Related papers: New Algebraic Formulation of Density Functional Ca…

A further significant extension is presented of the infinitely large class of differential algebras of generalized functions which are the basic structures in the nonlinear algebraic theory listed under 46F30 in the AMS Mathematical Subject…

Learning about density functional approximations (DFAs), or approximations for the exchange-correlation functional, can be intimidating. Density Functional Theory is now one of the primary simulation tools for the practicing chemist or…

Machine learning algorithms use error function minimization to fit a large set of parameters in a preexisting model. However, error minimization eventually leads to a memorization of the training dataset, losing the ability to generalize to…

We consider a generalization of polynomial programs: algebraic programs, which are optimization or feasibility problems with algebraic objectives or constraints. Algebraic functions are defined as zeros of multivariate polynomials. They are…

We present a novel approach to Bayesian inference and general Bayesian computation that is defined through a sequential decision loop. Our method defines a recursive partitioning of the sample space. It neither relies on gradients nor…

While the success of density functional theory (DFT) has led to its use in a wide variety of fields such as physics, chemistry, materials science and biochemistry, it has long been recognised that conventional methods are very inefficient…

Density functional theory (DFT) has been a cornerstone in computational chemistry, physics, and materials science for decades, benefiting from advancements in computational power and theoretical methods. This paper introduces a novel,…

The work is devoted to the construction of a new interval arithmetic which would combine algorithmic efficiency and high quality estimation of the ranges of expressions.

The combination of deep learning and ab initio materials calculations is emerging as a trending frontier of materials science research, with deep-learning density functional theory (DFT) electronic structure being particularly promising. In…

Functional data that are nonnegative and have a constrained integral can be considered as samples of one-dimensional density functions. Such data are ubiquitous. Due to the inherent constraints, densities do not live in a vector space and,…

At the core of any inference procedure in deep neural networks are dot product operations, which are the component that require the highest computational resources. A common approach to reduce the cost of inference is to reduce its memory…

This article is a rough, quirky overview of both the history and present state of the art of density functional theory. The field is so huge that no attempt to be comprehensive is made. We focus on the underlying exact theory, the origin of…

We propose a unique scheme to construct fully optimized atomic basis sets for density-functional calculations. The shapes of the radial functions are optimized by minimizing the {\it spillage} of the wave functions between the atomic…

Fast, gradient-based structural optimization has long been limited to a highly restricted subset of problems -- namely, density-based compliance minimization -- for which gradients can be analytically derived. For other objective functions,…

Recent work shows that density functional theory calculations accurately describe materials exhibiting turbostratic disorder between layers of incommensurate constituents. These calculations approximate one of the constituents as a finite…

In classical density (or density-functional) estimation, it is standard to assume that the underlying distribution has a density with respect to the Lebesgue measure. However, when the data distribution is a mixture of continuous and…

At present there are two vastly different ab initio approaches to the description of the the many-body dynamics: the Density Functional Theory (DFT) and the functional integral (path integral) approaches. On one hand, if implemented…

We describe an efficient quantum embedding framework for realistic ab initio density matrix embedding (DMET) calculations in solids. We discuss in detail the choice of orbitals and mapping to a lattice, treatment of the virtual space and…

A mathematical framework for reduced density matrix functional theory (RDMFT) is proposed. The work is inspired by and generalizes the work by E.H.~Lieb [E.H. Lieb, Int. J. Quant. Chem. 24(1983), pp.243--277] on density-functional theory…

This work connects two mathematical fields - computational complexity and interval linear algebra. It introduces the basic topics of interval linear algebra - regularity and singularity, full column rank, solving a linear system, deciding…