Related papers: Bayesian Error Estimation in Density Functional Th…

Phase diagrams serve as a highly informative tool for materials design, encapsulating information about the phases that a material can manifest under specific conditions. In this work, we develop a method in which Bayesian inference is…

Estimating the ratio of two probability densities from a finite number of observations is a central machine learning problem. A common approach is to construct estimators using binary classifiers that distinguish observations from the two…

Accurate prediction of molecular vibrational frequencies is important to identify spectroscopic signatures and reaction thermodynamics. In this work, we develop a method to quantify uncertainty associated with density functional theory…

The difference Delta F between free energies has applications in biology, chemistry, and pharmacology. The value of Delta F can be estimated from experiments or simulations, via fluctuation theorems developed in statistical mechanics.…

Density Functional Theory (DFT) is one of the most widely used methods for "ab initio" calculations of the structure of atoms, molecules, crystals, surfaces, and their interactions. Unfortunately, the customary introduction to DFT is often…

Systematic inaccuracy is inherent in any computational estimate of a non-linear average, due to the availability of only a finite number of data values, N. Free energy differences (DF) between two states or systems are critically important…

The concept of chemical bonding is a crucial aspect of chemistry that aids in understanding the complexity and reactivity of molecules and materials. However, the interpretation of chemical bonds can be hindered by the choice of the…

Nuclear density functional theory (DFT) is the only microscopic, global approach to the structure of atomic nuclei. It is used in numerous applications, from determining the limits of stability to gaining a deep understanding of the…

Finite-temperature effects can be included by calculating the vibrations properties and this can greatly improve the fidelity of computational screening. An important challenge for DFT-based screening is the sensitivity of the predictions…

Fitting a simplifying model with several parameters to real data of complex objects is a highly nontrivial task, but enables the possibility to get insights into the objects physics. Here, we present a method to infer the parameters of the…

DFT calculations have become widespread in both chemistry and materials, because they usually provide useful accuracy at much lower computational cost than wavefunction-based methods. All practical DFT calculations require an approximation…

The Design of Experiments (DOEs) is a fundamental scientific methodology that provides researchers with systematic principles and techniques to enhance the validity, reliability, and efficiency of experimental outcomes. In this study, we…

An exchange energy functional is proposed and tested for obtaining a class of excited-state energies using density-functional formalism. The functional is the excited-state counterpart of the local-density approximation functional for the…

The package "fhi96md" is an efficient code to perform density-functional theory total-energy calculations for materials ranging from insulators to transition metals. The package employs first-principles pseudopotentials, and a plane-wave…

The problem of the determination of the charge density from limited information about the charge form factor is an ill-posed inverse problem. A Bayesian probabilistic approach to this problem which permits to take into account both errors…

Recent studies have shown that ensemble approaches could not only improve accuracy and but also estimate model uncertainty in deep learning. However, it requires a large number of parameters according to the increase of ensemble models for…

Superstatistics generalizes Boltzmann statistics by assuming spatio-temporal fluctuations of the intensive variables. It has many applications in the analysis of experimental and simulated data. The fluctuation of the intensity variable is…

We derive an exact representation of the exchange-correlation energy within density functional theory (DFT) which spawns a class of approximations leading to correct long-range asymptotic behavior. In what amounts to be the simplest…

This paper develops a mathematical and computational framework for analyzing the expected performance of Bayesian data fusion, or joint statistical inference, within a sensor network. We use variational techniques to obtain the posterior…

Density functional theory is routinely applied to predict crystal structures. The most common exchange-correlation functionals used to this end are the Perdew-Burke-Ernzerhof (PBE) approximation and its variant PBEsol. We investigate the…