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Kohn-Sham density functional theory is one of the most widely used electronic structure theories. In the pseudopotential framework, uniform discretization of the Kohn-Sham Hamiltonian generally results in a large number of basis functions…

The systematic underestimation of band gaps is one of the most fundamental challenges in semilocal density functional theory (DFT). In addition to hindering the application of DFT to predicting electronic properties, the band gap problem is…

Overparameterized models that achieve zero training error are observed to generalize well on average, but degrade in performance when faced with data that is under-represented in the training sample. In this work, we study an…

The Cabibbo-Kobayashi-Maskawa matrix element $|V_{\rm cb}|$ is an important Standard Model parameter, whose value can be determined by using the semi-leptonic decay $B\rightarrow D^{*}\ell{\bar \nu}_\ell$. The perturbative QCD (pQCD)…

Density functional approximations (DFAs) suffer from delocalization error, which limits their accuracy in predicting electron affinities (EAs), ionization potentials (IPs), and quasiparticle energies. In this work, we present a theoretical…

This paper develops a framework for the error analysis in nonparametric model fitting of fractional stochastic differential equations based on discrete observations. We identify and quantify the main error sources -- time discretization,…

We formulate the Kohn-Sham density functional theory (KS-DFT) as a statistical theory in which the electron density is deter-mined from an average of correlated stochastic densities in a trace formula. The key idea is that it is sufficient…

Kohn-Sham density functional theory is the base of modern computational approaches to electronic structures. Their accuracy vitally relies on the exchange-correlation energy functional, which encapsulates electron-electron interaction…

Quantification learning deals with the task of estimating the target label distribution under label shift. In this paper, we first present a unifying framework, distribution feature matching (DFM), that recovers as particular instances…

Conformal prediction, which makes no distributional assumptions about the data, has emerged as a powerful and reliable approach to uncertainty quantification in practical applications. The nonconformity measure used in conformal prediction…

We propose a simple yet very predictive form, based on a Poisson's equation, for the functional dependence of the cost from the density of points in the Euclidean bipartite matching problem. This leads, for quadratic costs, to the analytic…

The strongly constrained and appropriately normed (SCAN) semilocal density functional [J. Sun, A. Ruzsinszky, J. P. Perdew \textit{Phys. Rev. Lett.} {\bf 115}, 036402 (2015)] obeys all 17 known exact constraints for…

The usefulness of semi-analytical thermal models for predicting the connection between process, microstructure and properties in powder bed fusion has been well illustrated in recent years. Such an approach provides the promise of accuracy…

Accounting for dispersion interactions is essential in approximate density functional theory (DFT). Often, a correction potential based on the London formula is added, which is damped at short distances to avoid divergence and double…

Accurate first-principles calculations for the energies, charge distributions, and spin symmetries of many-electron systems are essential to understand and predict the electronic and structural properties of molecules and materials.…

We propose a novel framework for fitting additive quantile regression models, which provides well calibrated inference about the conditional quantiles and fast automatic estimation of the smoothing parameters, for model structures as…

Density functional theory underlies the most successful and widely used numerical methods for electronic structure prediction of solids. However, it has the fundamental shortcoming that the universal density functional is unknown. In…

The electron density of a molecule or material has recently received major attention as a target quantity of machine-learning models. A natural choice to construct a model that yields transferable and linear-scaling predictions is to…

This study examines the optimal selections of bandwidth and semi-metric for a functional partial linear model. Our proposed method begins by estimating the unknown error density using a kernel density estimator of residuals, where the…

In this thesis we study adaptive nonparametric regression with noise misspecification and the complexity of approximation of random fields in dependence of the dimension. First, we consider the problem of pointwise estimation in…