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Adaptive Gradient Descent with Energy (AEGD) is a variant of gradient descent (GD) designed to mitigate step-size sensitivity through an energy-based formulation. AEGD is notable for its unconditional energy stability, which guarantees…
For a class of interacting particle systems in continuous space, we show that finite-volume approximations of the bulk diffusion matrix converge at an algebraic rate. The models we consider are reversible with respect to the Poisson…
Many matching, tracking, sorting, and ranking problems require probabilistic reasoning about possible permutations, a set that grows factorially with dimension. Combinatorial optimization algorithms may enable efficient point estimation,…
P representation techniques, which have been very successful in quantum optics and in other fields, are also useful for general bosonic quantum dynamical many-body calculations such as Bose-Einstein condensation. We introduce a…
The proximal gradient method is a generic technique introduced to tackle the non-smoothness in optimization problems, wherein the objective function is expressed as the sum of a differentiable convex part and a non-differentiable…
We investigate the growth kinetics on vicinal GaAs(001) surfaces by making detailed comparisons between reflection high--energy electron--diffraction specular intensity measured near in--phase diffraction conditions and the surface step…
Efficient hybrid DFT simulations of solid state materials would be extremely beneficial for computational chemistry and materials science, but is presently bottlenecked by difficulties in computing Hartree-Fock (HF) exchange with plane wave…
A generalized master equation (GME) governing quantum evolution of modular exciton density (MED) is derived for large scale light harvesting systems composed of weakly interacting modules of multiple chromophores. The GME-MED offers a…
The reconstruction of smooth density fields from scattered data points is a procedure that has multiple applications in a variety of disciplines, including Lagrangian (particle-based) models of solute transport in fluids. In random walk…
Unlike the local density approximation (LDA) and the generalized gradient approximation (GGA), calculations with meta-generalized gradient approximations (meta-GGA) are usually done according to the generalized Kohn-Sham (gKS) formalism.…
First principles molecular dynamics simulation protocol is established using revised functional of Perdew-Burke-Ernzerhof (revPBE) in conjunction with Grimme's third generation of dispersion (D3) correction to describe properties of water…
Boltzmann transport calculations based on band structures generated with density functional theory (DFT) are often used in the discovery and analysis of thermoelectric materials. In standard implementations, such calculations require dense…
Topological insulators (TIs) are materials that are insulating in the bulk but have zero band gap surface states with linear dispersion and are protected by time reversal symmetry. These unique characteristics could pave the way for many…
Multiple scattering of an electromagnetic wave as it passes through an object is a fundamental problem that limits the performance of current imaging systems. In this paper, we describe a new technique-called Series Expansion with…
We consider adaptive finite element methods (AFEMs) with inexact algebraic solvers for second-order symmetric linear elliptic diffusion problems. Optimal complexity of AFEM, i.e., optimal convergence rates with respect to the overall…
Motivated by approximation Bayesian computation using mean-field variational approximation and the computation of equilibrium in multi-species systems with cross-interaction, this paper investigates the composite geodesically convex…
We performed density functional calculations to estimate the formation energies of intermetallic alloys. We used two semilocal approximations, the generalized gradient approximation (GGA) by Perdew-Burke-Ernzerhof (PBE) and the strongly…
Various types of parameter restart schemes have been proposed for accelerated gradient algorithms to facilitate their practical convergence in convex optimization. However, the convergence properties of accelerated gradient algorithms under…
In this paper, we provide a new PDE proof for the celebrated Borell--Brascamp--Lieb inequality. Our approach reveals a deep connection between the Borell--Brascamp--Lieb inequality and properties of diffusion equations of porous medium type…
A generalised phase-space kinetic Boltzmann equation for highly non-equilibrium charged particle transport via localised and delocalised states is used to develop continuity, momentum and energy balance equations, accounting explicitly for…