Related papers: Direct Scheme Calculation of the Kinetic Energy Fu…
Inferring parameters of macro-kinetic growth models, typically represented by Ordinary Differential Equations (ODE), from the experimental data is a crucial step in bioprocess engineering. Conventionally, estimates of the parameters are…
Important classes of active matter systems can be modeled using kinetic theories. However, kinetic theories can be high dimensional and challenging to simulate. Reduced-order representations based on tracking only low-order moments of the…
We train a neural network as the universal exchange-correlation functional of density-functional theory that simultaneously reproduces both the exact exchange-correlation energy and potential. This functional is extremely non-local, but…
The present paper proposes an adaptive biasing potential for the computation of free energy landscapes. It is motivated by statistical learning arguments and unifies the tasks of biasing the molecular dynamics to escape free energy wells…
We demonstrate a machine learning based approach which can learn the time-dependent electronic excitation dynamics of small molecules subjected to ion irradiation. Ensembles of recurrent neural networks are trained on data generated by…
The non-additive non-interacting kinetic energy is calculated exactly for fragments of H$_2$, Li$_2$, Be$_2$, C$_2$, N$_2$, F$_2$, and Na$_2$ within partition density-functional theory. The resulting fragments are uniquely determined and…
The development of kinetic energy functional (KEF) is known as one of the most difficult subjects in the electronic density functional theory (DFT). In particular, the sound description of chemical bonds using a KEF is a matter of great…
The existing discrete variational derivative method is only second-order accurate and fully implicit. In this paper, we propose a framework to construct an arbitrary high-order implicit (original) energy stable scheme and a second-order…
Kohn-Sham density functional theory calculations using conventional diagonalization based methods become increasingly expensive as temperature increases due to the need to compute increasing numbers of partially occupied states. We present…
Structural learning, a method to estimate the parameters for discrete energy minimization, has been proven to be effective in solving computer vision problems, especially in 3D scene parsing. As the complexity of the models increases,…
We have formulated and implemented a fully charge-self-consistent density functional theory plus dynamical mean field theory methodology which enables an efficient calculation of the total energy of realistic correlated electron systems.…
We consider the task of learning a dynamical system from high-dimensional time-course data. For instance, we might wish to estimate a gene regulatory network from gene expression data measured at discrete time points. We model the dynamical…
Recently, we have proposed a new diffusive representation for fractional derivatives and, based on this representation, suggested an algorithm for their numerical computation. From the construction of the algorithm, it is immediately…
We introduce a spectral density functional theory which can be used to compute energetics and spectra of real strongly--correlated materials using methods, algorithms and computer programs of the electronic structure theory of solids. The…
We propose a function-on-function linear regression model for time-dependent curve data that is consistently estimated by imposing factor structures on the regressors. An integral operator based on cross-covariances identifies two…
A combination of systematic density functional theory (DFT) calculations and machine learning techniques has a wide range of potential applications. This study presents an application of the combination of systematic DFT calculations and…
We investigate the orientational properties of a homogeneous and inhomogeneous tetrahedral 4-patch fluid (Kern--Frenkel model). Using integral equations, either (i) HNC or (ii) a modified HNC scheme with simulation input, the full…
Situations of a functional predictor paired with a scalar response are increasingly encountered in data analysis. Predictors are often appropriately modeled as square integrable smooth random functions. Imposing minimal assumptions on the…
Two equations are constructed which reflect, for fermions moving independently in a spherical harmonic potential, a differential virial theorem and a relation between the turning points of kinetic energy and particle densities. These…
When solving partial differential equations using classical schemes such as finite difference or finite volume methods, sufficiently fine meshes and carefully designed schemes are required to achieve high-order accuracy of numerical…