Related papers: On the Atomic Cluster Expansion: interatomic poten…
With the development of deep learning, standard classification problems have achieved good results. However, conventional classification problems are often too idealistic. Most data in the natural world usually have imbalanced distribution…
Under quite general conditions critical phenomena can be described with high order linked cluster expansions. The coefficients of the series admit a graphical expansion that is generated with the aid of computers. Our generalization of…
Statistical learning algorithms are finding more and more applications in science and technology. Atomic-scale modeling is no exception, with machine learning becoming commonplace as a tool to predict energy, forces and properties of…
Crystalline alloys and related mixed systems make up a large family of materials with high tunability which have been proposed as the solution to a large number of energy related materials design problems. Due to the presence of chemical…
Long-standing challenges in cluster expansion (CE) construction include choosing how to truncate the expansion and which crystal structures to use for training. Compressive sensing (CS), which is emerging as a powerful tool for model…
A cluster expansion is proposed, that applies to both continuous and discrete systems. The assumption for its convergence involves an extension of the neat Kotecky-Preiss criterion. Expressions and estimates for correlation functions are…
Excited-state electronic structure in strongly correlated systems remains challenging due to the exponential scaling of the many-body Hilbert space and the difficulty of constructing systematically controlled active spaces. Building on the…
Density functional theory (DFT)-based simulations of materials have first-principles accuracy, but are very computationally expensive. For simulating various properties of multi-component alloys, the cluster expansion (CE) technique has…
Atomistic simulations often rely on interatomic potentials to access greater time- and length- scales than those accessible to first principles methods such as density functional theory (DFT). However, since a parameterised potential…
A ubiquitous approach to obtain transferable machine learning-based models of potential energy surfaces for atomistic systems is to decompose the total energy into a sum of local atom-centred contributions. However, in many systems…
The arising of central extensions is discussed in two contexts. At first classical counterparts of quantum anomalies (deserving being named as "classical anomalies") are associated with a peculiar subclass of the non-equivariant maps.…
Modeling distributions of covariates, or density estimation, is a core challenge in unsupervised learning. However, the majority of work only considers the joint distribution, which has limited utility in practical situations. A more…
The force field describing the calculated interaction between atoms or molecules is the key to the accuracy of many molecular dynamics (MD) simulation results. Compared with traditional or semi-empirical force fields, machine learning force…
Expanding products of invariant functions of a group element as a series in the basis of characters of the irreducible representations of a group is widely used in many areas of physics and related fields. In this contribution a formula to…
Consensus clustering fuses diverse basic partitions (i.e., clustering results obtained from conventional clustering methods) into an integrated one, which has attracted increasing attention in both academic and industrial areas due to its…
This paper introduces the Chemical Environment Modeling Theory (CEMT), a novel, generalized framework designed to overcome the limitations inherent in traditional atom-centered Machine Learning Force Field (MLFF) models, widely used in…
A non-empirical minimal atomic multipole expansion (MAME) defines atomic charges or higher multipoles that reproduce electrostatic potential outside molecules. MAME eliminates problems associated with redundancy and with statistical…
Recently, machine learning potentials have been advanced as candidates to combine the high-accuracy of quantum mechanical simulations with the speed of classical interatomic potentials. A crucial component of a machine learning potential is…
Interacting particle systems in a finite-volume in equilibrium are often described by a grand-canonical ensemble induced by the corresponding Hamiltonian, i.e. a finite-volume Gibbs measure. However, in practice, directly measuring this…
Since the discovery of molecular resonances in $^{12}$C+$^{12}$C in the early sixties a great deal of research work has been undertaken to study alpha-clustering. Our knowledge on physics of nuclear molecules has increased considerably and…