half {\it XXZ} model on the square lattice is presented. Low orders of…
We derive an adaptive hierarchical method of estimating high dimensional probability density functions. We call this method of density estimation the "adaptive cluster expansion" or ACE for short. We present an application of this approach,…
Modern battery materials can contain many elements with substantial site disorder, and their configurational state has been shown to be critical for their performance. The intercalation voltage profile is a critical parameter to evaluate…
The incorporation of appropriate inductive bias plays a critical role in learning dynamics from data. A growing body of work has been exploring ways to enforce energy conservation in the learned dynamics by encoding Lagrangian or…
Statistical modelling strategy is the key for success in data analysis. The trade-off between flexibility and parsimony plays a vital role in statistical modelling. In clustered data analysis, in order to account for the heterogeneity…
Agglomerative hierarchical clustering can be implemented with several strategies that differ in the way elements of a collection are grouped together to build a hierarchy of clusters. Here we introduce versatile linkage, a new infinite…
We extend to quenched disordered systems the variational scheme for real space renormalization group calculations that we recently introduced for homogeneous spin Hamiltonians. When disorder is present our approach gives access to the flow…
This letter studies symmetric and symplectic exponential integrators when applied to numerically computing nonlinear Hamiltonian systems. We first establish the symmetry and symplecticity conditions of exponential integrators and then show…
In the last several years, tightly coupled PC clusters have become widely applied, cost effective resources for lattice gauge computations. This paper discusses the practice of building such clusters, in particular balanced design…
Linked cluster expansions are generalized from an infinite to a finite volume. They are performed to 20th order in the expansion parameter to approach the critical region from the symmetric phase. A new criterion is proposed to distinguish…
We propose a novel numerical approach for nonlocal diffusion equations [8] with integrable kernels, based on the relationship between the backward Kolmogorov equation and backward stochastic differential equations (BSDEs) driven by L\`{e}vy…
Clustering aims to group unlabelled samples based on their similarities. It has become a significant tool for the analysis of high-dimensional data. However, most of the clustering methods merely generate pseudo labels and thus are unable…
Clustering explores meaningful patterns in the non-labeled data sets. Cluster Ensemble Selection (CES) is a new approach, which can combine individual clustering results for increasing the performance of the final results. Although CES can…