Related papers: Density-gradient-corrected embedded atom method
This thesis synthesizes probability and entropic inference with Quantum Mechanics (QM) and quantum measurement [1-6]. It is shown that the standard and quantum relative entropies are tools designed for the purpose of updating probability…
Adaptive gradient methods, which adopt historical gradient information to automatically adjust the learning rate, despite the nice property of fast convergence, have been observed to generalize worse than stochastic gradient descent (SGD)…
A major effort in modern high-dimensional statistics has been devoted to the analysis of linear predictors trained on nonlinear feature embeddings via empirical risk minimization (ERM). Gaussian equivalence theory (GET) has emerged as a…
Training data attribution (TDA) methods ask which training documents are responsible for a model behavior. However, models often learn broad concepts shared across many examples. Moreover, existing TDA methods are supervised -- they require…
We test the Coulomb exchange and correlation energy density functionals of electron systems for atomic nuclei in the local density approximation (LDA) and the generalized gradient approximation (GGA). For the exchange Coulomb energies, it…
Density estimation is a central task in statistics and machine learning. This problem aims to determine the underlying probability density function that best aligns with an observed data set. Some of its applications include statistical…
We introduce Effective Atom Theory (EAT), a framework that transforms combinatorial materials design into a smooth, gradient-driven optimization within density functional theory (DFT). Atoms are represented as probabilistic mixtures of…
Distributed stochastic optimization algorithms can simultaneously process large-scale datasets, significantly accelerating model training. However, their effectiveness is often hindered by the sparsity of distributed networks and data…
We develop a method in which the electronic densities of small fragments determined by Kohn-Sham density functional theory (DFT) are embedded using stochastic DFT to form the exact density of the full system. The new method preserves the…
Quantum embedding theories are powerful tools for approximately solving large-scale strongly correlated quantum many-body problems. The main idea of quantum embedding is to glue together a highly accurate quantum theory at the local scale…
We present a correction method for the pair density (PD) to get close to the ground state one. The PD is corrected to be a variationally-best PD within the search region that is extended by adding the uniformly-scaled PDs to its elements.…
One of the primary challenges in quantum chemistry is the accurate modeling of strong electron correlation. While multireference methods effectively capture such correlation, their steep scaling with system size prohibits their application…
Developing reliable interatomic potential models with quantified predictive accuracy is crucial for atomistic simulations. Commonly used potentials, such as those constructed through the embedded atom method (EAM), are derived from…
The scaling of neutral atoms to large $Z$, combining periodicity with a gradual trend to homogeneity, is a fundamental probe of density functional theory, one that has driven recent advances in understanding both the kinetic and…
We consider the cumulant expansion of the PAM employing the hybridization as perturbation (Phys. Rev. B 50, 17933 (1994)), and we obtain formally exact one-electron Green's functions (GF). These GF contain effective cumulants that are as…
Quantum embedding is an appealing route to fragment a large interacting quantum system into several smaller auxiliary `cluster' problems to exploit the locality of the correlated physics. In this work we critically review approaches to…
A simple exact-exchange density-functional method for a quasi-two-dimensional electron gas with variable density is presented. An analytical expression for the exact-exchange potential with only one occupied subband is provided, without…
We present a study of the equilibrium properties of $sp$-bonded solids within the pseudopotential approach, employing recently proposed generalized gradient approximation (GGA) exchange correlation functionals. We analyze the effects of the…
Quantum embedding methods enable the study of large, strongly correlated quantum systems by (usually self-consistent) decomposition into computationally manageable subproblems, in the spirit of divide-and-conquer methods. Among these,…
Quantum annealing provides a promising route for the development of quantum optimization devices, but the usefulness of such devices will be limited in part by the range of implementable problems as dictated by hardware constraints. To…