Related papers: A Bayesian Approach for the Determination of the C…

Electron charge density is a fundamental physical quantity, determining various properties of matter. In this study, we have proposed a deep-learning model for accurate charge density prediction. Our model naturally preserves physical…

This study proposes a novel approach to quantifying uncertainties of constitutive relations inferred from noisy experimental data using inverse modelling. We focus on electrochemical systems in which charged species (e.g., Lithium ions) are…

We present a new approach to the electromagnetic inverse problem that explicitly addresses the ambiguity associated with its ill-posed character. Rather than calculating a single ``best'' solution according to some criterion, our approach…

The model independent procedure of extracting charge density distributions from elastic electron scattering data is investigated. The charge density distributions are expanded on an orthonormal basis and the parameters of the expansions are…

Electromagnetic form factors have long been used to probe the underlying charge and magnetization densities of hadrons and nuclei. Traditional three-dimensional Fourier transform methods are not rigorously applicable for systems with…

Bayesian methods have been very successful in quantifying uncertainty in physics-based problems in parameter estimation and prediction. In these cases, physical measurements y are modeled as the best fit of a physics-based model…

This paper presents a Bayesian parameter estimation approach and identifiability analysis for a lithium-ion battery model, to determine the uniqueness, evaluate the sensitivity and quantify the uncertainty of a subset of the model…

This paper considers the problem of computing Bayesian estimates of both states and model parameters for nonlinear state-space models. Generally, this problem does not have a tractable solution and approximations must be utilised. In this…

This paper proposes a hierarchical Bayesian model for probabilistic estimation of the electric vehicle battery capacity fade. Since the battery aging factors such as temperature, current, and state of charge are not fixed, and they change…

A density estimation method in a Bayesian nonparametric framework is presented when recorded data are not coming directly from the distribution of interest, but from a length biased version. From a Bayesian perspective, efforts to…

This paper presents an efficient Bayesian framework for solving nonlinear, high-dimensional model calibration problems. It is based on a Variational Bayesian formulation that aims at approximating the exact posterior by means of solving an…

We propose a Bayesian inference framework to estimate uncertainties in inverse scattering problems. Given the observed data, the forward model and their uncertainties, we find the posterior distribution over a finite parameter field…

We suggest to include the density of electron charge explicitly in the electron potential of density functional theory, rather than implicitly via exchange-correlation functionals. The advantages of the approach are conceptual and…

When modeling a probability distribution with a Bayesian network, we are faced with the problem of how to handle continuous variables. Most previous work has either solved the problem by discretizing, or assumed that the data are generated…

Faithful representations of atomic environments and general models for regression can be harnessed to learn electron densities that are close to the ground state. One of the applications of data-derived electron densities is to orbital-free…

We address the problem of estimating the uncertainty in the solution of power grid inverse problems within the framework of Bayesian inference. We investigate two approaches, an adjoint-based method and a stochastic spectral method. These…

In density functional theory, charge density is the core attribute of atomic systems from which all chemical properties can be derived. Machine learning methods are promising in significantly accelerating charge density prediction, yet…

This paper extends the work of Clarke [1] on the Bayesian foundations of the biomagnetic inverse problem. It derives expressions for the expectation and variance of the a posteriori source current probability distribution given a prior…

In this paper the Bayesian analysis is applied to assign a probability density to the value of a quantity having a definite sign. This analysis is logically consistent with the results, positive or negative, of repeated measurements.…

We formulate, and present a numerical method for solving, an inverse problem for inferring parameters of a deterministic model from stochastic observational data (quantities of interest). The solution, given as a probability measure, is…